|
|
| Ligne 1 279 : |
Ligne 1 279 : |
| | doubt. If the premises are not in fact doubted at all, they | | doubt. If the premises are not in fact doubted at all, they |
| | cannot be more satisfactory than they are.</p> | | cannot be more satisfactory than they are.</p> |
| − |
| |
| − | <p class='c005'>3. Some people seem to love to argue a point after all
| |
| − | the world is fully convinced of it. But no further advance
| |
| − | can be made. When doubt ceases, mental action on the
| |
| − | subject comes to an end; and, if it did go on, it would be
| |
| − | without a purpose.</p>
| |
| − | <h4 class='c012'>V</h4>
| |
| − | <p class='c006'>If the settlement of opinion is the sole object of inquiry,
| |
| − | and if belief is of the nature of a habit, why should we not
| |
| − | attain the desired end, by taking any answer to a question,
| |
| − | which we may fancy, and constantly reiterating it to ourselves,
| |
| − | dwelling on all which may conduce to that belief,
| |
| − | <span class='pageno' id='Page_18'>18</span>and learning to turn with contempt and hatred from anything
| |
| − | which might disturb it? This simple and direct
| |
| − | method is really pursued by many men. I remember once
| |
| − | being entreated not to read a certain newspaper lest it might
| |
| − | change my opinion upon free-trade. “Lest I might be entrapped
| |
| − | by its fallacies and misstatements,” was the form of
| |
| − | expression. “You are not,” my friend said, “a special
| |
| − | student of political economy. You might, therefore, easily
| |
| − | be deceived by fallacious arguments upon the subject. You
| |
| − | might, then, if you read this paper, be led to believe in
| |
| − | protection. But you admit that free-trade is the true doctrine;
| |
| − | and you do not wish to believe what is not true.”
| |
| − | I have often known this system to be deliberately adopted.
| |
| − | Still oftener, the instinctive dislike of an undecided state
| |
| − | of mind, exaggerated into a vague dread of doubt, makes
| |
| − | men cling spasmodically to the views they already take.
| |
| − | The man feels that, if he only holds to his belief without
| |
| − | wavering, it will be entirely satisfactory. Nor can it be
| |
| − | denied that a steady and immovable faith yields great peace
| |
| − | of mind. It may, indeed, give rise to inconveniences, as if
| |
| − | a man should resolutely continue to believe that fire would
| |
| − | not burn him, or that he would be eternally damned if he
| |
| − | received his <i>ingesta</i> otherwise than through a stomach-pump.
| |
| − | But then the man who adopts this method will not
| |
| − | allow that its inconveniences are greater than its advantages.
| |
| − | He will say, “I hold steadfastly to the truth and the truth
| |
| − | is always wholesome.” And in many cases it may very
| |
| − | well be that the pleasure he derives from his calm faith
| |
| − | overbalances any inconveniences resulting from its deceptive
| |
| − | character. Thus, if it be true that death is annihilation,
| |
| − | <span class='pageno' id='Page_19'>19</span>then the man who believes that he will certainly go
| |
| − | straight to heaven when he dies, provided he have fulfilled
| |
| − | certain simple observances in this life, has a cheap pleasure
| |
| − | which will not be followed by the least disappointment.
| |
| − | A similar consideration seems to have weight with many
| |
| − | persons in religious topics, for we frequently hear it said,
| |
| − | “Oh, I could not believe so-and-so, because I should be
| |
| − | wretched if I did.” When an ostrich buries its head in the
| |
| − | sand as danger approaches, it very likely takes the happiest
| |
| − | course. It hides the danger, and then calmly says there
| |
| − | is no danger; and, if it feels perfectly sure there is none,
| |
| − | why should it raise its head to see? A man may go through
| |
| − | life, systematically keeping out of view all that might cause
| |
| − | a change in his opinions, and if he only succeeds—basing
| |
| − | his method, as he does, on two fundamental psychological
| |
| − | laws—I do not see what can be said against his doing so.
| |
| − | It would be an egotistical impertinence to object that his
| |
| − | procedure is irrational, for that only amounts to saying
| |
| − | that his method of settling belief is not ours. He does not
| |
| − | propose to himself to be rational, and indeed, will often
| |
| − | talk with scorn of man’s weak and illusive reason. So let
| |
| − | him think as he pleases.</p>
| |
| − |
| |
| − | <p class='c005'>But this method of fixing belief, which may be called
| |
| − | the method of tenacity, will be unable to hold its ground
| |
| − | in practice. The social impulse is against it. The man
| |
| − | who adopts it will find that other men think differently from
| |
| − | him, and it will be apt to occur to him in some saner moment
| |
| − | that their opinions are quite as good as his own, and this
| |
| − | will shake his confidence in his belief. This conception,
| |
| − | that another man’s thought or sentiment may be equivalent
| |
| − | <span class='pageno' id='Page_20'>20</span>to one’s own, is a distinctly new step, and a highly important
| |
| − | one. It arises from an impulse too strong in man to be
| |
| − | suppressed, without danger of destroying the human species.
| |
| − | Unless we make ourselves hermits, we shall necessarily influence
| |
| − | each other’s opinions; so that the problem becomes
| |
| − | how to fix belief, not in the individual merely, but in the
| |
| − | community.</p>
| |
| − |
| |
| − | <p class='c005'>Let the will of the state act, then, instead of that of the
| |
| − | individual. Let an institution be created which shall have
| |
| − | for its object to keep correct doctrines before the attention
| |
| − | of the people, to reiterate them perpetually, and to teach
| |
| − | them to the young; having at the same time power to prevent
| |
| − | contrary doctrines from being taught, advocated, or
| |
| − | expressed. Let all possible causes of a change of mind
| |
| − | be removed from men’s apprehensions. Let them be kept
| |
| − | ignorant, lest they should learn of some reason to think
| |
| − | otherwise than they do. Let their passions be enlisted, so
| |
| − | that they may regard private and unusual opinions with
| |
| − | hatred and horror. Then, let all men who reject the established
| |
| − | belief be terrified into silence. Let the people turn
| |
| − | out and tar-and-feather such men, or let inquisitions be
| |
| − | made into the manner of thinking of suspected persons,
| |
| − | and, when they are found guilty of forbidden beliefs, let
| |
| − | them be subjected to some signal punishment. When complete
| |
| − | agreement could not otherwise be reached, a general
| |
| − | massacre of all who have not thought in a certain way has
| |
| − | proved a very effective means of settling opinion in a
| |
| − | country. If the power to do this be wanting, let a list of
| |
| − | opinions be drawn up, to which no man of the least independence
| |
| − | of thought can assent, and let the faithful be required
| |
| − | <span class='pageno' id='Page_21'>21</span>to accept all these propositions, in order to segregate
| |
| − | them as radically as possible from the influence of the rest
| |
| − | of the world.</p>
| |
| − |
| |
| − | <p class='c005'>This method has, from the earliest times, been one of
| |
| − | the chief means of upholding correct theological and political
| |
| − | doctrines, and of preserving their universal or catholic
| |
| − | character. In Rome, especially, it has been practiced from
| |
| − | the days of Numa Pompilius to those of Pius Nonus. This
| |
| − | is the most perfect example in history; but wherever there
| |
| − | is a priesthood—and no religion has been without one—this
| |
| − | method has been more or less made use of. Wherever
| |
| − | there is aristocracy, or a guild, or any association of a class
| |
| − | of men whose interests depend or are supposed to depend
| |
| − | on certain propositions, there will be inevitably found some
| |
| − | traces of this natural product of social feeling. Cruelties
| |
| − | always accompany this system; and when it is consistently
| |
| − | carried out, they become atrocities of the most horrible
| |
| − | kind in the eyes of any rational man. Nor should this
| |
| − | occasion surprise, for the officer of a society does not feel
| |
| − | justified in surrendering the interests of that society for
| |
| − | the sake of mercy, as he might his own private interests.
| |
| − | It is natural, therefore, that sympathy and fellowship should
| |
| − | thus produce a most ruthless power.</p>
| |
| − |
| |
| − | <p class='c005'>In judging this method of fixing belief, which may be
| |
| − | called the method of authority, we must in the first place,
| |
| − | allow its immeasurable mental and moral superiority to
| |
| − | the method of tenacity. Its success is proportionally
| |
| − | greater; and in fact it has over and over again worked the
| |
| − | most majestic results. The mere structures of stone which
| |
| − | it has caused to be put together—in Siam, for example,
| |
| − | <span class='pageno' id='Page_22'>22</span>in Egypt, and in Europe—have many of them a sublimity
| |
| − | hardly more than rivaled by the greatest works of Nature.
| |
| − | And, except the geological epochs, there are no periods of
| |
| − | time so vast as those which are measured by some of these
| |
| − | organized faiths. If we scrutinize the matter closely, we
| |
| − | shall find that there has not been one of their creeds which
| |
| − | has remained always the same; yet the change is so slow
| |
| − | as to be imperceptible during one person’s life, so that individual
| |
| − | belief remains sensibly fixed. For the mass of
| |
| − | mankind, then, there is perhaps no better method than this.
| |
| − | If it is their highest impulse to be intellectual slaves, then
| |
| − | slaves they ought to remain.</p>
| |
| − |
| |
| − | <p class='c005'>But no institution can undertake to regulate opinions
| |
| − | upon every subject. Only the most important ones can be
| |
| − | attended to, and on the rest men’s minds must be left to
| |
| − | the action of natural causes. This imperfection will be
| |
| − | no source of weakness so long as men are in such a state
| |
| − | of culture that one opinion does not influence another—that
| |
| − | is, so long as they cannot put two and two together.
| |
| − | But in the most priest-ridden states some individuals will
| |
| − | be found who are raised above that condition. These men
| |
| − | possess a wider sort of social feeling; they see that men in
| |
| − | other countries and in other ages have held to very different
| |
| − | doctrines from those which they themselves have been
| |
| − | brought up to believe; and they cannot help seeing that it
| |
| − | is the mere accident of their having been taught as they
| |
| − | have, and of their having been surrounded with the manners
| |
| − | and associations they have, that has caused them to believe
| |
| − | as they do and not far differently. And their candor cannot
| |
| − | resist the reflection that there is no reason to rate their
| |
| − | <span class='pageno' id='Page_23'>23</span>own views at a higher value than those of other nations
| |
| − | and other centuries; and this gives rise to doubts in their
| |
| − | minds.</p>
| |
| − |
| |
| − | <p class='c005'>They will further perceive that such doubts as these
| |
| − | must exist in their minds with reference to every belief
| |
| − | which seems to be determined by the caprice either of
| |
| − | themselves or of those who originated the popular opinions.
| |
| − | The willful adherence to a belief, and the arbitrary forcing
| |
| − | of it upon others, must, therefore, both be given up and a
| |
| − | new method of settling opinions must be adopted, which
| |
| − | shall not only produce an impulse to believe, but shall also
| |
| − | decide what proposition it is which is to be believed. Let
| |
| − | the action of natural preferences be unimpeded, then, and
| |
| − | under their influence let men conversing together and regarding
| |
| − | matters in different lights, gradually develop beliefs
| |
| − | in harmony with natural causes. This method resembles
| |
| − | that by which conceptions of art have been brought to
| |
| − | maturity. The most perfect example of it is to be found
| |
| − | in the history of metaphysical philosophy. Systems of this
| |
| − | sort have not usually rested upon observed facts, at least
| |
| − | not in any great degree. They have been chiefly adopted
| |
| − | because their fundamental propositions seemed “agreeable
| |
| − | to reason.” This is an apt expression; it does not mean
| |
| − | that which agrees with experience, but that which we find
| |
| − | ourselves inclined to believe. Plato, for example, finds it
| |
| − | agreeable to reason that the distances of the celestial spheres
| |
| − | from one another should be proportional to the different
| |
| − | lengths of strings which produce harmonious chords. Many
| |
| − | philosophers have been led to their main conclusions by
| |
| − | considerations like this; but this is the lowest and least
| |
| − | <span class='pageno' id='Page_24'>24</span>developed form which the method takes, for it is clear that
| |
| − | another man might find Kepler’s [earlier] theory, that the
| |
| − | celestial spheres are proportional to the inscribed and circumscribed
| |
| − | spheres of the different regular solids, more
| |
| − | agreeable to <i>his</i> reason. But the shock of opinions will soon
| |
| − | lead men to rest on preferences of a far more universal
| |
| − | nature. Take, for example, the doctrine that man only
| |
| − | acts selfishly—that is, from the consideration that acting
| |
| − | in one way will afford him more pleasure than acting in
| |
| − | another. This rests on no fact in the world, but it has had
| |
| − | a wide acceptance as being the only reasonable theory.</p>
| |
| − |
| |
| − | <p class='c005'>This method is far more intellectual and respectable
| |
| − | from the point of view of reason than either of the others
| |
| − | which we have noticed. But its failure has been the most
| |
| − | manifest. It makes of inquiry something similar to the
| |
| − | development of taste; but taste, unfortunately, is always
| |
| − | more or less a matter of fashion, and accordingly, meta-physicians
| |
| − | have never come to any fixed agreement, but
| |
| − | the pendulum has swung backward and forward between
| |
| − | a more material and a more spiritual philosophy, from the
| |
| − | earliest times to the latest. And so from this, which has
| |
| − | been called the <i>a priori</i> method, we are driven, in Lord
| |
| − | Bacon’s phrase, to a true induction. We have examined
| |
| − | into this <i>a priori</i> method as something which promised to
| |
| − | deliver our opinions from their accidental and capricious
| |
| − | element. But development, while it is a process which
| |
| − | eliminates the effect of some casual circumstances, only
| |
| − | magnifies that of others. This method, therefore, does not
| |
| − | differ in a very essential way from that of authority. The
| |
| − | government may not have lifted its finger to influence my
| |
| − | <span class='pageno' id='Page_25'>25</span>convictions; I may have been left outwardly quite free to
| |
| − | choose, we will say, between monogamy and polygamy,
| |
| − | and appealing to my conscience only, I may have concluded
| |
| − | that the latter practice is in itself licentious. But when I
| |
| − | come to see that the chief obstacle to the spread of Christianity
| |
| − | among a people of as high culture as the Hindoos
| |
| − | has been a conviction of the immorality of our way of
| |
| − | treating women, I cannot help seeing that, though governments
| |
| − | do not interfere, sentiments in their development
| |
| − | will be very greatly determined by accidental causes. Now,
| |
| − | there are some people, among whom I must suppose that
| |
| − | my reader is to be found, who, when they see that any belief
| |
| − | of theirs is determined by any circumstance extraneous
| |
| − | to the facts, will from that moment not merely admit in
| |
| − | words that that belief is doubtful, but will experience a real
| |
| − | doubt of it, so that it ceases to be a belief.</p>
| |
| − |
| |
| − | <p class='c005'>To satisfy our doubts, therefore, it is necessary that a
| |
| − | method should be found by which our beliefs may be caused
| |
| − | by nothing human, but by some external permanency—by
| |
| − | something upon which our thinking has no effect. Some
| |
| − | mystics imagine that they have such a method in a private
| |
| − | inspiration from on high. But that is only a form of the
| |
| − | method of tenacity, in which the conception of truth as
| |
| − | something public is not yet developed. Our external permanency
| |
| − | would not be external, in our sense, if it was restricted
| |
| − | in its influence to one individual. It must be something
| |
| − | which affects, or might affect, every man. And,
| |
| − | though these affections are necessarily as various as are
| |
| − | individual conditions, yet the method must be such that
| |
| − | the ultimate conclusion of every man shall be the same.
| |
| − | <span class='pageno' id='Page_26'>26</span>Such is the method of science. Its fundamental hypothesis,
| |
| − | restated in more familiar language, is this: There are real
| |
| − | things, whose characters are entirely independent of our
| |
| − | opinions about them; whose realities affect our senses according
| |
| − | to regular laws, and, though our sensations are
| |
| − | as different as our relations to the objects, yet, by taking
| |
| − | advantage of the laws of perception, we can ascertain by
| |
| − | reasoning how things really are, and any man, if he have sufficient
| |
| − | experience and reason enough about it, will be led to
| |
| − | the one true conclusion. The new conception here involved
| |
| − | is that of reality. It may be asked how I know that there
| |
| − | are any realities. If this hypothesis is the sole support of
| |
| − | my method of inquiry, my method of inquiry must not be
| |
| − | used to support my hypothesis. The reply is this: 1. If
| |
| − | investigation cannot be regarded as proving that there are
| |
| − | real things, it at least does not lead to a contrary conclusion;
| |
| − | but the method and the conception on which it is
| |
| − | based remain ever in harmony. No doubts of the method,
| |
| − | therefore, necessarily arise from its practice, as is the case
| |
| − | with all the others. 2. The feeling which gives rise to any
| |
| − | method of fixing belief is a dissatisfaction at two repugnant
| |
| − | propositions. But here already is a vague concession that
| |
| − | there is some <i>one</i> thing to which a proposition should conform.
| |
| − | Nobody, therefore, can really doubt that there are
| |
| − | realities, or, if he did, doubt would not be a source of dissatisfaction.
| |
| − | The hypothesis, therefore, is one which every
| |
| − | mind admits. So that the social impulse does not cause
| |
| − | me to doubt it. 3. Everybody uses the scientific method
| |
| − | about a great many things, and only ceases to use it when
| |
| − | he does not know how to apply it. 4. Experience of the
| |
| − | <span class='pageno' id='Page_27'>27</span>method has not led me to doubt it, but, on the contrary,
| |
| − | scientific investigation has had the most wonderful triumphs
| |
| − | in the way of settling opinion. These afford the explanation
| |
| − | of my not doubting the method or the hypothesis which
| |
| − | it supposes; and not having any doubt, nor believing that
| |
| − | anybody else whom I could influence has, it would be the
| |
| − | merest babble for me to say more about it. If there be
| |
| − | anybody with a living doubt upon the subject, let him
| |
| − | consider it.</p>
| |
| − |
| |
| − | <p class='c005'>To describe the method of scientific investigation is the
| |
| − | object of this series of papers. At present I have only room
| |
| − | to notice some points of contrast between it and other
| |
| − | methods of fixing belief.</p>
| |
| − |
| |
| − | <p class='c005'>This is the only one of the four methods which presents
| |
| − | any distinction of a right and a wrong way. If I adopt the
| |
| − | method of tenacity and shut myself out from all influences,
| |
| − | whatever I think necessary to doing this is necessary according
| |
| − | to that method. So with the method of authority: the
| |
| − | state may try to put down heresy by means which, from a
| |
| − | scientific point of view, seems very ill-calculated to accomplish
| |
| − | its purposes; but the only test <i>on that method</i> is
| |
| − | what the state thinks, so that it cannot pursue the method
| |
| − | wrongly. So with the <i>a priori</i> method. The very essence of
| |
| − | it is to think as one is inclined to think. All metaphysicians
| |
| − | will be sure to do that, however they may be inclined to
| |
| − | judge each other to be perversely wrong. The Hegelian
| |
| − | system recognizes every natural tendency of thought as
| |
| − | logical, although it is certain to be abolished by counter-tendencies.
| |
| − | Hegel thinks there is a regular system in the
| |
| − | succession of these tendencies, in consequence of which,
| |
| − | <span class='pageno' id='Page_28'>28</span>after drifting one way and the other for a long time, opinion
| |
| − | will at last go right. And it is true that metaphysicians get
| |
| − | the right ideas at last; Hegel’s system of Nature represents
| |
| − | tolerably the science of that day; and one may be sure that
| |
| − | whatever scientific investigation has put out of doubt will
| |
| − | presently receive <i>a priori</i> demonstration on the part of the
| |
| − | metaphysicians. But with the scientific method the case
| |
| − | is different. I may start with known and observed facts
| |
| − | to proceed to the unknown; and yet the rules which I follow
| |
| − | in doing so may not be such as investigation would approve.
| |
| − | The test of whether I am truly following the
| |
| − | method is not an immediate appeal to my feelings and purposes,
| |
| − | but, on the contrary, itself involves the application
| |
| − | of the method. Hence it is that bad reasoning as well as
| |
| − | good reasoning is possible; and this fact is the foundation
| |
| − | of the practical side of logic.</p>
| |
| − |
| |
| − | <p class='c005'>It is not to be supposed that the first three methods of
| |
| − | settling opinion present no advantage whatever over the
| |
| − | scientific method. On the contrary, each has some peculiar
| |
| − | convenience of its own. The <i>a priori</i> method is distinguished
| |
| − | for its comfortable conclusions. It is the nature
| |
| − | of the process to adopt whatever belief we are inclined to,
| |
| − | and there are certain flatteries to one’s vanities which we
| |
| − | all believe by nature, until we are awakened from our pleasing
| |
| − | dream by rough facts. The method of authority will
| |
| − | always govern the mass of mankind; and those who wield
| |
| − | the various forms of organized force in the state will never
| |
| − | be convinced that dangerous reasoning ought not to be
| |
| − | suppressed in some way. If liberty of speech is to be untrammeled
| |
| − | from the grosser forms of constraint, then uniformity
| |
| − | <span class='pageno' id='Page_29'>29</span>of opinion will be secured by a moral terrorism to
| |
| − | which the respectability of society will give its thorough
| |
| − | approval. Following the method of authority is the path
| |
| − | of peace. Certain non-conformities are permitted; certain
| |
| − | others (considered unsafe) are forbidden. These are different
| |
| − | in different countries and in different ages; but,
| |
| − | wherever you are let it be known that you seriously hold
| |
| − | a tabooed belief, and you may be perfectly sure of being
| |
| − | treated with a cruelty no less brutal but more refined than
| |
| − | hunting you like a wolf. Thus, the greatest intellectual
| |
| − | benefactors of mankind have never dared, and dare not
| |
| − | now, to utter the whole of their thought; and thus a shade
| |
| − | of <i>prima facie</i> doubt is cast upon every proposition which
| |
| − | is considered essential to the security of society. Singularly
| |
| − | enough, the persecution does not all come from without;
| |
| − | but a man torments himself and is oftentimes most
| |
| − | distressed at finding himself believing propositions which
| |
| − | he has been brought up to regard with aversion. The
| |
| − | peaceful and sympathetic man will, therefore, find it hard
| |
| − | to resist the temptation to submit his opinions to authority.
| |
| − | But most of all I admire the method of tenacity for its
| |
| − | strength, simplicity, and directness. Men who pursue it
| |
| − | are distinguished for their decision of character, which becomes
| |
| − | very easy with such a mental rule. They do not
| |
| − | waste time in trying to make up their minds to what they
| |
| − | want, but, fastening like lightning upon whatever alternative
| |
| − | comes first, they hold to it to the end, whatever
| |
| − | happens, without an instant’s irresolution. This is one of
| |
| − | the splendid qualities which generally accompany brilliant,
| |
| − | unlasting success. It is impossible not to envy the man who
| |
| − | <span class='pageno' id='Page_30'>30</span>can dismiss reason, although we know how it must turn out
| |
| − | at last.</p>
| |
| − |
| |
| − | <p class='c005'>Such are the advantages which the other methods of
| |
| − | settling opinions have over scientific investigation. A man
| |
| − | should consider well of them; and then he should consider
| |
| − | that, after all, he wishes his opinions to coincide with the
| |
| − | fact, and that there is no reason why the results of these
| |
| − | three methods should do so. To bring about this effect is the
| |
| − | prerogative of the method of science. Upon such considerations
| |
| − | he has to make his choice—a choice which is far
| |
| − | more than the adoption of any intellectual opinion, which
| |
| − | is one of the ruling decisions of his life, to which when once
| |
| − | made he is bound to adhere. The force of habit will sometimes
| |
| − | cause a man to hold on to old beliefs, after he is in
| |
| − | a condition to see that they have no sound basis. But reflection
| |
| − | upon the state of the case will overcome these
| |
| − | habits, and he ought to allow reflection full weight. People
| |
| − | sometimes shrink from doing this, having an idea that beliefs
| |
| − | are wholesome which they cannot help feeling rest on
| |
| − | nothing. But let such persons suppose an analogous though
| |
| − | different case from their own. Let them ask themselves
| |
| − | what they would say to a reformed Mussulman who should
| |
| − | hesitate to give up his old notions in regard to the relations
| |
| − | of the sexes; or to a reformed Catholic who should still
| |
| − | shrink from the Bible. Would they not say that these
| |
| − | persons ought to consider the matter fully, and clearly
| |
| − | understand the new doctrine, and then ought to embrace it
| |
| − | in its entirety? But, above all, let it be considered that
| |
| − | what is more wholesome than any particular belief, is integrity
| |
| − | of belief; and that to avoid looking into the support
| |
| − | <span class='pageno' id='Page_31'>31</span>of any belief from a fear that it may turn out rotten is
| |
| − | quite as immoral as it is disadvantageous. The person who
| |
| − | confesses that there is such a thing as truth, which is distinguished
| |
| − | from falsehood simply by this, that if acted on
| |
| − | it will carry us to the point we aim at and not astray, and
| |
| − | then though convinced of this, dares not know the truth
| |
| − | and seeks to avoid it, is in a sorry state of mind, indeed.</p>
| |
| − |
| |
| − | <p class='c005'>Yes, the other methods do have their merits: a clear
| |
| − | logical conscience does cost something—just as any virtue,
| |
| − | just as all that we cherish, costs us dear. But, we should
| |
| − | not desire it to be otherwise. The genius of a man’s logical
| |
| − | method should be loved and reverenced as his bride, whom
| |
| − | he has chosen from all the world. He need not condemn
| |
| − | the others; on the contrary, he may honor them deeply,
| |
| − | and in doing so he only honors her the more. But she is
| |
| − | the one that he has chosen, and he knows that he was right
| |
| − | in making that choice. And having made it, he will work
| |
| − | and fight for her, and will not complain that there are blows
| |
| − | to take, hoping that there may be as many and as hard to
| |
| − | give, and will strive to be the worthy knight and champion
| |
| − | of her from the blaze of whose splendors he draws his
| |
| − | inspiration and his courage.</p>
| |
| − |
| |
| − | <div>
| |
| − | <span class='pageno' id='Page_32'>32</span>
| |
| − | <h3 id='chap1-2' class='c001'>SECOND PAPER <br /> HOW TO MAKE OUR IDEAS CLEAR<a id='r31' /><a href='#f31' class='c011'><sup>[31]</sup></a></h3>
| |
| − | </div>
| |
| − | <h4 class='c012'>I</h4>
| |
| − | <p class='c006'>Whoever has looked into a modern treatise on logic of the
| |
| − | common sort, will doubtless remember the two distinctions
| |
| − | between <i>clear</i> and <i>obscure</i> conceptions, and between <i>distinct</i>
| |
| − | and <i>confused</i> conceptions. They have lain in the
| |
| − | books now for nigh two centuries, unimproved and unmodified,
| |
| − | and are generally reckoned by logicians as among
| |
| − | the gems of their doctrine.</p>
| |
| − |
| |
| − | <p class='c005'>A clear idea is defined as one which is so apprehended
| |
| − | that it will be recognized wherever it is met with, and so
| |
| − | that no other will be mistaken for it. If it fails of this
| |
| − | clearness, it is said to be obscure.</p>
| |
| − |
| |
| − | <p class='c005'>This is rather a neat bit of philosophical terminology;
| |
| − | yet, since it is clearness that they were defining, I wish the
| |
| − | logicians had made their definition a little more plain.
| |
| − | Never to fail to recognize an idea, and under no circumstances
| |
| − | to mistake another for it, let it come in how recondite
| |
| − | a form it may, would indeed imply such prodigious
| |
| − | force and clearness of intellect as is seldom met with in this
| |
| − | world. On the other hand, merely to have such an acquaintance
| |
| − | with the idea as to have become familiar with it,
| |
| − | and to have lost all hesitancy in recognizing it in ordinary
| |
| − | <span class='pageno' id='Page_33'>33</span>cases, hardly seems to deserve the name of clearness of
| |
| − | apprehension, since after all it only amounts to a subjective
| |
| − | feeling of mastery which may be entirely mistaken. I take
| |
| − | it, however, that when the logicians speak of “clearness,”
| |
| − | they mean nothing more than such a familiarity with an
| |
| − | idea, since they regard the quality as but a small merit,
| |
| − | which needs to be supplemented by another, which they call
| |
| − | <i>distinctness</i>.</p>
| |
| − |
| |
| − | <p class='c005'>A distinct idea is defined as one which contains nothing
| |
| − | which is not clear. This is technical language; by the
| |
| − | <i>contents</i> of an idea logicians understand whatever is contained
| |
| − | in its definition. So that an idea is <i>distinctly</i> apprehended,
| |
| − | according to them, when we can give a precise
| |
| − | definition of it, in abstract terms. Here the professional
| |
| − | logicians leave the subject; and I would not have troubled
| |
| − | the reader with what they have to say, if it were not such
| |
| − | a striking example of how they have been slumbering
| |
| − | through ages of intellectual activity, listlessly disregarding
| |
| − | the enginery of modern thought, and never dreaming of
| |
| − | applying its lessons to the improvement of logic. It is easy
| |
| − | to show that the doctrine that familiar use and abstract
| |
| − | distinctness make the perfection of apprehension, has its
| |
| − | only true place in philosophies which have long been extinct;
| |
| − | and it is now time to formulate the method of attaining
| |
| − | to a more perfect clearness of thought, such as we see
| |
| − | and admire in the thinkers of our own time.</p>
| |
| − |
| |
| − | <p class='c005'>When Descartes set about the reconstruction of philosophy,
| |
| − | his first step was to (theoretically) permit skepticism
| |
| − | and to discard the practice of the schoolmen of looking to
| |
| − | authority as the ultimate source of truth. That done, he
| |
| − | <span class='pageno' id='Page_34'>34</span>sought a more natural fountain of true principles, and professed
| |
| − | to find it in the human mind; thus passing, in the
| |
| − | directest way, from the method of authority to that of
| |
| − | apriority, as described in my first paper. Self-consciousness
| |
| − | was to furnish us with our fundamental truths, and to
| |
| − | decide what was agreeable to reason. But since, evidently,
| |
| − | not all ideas are true, he was led to note, as the first condition
| |
| − | of infallibility, that they must be clear. The distinction
| |
| − | between an idea <i>seeming</i> clear and really being so,
| |
| − | never occurred to him. Trusting to introspection, as he
| |
| − | did, even for a knowledge of external things, why should
| |
| − | he question its testimony in respect to the contents of our
| |
| − | own minds? But then, I suppose, seeing men, who seemed
| |
| − | to be quite clear and positive, holding opposite opinions
| |
| − | upon fundamental principles, he was further led to say that
| |
| − | clearness of ideas is not sufficient, but that they need also
| |
| − | to be distinct, i.e., to have nothing unclear about them.
| |
| − | What he probably meant by this (for he did not explain
| |
| − | himself with precision) was, that they must sustain the test
| |
| − | of dialectical examination; that they must not only seem
| |
| − | clear at the outset, but that discussion must never be able
| |
| − | to bring to light points of obscurity connected with them.</p>
| |
| − |
| |
| − | <p class='c005'>Such was the distinction of Descartes, and one sees that
| |
| − | it was precisely on the level of his philosophy. It was
| |
| − | somewhat developed by Leibnitz. This great and singular
| |
| − | genius was as remarkable for what he failed to see as for
| |
| − | what he saw. That a piece of mechanism could not do
| |
| − | work perpetually without being fed with power in some
| |
| − | form, was a thing perfectly apparent to him; yet he did not
| |
| − | understand that the machinery of the mind can only transform
| |
| − | <span class='pageno' id='Page_35'>35</span>knowledge, but never originate it, unless it be fed
| |
| − | with facts of observation. He thus missed the most essential
| |
| − | point of the Cartesian philosophy, which is, that to
| |
| − | accept propositions which seem perfectly evident to us is
| |
| − | a thing which, whether it be logical or illogical, we cannot
| |
| − | help doing. Instead of regarding the matter in this way,
| |
| − | he sought to reduce the first principles of science to formulas
| |
| − | which cannot be denied without self-contradiction, and was
| |
| − | apparently unaware of the great difference between his
| |
| − | position and that of Descartes. So he reverted to the old
| |
| − | formalities of logic, and, above all, abstract definitions
| |
| − | played a great part in his philosophy. It was quite natural,
| |
| − | therefore, that on observing that the method of Descartes
| |
| − | labored under the difficulty that we may seem to ourselves
| |
| − | to have clear apprehensions of ideas which in truth are
| |
| − | very hazy, no better remedy occurred to him than to require
| |
| − | an abstract definition of every important term. Accordingly,
| |
| − | in adopting the distinction of <i>clear</i> and <i>distinct</i>
| |
| − | notions, he described the latter quality as the clear apprehension
| |
| − | of everything contained in the definition; and the
| |
| − | books have ever since copied his words. There is no danger
| |
| − | that his chimerical scheme will ever again be over-valued.
| |
| − | Nothing new can ever be learned by analyzing definitions.
| |
| − | Nevertheless, our existing beliefs can be set in order by this
| |
| − | process, and order is an essential element of intellectual
| |
| − | economy, as of every other. It may be acknowledged,
| |
| − | therefore, that the books are right in making familiarity
| |
| − | with a notion the first step toward clearness of apprehension,
| |
| − | and the defining of it the second. But in omitting
| |
| − | all mention of any higher perspicuity of thought, they
| |
| − | <span class='pageno' id='Page_36'>36</span>simply mirror a philosophy which was exploded a hundred
| |
| − | years ago. That much-admired “ornament of logic”—the
| |
| − | doctrine of clearness and distinctness—may be pretty
| |
| − | enough, but it is high time to relegate to our cabinet of
| |
| − | curiosities the antique <i>bijou</i>, and to wear about us something
| |
| − | better adapted to modern uses.</p>
| |
| − |
| |
| − | <p class='c005'>The very first lesson that we have a right to demand
| |
| − | that logic shall teach us is, how to make our ideas clear;
| |
| − | and a most important one it is, depreciated only by minds
| |
| − | who stand in need of it. To know what we think, to be
| |
| − | masters of our own meaning, will make a solid foundation
| |
| − | for great and weighty thought. It is most easily learned
| |
| − | by those whose ideas are meagre and restricted; and far
| |
| − | happier they than such as wallow helplessly in a rich mud
| |
| − | of conceptions. A nation, it is true, may, in the course of
| |
| − | generations, overcome the disadvantage of an excessive
| |
| − | wealth of language and its natural concomitant, a vast,
| |
| − | unfathomable deep of ideas. We may see it in history,
| |
| − | slowly perfecting its literary forms, sloughing at length its
| |
| − | metaphysics, and, by virtue of the untirable patience which
| |
| − | is often a compensation, attaining great excellence in every
| |
| − | branch of mental acquirement. The page of history is not
| |
| − | yet unrolled which is to tell us whether such a people will
| |
| − | or will not in the long run prevail over one whose ideas
| |
| − | (like the words of their language) are few, but which possesses
| |
| − | a wonderful mastery over those which it has. For
| |
| − | an individual, however, there can be no question that a
| |
| − | few clear ideas are worth more than many confused ones.
| |
| − | A young man would hardly be persuaded to sacrifice the
| |
| − | greater part of his thoughts to save the rest; and the
| |
| − | <span class='pageno' id='Page_37'>37</span>muddled head is the least apt to see the necessity of such
| |
| − | a sacrifice. Him we can usually only commiserate, as a
| |
| − | person with a congenital defect. Time will help him, but
| |
| − | intellectual maturity with regard to clearness comes rather
| |
| − | late, an unfortunate arrangement of Nature, inasmuch as
| |
| − | clearness is of less use to a man settled in life, whose errors
| |
| − | have in great measure had their effect, than it would be
| |
| − | to one whose path lies before him. It is terrible to see how
| |
| − | a single unclear idea, a single formula without meaning,
| |
| − | lurking in a young man’s head, will sometimes act like an
| |
| − | obstruction of inert matter in an artery, hindering the nutrition
| |
| − | of the brain, and condemning its victim to pine away
| |
| − | in the fullness of his intellectual vigor and in the midst of
| |
| − | intellectual plenty. Many a man has cherished for years
| |
| − | as his hobby some vague shadow of an idea, too meaningless
| |
| − | to be positively false; he has, nevertheless, passionately
| |
| − | loved it, has made it his companion by day and by night,
| |
| − | and has given to it his strength and his life, leaving all other
| |
| − | occupations for its sake, and in short has lived with it and
| |
| − | for it, until it has become, as it were, flesh of his flesh and
| |
| − | bone of his bone; and then he has waked up some bright
| |
| − | morning to find it gone, clean vanished away like the beautiful
| |
| − | Melusina of the fable, and the essence of his life gone
| |
| − | with it. I have myself known such a man; and who can
| |
| − | tell how many histories of circle-squarers, metaphysicians,
| |
| − | astrologers, and what not, may not be told in the old German
| |
| − | story?</p>
| |
| − | <div>
| |
| − | <span class='pageno' id='Page_38'>38</span>
| |
| − | <h4 class='c012'>II</h4>
| |
| − | </div>
| |
| − | <p class='c006'>The principles set forth in the first of these papers lead,
| |
| − | at once, to a method of reaching a clearness of thought of
| |
| − | a far higher grade than the “distinctness” of the logicians.
| |
| − | We have there found that the action of thought is excited
| |
| − | by the irritation of doubt, and ceases when belief is attained;
| |
| − | so that the production of belief is the sole function
| |
| − | of thought. All these words, however, are too strong for
| |
| − | my purpose. It is as if I had described the phenomena
| |
| − | as they appear under a mental microscope. Doubt and
| |
| − | Belief, as the words are commonly employed, relate to
| |
| − | religious or other grave discussions. But here I use them
| |
| − | to designate the starting of any question, no matter how
| |
| − | small or how great, and the resolution of it. If, for instance,
| |
| − | in a horse-car, I pull out my purse and find a five-cent
| |
| − | nickel and five coppers, I decide, while my hand is
| |
| − | going to the purse, in which way I will pay my fare. To
| |
| − | call such a question Doubt, and my decision Belief, is certainly
| |
| − | to use words very disproportionate to the occasion.
| |
| − | To speak of such a doubt as causing an irritation which
| |
| − | needs to be appeased, suggests a temper which is uncomfortable
| |
| − | to the verge of insanity. Yet, looking at the matter
| |
| − | minutely, it must be admitted that, if there is the least
| |
| − | hesitation as to whether I shall pay the five coppers or the
| |
| − | nickel (as there will be sure to be, unless I act from some
| |
| − | previously contracted habit in the matter), though irritation
| |
| − | is too strong a word, yet I am excited to such small mental
| |
| − | activity as may be necessary to deciding how I shall act.
| |
| − | Most frequently doubts arise from some indecision, however
| |
| − | <span class='pageno' id='Page_39'>39</span>momentary, in our action. Sometimes it is not so. I have,
| |
| − | for example, to wait in a railway-station, and to pass the
| |
| − | time I read the advertisements on the walls, I compare the
| |
| − | advantages of different trains and different routes which
| |
| − | I never expect to take, merely fancying myself to be in a
| |
| − | state of hesitancy, because I am bored with having nothing
| |
| − | to trouble me. Feigned hesitancy, whether feigned for
| |
| − | mere amusement or with a lofty purpose, plays a great part
| |
| − | in the production of scientific inquiry. However the doubt
| |
| − | may originate, it stimulates the mind to an activity which
| |
| − | may be slight or energetic, calm or turbulent. Images pass
| |
| − | rapidly through consciousness, one incessantly melting into
| |
| − | another, until at last, when all is over—it may be in a
| |
| − | fraction of a second, in an hour, or after long years—we
| |
| − | find ourselves decided as to how we should act under such
| |
| − | circumstances as those which occasioned our hesitation.
| |
| − | In other words, we have attained belief.</p>
| |
| − |
| |
| − | <p class='c005'>In this process we observe two sorts of elements of consciousness,
| |
| − | the distinction between which may best be made
| |
| − | clear by means of an illustration. In a piece of music
| |
| − | there are the separate notes, and there is the air. A single
| |
| − | tone may be prolonged for an hour or a day, and it exists
| |
| − | as perfectly in each second of that time as in the whole
| |
| − | taken together; so that, as long as it is sounding, it might
| |
| − | be present to a sense from which everything in the past was
| |
| − | as completely absent as the future itself. But it is different
| |
| − | with the air, the performance of which occupies a certain
| |
| − | time, during the portions of which only portions of it are
| |
| − | played. It consists in an orderliness in the succession of
| |
| − | sounds which strike the ear at different times; and to perceive
| |
| − | <span class='pageno' id='Page_40'>40</span>it there must be some continuity of consciousness
| |
| − | which makes the events of a lapse of time present to us.
| |
| − | We certainly only perceive the air by hearing the separate
| |
| − | notes; yet we cannot be said to directly hear it, for we hear
| |
| − | only what is present at the instant, and an orderliness of
| |
| − | succession cannot exist in an instant. These two sorts of
| |
| − | objects, what we are <i>immediately</i> conscious of and what
| |
| − | we are <i>mediately</i> conscious of, are found in all consciousness.
| |
| − | Some elements (the sensations) are completely present
| |
| − | at every instant so long as they last, while others (like
| |
| − | thought) are actions having beginning, middle, and end,
| |
| − | and consist in a congruence in the succession of sensations
| |
| − | which flow through the mind. They cannot be immediately
| |
| − | present to us, but must cover some portion of the past or
| |
| − | future. Thought is a thread of melody running through
| |
| − | the succession of our sensations.</p>
| |
| − |
| |
| − | <p class='c005'>We may add that just as a piece of music may be written
| |
| − | in parts, each part having its own air, so various systems
| |
| − | of relationship of succession subsist together between the
| |
| − | same sensations. These different systems are distinguished
| |
| − | by having different motives, ideas, or functions. Thought
| |
| − | is only one such system; for its sole motive, idea, and function
| |
| − | is to produce belief, and whatever does not concern
| |
| − | that purpose belongs to some other system of relations.
| |
| − | The action of thinking may incidentally have other results.
| |
| − | It may serve to amuse us, for example, and among <i>dilettanti</i>
| |
| − | it is not rare to find those who have so perverted thought
| |
| − | to the purposes of pleasure that it seems to vex them to
| |
| − | think that the questions upon which they delight to exercise
| |
| − | it may ever get finally settled; and a positive discovery
| |
| − | <span class='pageno' id='Page_41'>41</span>which takes a favorite subject out of the arena of literary
| |
| − | debate is met with ill-concealed dislike. This disposition
| |
| − | is the very debauchery of thought. But the soul and meaning
| |
| − | of thought, abstracted from the other elements which
| |
| − | accompany it, though it may be voluntarily thwarted, can
| |
| − | never be made to direct itself toward anything but the production
| |
| − | of belief. Thought in action has for its only possible
| |
| − | motive the attainment of thought at rest; and whatever
| |
| − | does not refer to belief is no part of the thought itself.</p>
| |
| − |
| |
| − | <p class='c005'>And what, then, is belief? It is the demi-cadence which
| |
| − | closes a musical phrase in the symphony of our intellectual
| |
| − | life. We have seen that it has just three properties: First,
| |
| − | it is something that we are aware of; second, it appeases
| |
| − | the irritation of doubt; and, third, it involves the establishment
| |
| − | in our nature of a rule of action, or, say for short, a
| |
| − | <i>habit</i>. As it appeases the irritation of doubt, which is the
| |
| − | motive for thinking, thought relaxes, and comes to rest for
| |
| − | a moment when belief is reached. But, since belief is a
| |
| − | rule for action, the application of which involves further
| |
| − | doubt and further thought, at the same time that it is a
| |
| − | stopping-place, it is also a new starting-place for thought.
| |
| − | That is why I have permitted myself to call it thought at
| |
| − | rest, although thought is essentially an action. The <i>final</i>
| |
| − | upshot of thinking is the exercise of volition, and of this
| |
| − | thought no longer forms a part; but belief is only a stadium
| |
| − | of mental action, an effect upon our nature due to thought,
| |
| − | which will influence future thinking.</p>
| |
| − |
| |
| − | <div class='figcenter id002'>
| |
| − | <img src='images/fig1.png' alt='Fig. 1.' class='ig001' />
| |
| − | <div class='ic002'>
| |
| − | <p>Figure 1.</p>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <div class='figcenter id002'>
| |
| − | <img src='images/fig2.png' alt='Fig. 2.' class='ig001' />
| |
| − | <div class='ic002'>
| |
| − | <p>Figure 2.</p>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c005'>The essence of belief is the establishment of a habit,
| |
| − | and different beliefs are distinguished by the different modes
| |
| − | of action to which they give rise. If beliefs do not differ
| |
| − | <span class='pageno' id='Page_42'>42</span>in this respect, if they appease the same doubt by producing
| |
| − | the same rule of action, then no mere differences in the
| |
| − | manner of consciousness of them can make them different
| |
| − | beliefs, any more than playing a tune in different keys is
| |
| − | playing different tunes. Imaginary distinctions are often
| |
| − | drawn between beliefs which differ only in their mode of
| |
| − | expression;—the wrangling which ensues is real enough,
| |
| − | however. To believe that any objects are arranged as in
| |
| − | Fig. 1, and to believe that they are arranged as in Fig. 2, are
| |
| − | one and the same belief; yet it is conceivable that a man
| |
| − | should assert one proposition and deny the other. Such
| |
| − | false distinctions do as much harm as the confusion of beliefs
| |
| − | really different, and are among the pitfalls of which we
| |
| − | ought constantly to beware, especially when we are upon
| |
| − | metaphysical ground. One singular deception of this sort,
| |
| − | which often occurs, is to mistake the sensation produced
| |
| − | by our own unclearness of thought for a character of the
| |
| − | object we are thinking. Instead of perceiving that the
| |
| − | obscurity is purely subjective, we fancy that we contemplate
| |
| − | <span class='pageno' id='Page_43'>43</span>a quality of the object which is essentially mysterious;
| |
| − | and if our conception be afterward presented to us in a
| |
| − | clear form we do not recognize it as the same, owing to
| |
| − | the absence of the feeling of unintelligibility. So long as
| |
| − | this deception lasts, it obviously puts an impassable barrier
| |
| − | in the way of perspicuous thinking; so that it equally interests
| |
| − | the opponents of rational thought to perpetuate it,
| |
| − | and its adherents to guard against it.</p>
| |
| − |
| |
| − | <p class='c005'>Another such deception is to mistake a mere difference
| |
| − | in the grammatical construction of two words for a distinction
| |
| − | between the ideas they express. In this pedantic
| |
| − | age, when the general mob of writers attend so much more
| |
| − | to words than to things, this error is common enough. When
| |
| − | I just said that thought is an <i>action</i>, and that it consists
| |
| − | in a <i>relation</i>, although a person performs an action but not
| |
| − | a relation, which can only be the result of an action, yet
| |
| − | there was no inconsistency in what I said, but only a grammatical
| |
| − | vagueness.</p>
| |
| − |
| |
| − | <p class='c005'>From all these sophisms we shall be perfectly safe so long
| |
| − | as we reflect that the whole function of thought is to produce
| |
| − | habits of action; and that whatever there is connected
| |
| − | with a thought, but irrelevant to its purpose, is an accretion
| |
| − | to it, but no part of it. If there be a unity among our
| |
| − | sensations which has no reference to how we shall act on
| |
| − | a given occasion, as when we listen to a piece of music,
| |
| − | why we do not call that thinking. To develop its meaning,
| |
| − | we have, therefore, simply to determine what habits it produces,
| |
| − | for what a thing means is simply what habits it involves.
| |
| − | Now, the identity of a habit depends on how it
| |
| − | might lead us to act, not merely under such circumstances
| |
| − | <span class='pageno' id='Page_44'>44</span>as are likely to arise, but under such as might possibly
| |
| − | occur, no matter how improbable they may be. What the
| |
| − | habit is depends on <i>when</i> and <i>how</i> it causes us to act. As
| |
| − | for the <i>when</i>, every stimulus to action is derived from perception;
| |
| − | as for the <i>how</i>, every purpose of action is to produce
| |
| − | some sensible result. Thus, we come down to what is
| |
| − | tangible and practical, as the root of every real distinction
| |
| − | of thought, no matter how subtile it may be; and there is
| |
| − | no distinction of meaning so fine as to consist in anything
| |
| − | but a possible difference of practice.</p>
| |
| − |
| |
| − | <p class='c005'>To see what this principle leads to, consider in the light
| |
| − | of it such a doctrine as that of transubstantiation. The
| |
| − | Protestant churches generally hold that the elements of the
| |
| − | sacrament are flesh and blood only in a tropical sense; they
| |
| − | nourish our souls as meat and the juice of it would our
| |
| − | bodies. But the Catholics maintain that they are literally
| |
| − | just that; although they possess all the sensible qualities of
| |
| − | wafer-cakes and diluted wine. But we can have no conception
| |
| − | of wine except what may enter into a belief,
| |
| − | either—</p>
| |
| − |
| |
| − | <p class='c005'>1. That this, that, or the other, is wine; or,</p>
| |
| − |
| |
| − | <p class='c005'>2. That wine possesses certain properties.</p>
| |
| − |
| |
| − | <p class='c005'>Such beliefs are nothing but self-notifications that we
| |
| − | should, upon occasion, act in regard to such things as we
| |
| − | believe to be wine according to the qualities which we believe
| |
| − | wine to possess. The occasion of such action would
| |
| − | be some sensible perception, the motive of it to produce
| |
| − | some sensible result. Thus our action has exclusive reference
| |
| − | to what affects the senses, our habit has the same bearing
| |
| − | as our action, our belief the same as our habit, our
| |
| − | <span class='pageno' id='Page_45'>45</span>conception the same as our belief; and we can consequently
| |
| − | mean nothing by wine but what has certain effects, direct
| |
| − | or indirect, upon our senses; and to talk of something as
| |
| − | having all the sensible characters of wine, yet being in
| |
| − | reality blood, is senseless jargon. Now, it is not my object
| |
| − | to pursue the theological question; and having used it as
| |
| − | a logical example I drop it, without caring to anticipate
| |
| − | the theologian’s reply. I only desire to point out how impossible
| |
| − | it is that we should have an idea in our minds
| |
| − | which relates to anything but conceived sensible effects of
| |
| − | things. Our idea of anything <i>is</i> our idea of its sensible
| |
| − | effects; and if we fancy that we have any other we deceive
| |
| − | ourselves, and mistake a mere sensation accompanying the
| |
| − | thought for a part of the thought itself. It is absurd to say
| |
| − | that thought has any meaning unrelated to its only function.
| |
| − | It is foolish for Catholics and Protestants to fancy
| |
| − | themselves in disagreement about the elements of the sacrament,
| |
| − | if they agree in regard to all their sensible effects,
| |
| − | here or hereafter.</p>
| |
| − |
| |
| − | <p class='c005'>It appears, then, that the rule for attaining the third
| |
| − | grade of clearness of apprehension is as follows: Consider
| |
| − | what effects, which might conceivably have practical bearings,
| |
| − | we conceive the object of our conception to have.
| |
| − | Then, our conception of these effects is the whole of our
| |
| − | conception of the object.</p>
| |
| − | <h4 class='c012'>III</h4>
| |
| − | <p class='c006'>Let us illustrate this rule by some examples; and, to
| |
| − | begin with the simplest one possible, let us ask what we
| |
| − | mean by calling a thing <i>hard</i>. Evidently that it will not
| |
| − | <span class='pageno' id='Page_46'>46</span>be scratched by many other substances. The whole conception
| |
| − | of this quality, as of every other, lies in its conceived
| |
| − | effects. There is absolutely no difference between
| |
| − | a hard thing and a soft thing so long as they are not brought
| |
| − | to the test. Suppose, then, that a diamond could be crystallized
| |
| − | in the midst of a cushion of soft cotton, and should
| |
| − | remain there until it was finally burned up. Would it be
| |
| − | false to say that that diamond was soft? This seems a
| |
| − | foolish question, and would be so, in fact, except in the
| |
| − | realm of logic. There such questions are often of the
| |
| − | greatest utility as serving to bring logical principles into
| |
| − | sharper relief than real discussions ever could. In studying
| |
| − | logic we must not put them aside with hasty answers,
| |
| − | but must consider them with attentive care, in order to
| |
| − | make out the principles involved. We may, in the present
| |
| − | case, modify our question, and ask what prevents us from
| |
| − | saying that all hard bodies remain perfectly soft until they
| |
| − | are touched, when their hardness increases with the pressure
| |
| − | until they are scratched. Reflection will show that the
| |
| − | reply is this: there would be no <i>falsity</i> in such modes of
| |
| − | speech. They would involve a modification of our present
| |
| − | usage of speech with regard to the words hard and soft,
| |
| − | but not of their meanings. For they represent no fact to
| |
| − | be different from what it is; only they involve arrangements
| |
| − | of facts which would be exceedingly maladroit. This
| |
| − | leads us to remark that the question of what would occur
| |
| − | under circumstances which do not actually arise is not a
| |
| − | question of fact, but only of the most perspicuous arrangement
| |
| − | of them. For example, the question of free-will and
| |
| − | fate in its simplest form, stripped of verbiage, is something
| |
| − | <span class='pageno' id='Page_47'>47</span>like this: I have done something of which I am ashamed;
| |
| − | could I, by an effort of the will, have resisted the temptation,
| |
| − | and done otherwise? The philosophical reply is, that
| |
| − | this is not a question of fact, but only of the arrangement
| |
| − | of facts. Arranging them so as to exhibit what is particularly
| |
| − | pertinent to my question—namely, that I ought
| |
| − | to blame myself for having done wrong—it is perfectly
| |
| − | true to say that, if I had willed to do otherwise than I did,
| |
| − | I should have done otherwise. On the other hand, arranging
| |
| − | the facts so as to exhibit another important consideration,
| |
| − | it is equally true that, when a temptation has once
| |
| − | been allowed to work, it will, if it has a certain force, produce
| |
| − | its effect, let me struggle how I may. There is no
| |
| − | objection to a contradiction in what would result from a
| |
| − | false supposition. The <i>reductio ad absurdum</i> consists in
| |
| − | showing that contradictory results would follow from a
| |
| − | hypothesis which is consequently judged to be false. Many
| |
| − | questions are involved in the free-will discussion, and I am
| |
| − | far from desiring to say that both sides are equally right.
| |
| − | On the contrary, I am of opinion that one side denies important
| |
| − | facts, and that the other does not. But what I do
| |
| − | say is, that the above single question was the origin of the
| |
| − | whole doubt; that, had it not been for this question, the
| |
| − | controversy would never have arisen; and that this question
| |
| − | is perfectly solved in the manner which I have indicated.</p>
| |
| − |
| |
| − | <p class='c005'>Let us next seek a clear idea of Weight. This is another
| |
| − | very easy case. To say that a body is heavy means simply
| |
| − | that, in the absence of opposing force, it will fall. This
| |
| − | (neglecting certain specifications of how it will fall, etc.,
| |
| − | which exist in the mind of the physicist who uses the word)
| |
| − | <span class='pageno' id='Page_48'>48</span>is evidently the whole conception of weight. It is a fair
| |
| − | question whether some particular facts may not <i>account</i>
| |
| − | for gravity; but what we mean by the force itself is completely
| |
| − | involved in its effects.</p>
| |
| − |
| |
| − | <p class='c005'>This leads us to undertake an account of the idea of
| |
| − | Force in general. This is the great conception which,
| |
| − | developed in the early part of the seventeenth century
| |
| − | from the rude idea of a cause, and constantly improved
| |
| − | upon since, has shown us how to explain all the changes
| |
| − | of motion which bodies experience, and how to think about
| |
| − | all physical phenomena; which has given birth to modern
| |
| − | science, and changed the face of the globe; and which,
| |
| − | aside from its more special uses, has played a principal
| |
| − | part in directing the course of modern thought, and in
| |
| − | furthering modern social development. It is, therefore,
| |
| − | worth some pains to comprehend it. According to our
| |
| − | rule, we must begin by asking what is the immediate use
| |
| − | of thinking about force; and the answer is, that we thus
| |
| − | account for changes of motion. If bodies were left to
| |
| − | themselves, without the intervention of forces, every
| |
| − | motion would continue unchanged both in velocity and in
| |
| − | direction. Furthermore, change of motion never takes
| |
| − | place abruptly; if its direction is changed, it is always
| |
| − | through a curve without angles; if its velocity alters, it is
| |
| − | by degrees. The gradual changes which are constantly
| |
| − | taking place are conceived by geometers to be compounded
| |
| − | together according to the rules of the parallelogram of
| |
| − | forces. If the reader does not already know what this is,
| |
| − | he will find it, I hope, to his advantage to endeavor to
| |
| − | follow the following explanation; but if mathematics are
| |
| − | <span class='pageno' id='Page_49'>49</span>insupportable to him, pray let him skip three paragraphs
| |
| − | rather than that we should part company here.</p>
| |
| − |
| |
| − | <p class='c005'>A <i>path</i> is a line whose beginning and end are distinguished.
| |
| − | Two paths are considered to be equivalent, which,
| |
| − | beginning at the same point, lead to the same point. Thus
| |
| − | the two paths, <i>A B C D E</i> and <i>A F G H E</i> (Fig. 3), are
| |
| − | equivalent. Paths which do <i>not</i> begin at the same point are
| |
| − | considered to be equivalent, provided that, on moving either
| |
| − | of them without turning it, but keeping it always parallel to
| |
| − | its original position, [so that] when its beginning coincides
| |
| − | with that of the other path, the ends also coincide. Paths are
| |
| − | considered as geometrically added together, when one begins
| |
| − | where the other ends; thus the path <i>A E</i> is conceived to
| |
| − | be a sum of <i>A B</i>, <i>B C</i>, <i>C D</i>, and <i>D E</i>. In the parallelogram
| |
| − | of Fig. 4 the diagonal <i>A C</i> is the sum of <i>A B</i> and <i>B C</i>;
| |
| − | or, since <i>A D</i> is geometrically equivalent to <i>B C</i>, <i>A C</i> is
| |
| − | the geometrical sum of <i>A B</i> and <i>A D</i>.</p>
| |
| − |
| |
| − | <div class='figcenter id002'>
| |
| − | <img src='images/fig3.png' alt='Fig. 3.' class='ig001' />
| |
| − | <div class='ic002'>
| |
| − | <p>Figure 3.</p>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <div class='figcenter id002'>
| |
| − | <img src='images/fig4.png' alt='Fig. 4.' class='ig001' />
| |
| − | <div class='ic002'>
| |
| − | <p>Figure 4.</p>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c005'>All this is purely conventional. It simply amounts to
| |
| − | this: that we choose to call paths having the relations I
| |
| − | have described equal or added. But, though it is a convention,
| |
| − | it is a convention with a good reason. The rule
| |
| − | for geometrical addition may be applied not only to paths,
| |
| − | but to any other things which can be represented by paths.
| |
| − | Now, as a path is determined by the varying direction and
| |
| − | <span class='pageno' id='Page_50'>50</span>distance of the point which moves over it from the starting-point,
| |
| − | it follows that anything which from its beginning to
| |
| − | its end is determined by a varying direction and a varying
| |
| − | magnitude is capable of being represented by a line.
| |
| − | Accordingly, <i>velocities</i> may be represented by lines, for
| |
| − | they have only directions and rates. The same thing is
| |
| − | true of <i>accelerations</i>, or changes of velocities. This is
| |
| − | evident enough in the case of velocities; and it becomes
| |
| − | evident for accelerations if we consider that precisely what
| |
| − | velocities are to positions—namely, states of change of
| |
| − | them—that accelerations are to velocities.</p>
| |
| − |
| |
| − | <div class='figcenter id002'>
| |
| − | <img src='images/fig5.png' alt='Fig. 5.' class='ig001' />
| |
| − | <div class='ic002'>
| |
| − | <p>Figure 5.</p>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c005'>The so-called “parallelogram of forces” is simply a
| |
| − | rule for compounding accelerations. The rule is, to
| |
| − | represent the accelerations by paths, and then to geometrically
| |
| − | add the paths. The geometers, however, not
| |
| − | only use the “parallelogram of forces” to compound different
| |
| − | accelerations, but also to resolve one acceleration
| |
| − | into a sum of several. Let <i>A B</i> (Fig. 5) be the path
| |
| − | which represents a certain
| |
| − | acceleration—say, such a
| |
| − | change in the motion of a
| |
| − | body that at the end of
| |
| − | one second the body will,
| |
| − | under the influence of that
| |
| − | change, be in a position
| |
| − | different from what it
| |
| − | would have had if its motion had continued unchanged, such
| |
| − | that a path equivalent to <i>A B</i> would lead from the latter
| |
| − | position to the former. This acceleration may be considered
| |
| − | as the sum of the accelerations represented by <i>A C</i> and <i>C B</i>.
| |
| − | <span class='pageno' id='Page_51'>51</span>It may also be considered as the sum of the very different
| |
| − | accelerations represented by <i>A D</i> and <i>D B</i>, where <i>A D</i> is
| |
| − | almost the opposite of <i>A C</i>. And it is clear that there is
| |
| − | an immense variety of ways in which <i>A B</i> might be resolved
| |
| − | into the sum of two accelerations.</p>
| |
| − |
| |
| − | <p class='c005'>After this tedious explanation, which I hope, in view of
| |
| − | the extraordinary interest of the conception of force, may
| |
| − | not have exhausted the reader’s patience, we are prepared
| |
| − | at last to state the grand fact which this conception embodies.
| |
| − | This fact is that if the actual changes of motion
| |
| − | which the different particles of bodies experience are each
| |
| − | resolved in its appropriate way, each component acceleration
| |
| − | is precisely such as is prescribed by a certain law of
| |
| − | Nature, according to which bodies in the relative positions
| |
| − | which the bodies in question actually have at the moment,<a id='r32' /><a href='#f32' class='c011'><sup>[32]</sup></a>
| |
| − | always receive certain accelerations, which, being compounded
| |
| − | by geometrical addition, give the acceleration
| |
| − | which the body actually experiences.</p>
| |
| − |
| |
| − | <p class='c005'>This is the only fact which the idea of force represents,
| |
| − | and whoever will take the trouble clearly to apprehend
| |
| − | what this fact is, perfectly comprehends what force is.
| |
| − | Whether we ought to say that a force <i>is</i> an acceleration,
| |
| − | or that it <i>causes</i> an acceleration, is a mere question of propriety
| |
| − | of language, which has no more to do with our real
| |
| − | meaning than the difference between the French idiom “<i>Il
| |
| − | fait froid</i>” and its English equivalent “<i>It is cold</i>.” Yet
| |
| − | it is surprising to see how this simple affair has muddled
| |
| − | men’s minds. In how many profound treatises is not force
| |
| − | spoken of as a “mysterious entity,” which seems to be
| |
| − | <span class='pageno' id='Page_52'>52</span>only a way of confessing that the author despairs of ever
| |
| − | getting a clear notion of what the word means! In a recent
| |
| − | admired work on <i>Analytic Mechanics</i> it is stated
| |
| − | that we understand precisely the effect of force, but what
| |
| − | force itself is we do not understand! This is simply a self-contradiction.
| |
| − | The idea which the word force excites in
| |
| − | our minds has no other function than to affect our actions,
| |
| − | and these actions can have no reference to force otherwise
| |
| − | than through its effects. Consequently, if we know what
| |
| − | the effects of force are, we are acquainted with every fact
| |
| − | which is implied in saying that a force exists, and there is
| |
| − | nothing more to know. The truth is, there is some vague
| |
| − | notion afloat that a question may mean something which the
| |
| − | mind cannot conceive; and when some hair-splitting
| |
| − | philosophers have been confronted with the absurdity of
| |
| − | such a view, they have invented an empty distinction between
| |
| − | positive and negative conceptions, in the attempt to
| |
| − | give their non-idea a form not obviously nonsensical. The
| |
| − | nullity of it is sufficiently plain from the considerations
| |
| − | given a few pages back; and, apart from those considerations,
| |
| − | the quibbling character of the distinction must have
| |
| − | struck every mind accustomed to real thinking.</p>
| |
| − | <h4 class='c012'>IV</h4>
| |
| − | <p class='c006'>Let us now approach the subject of logic, and consider
| |
| − | a conception which particularly concerns it, that of <i>reality</i>.
| |
| − | Taking clearness in the sense of familiarity, no idea could
| |
| − | be clearer than this. Every child uses it with perfect confidence,
| |
| − | never dreaming that he does not understand it.
| |
| − | <span class='pageno' id='Page_53'>53</span>As for clearness in its second grade, however, it would
| |
| − | probably puzzle most men, even among those of a reflective
| |
| − | turn of mind, to give an abstract definition of the real.
| |
| − | Yet such a definition may perhaps be reached by considering
| |
| − | the points of difference between reality and its opposite,
| |
| − | fiction. A figment is a product of somebody’s imagination;
| |
| − | it has such characters as his thought impresses upon it.
| |
| − | That those characters are independent of how you or I
| |
| − | think is an external reality. There are, however, phenomena
| |
| − | within our own minds, dependent upon our thought,
| |
| − | which are at the same time real in the sense that we really
| |
| − | think them. But though their characters depend on how
| |
| − | we think, they do not depend on what we think those characters
| |
| − | to be. Thus, a dream has a real existence as a
| |
| − | mental phenomenon, if somebody has really dreamt it;
| |
| − | that he dreamt so and so, does not depend on what anybody
| |
| − | thinks was dreamt, but is completely independent of all
| |
| − | opinion on the subject. On the other hand, considering,
| |
| − | not the fact of dreaming, but the thing dreamt, it retains
| |
| − | its peculiarities by virtue of no other fact than that it was
| |
| − | dreamt to possess them. Thus we may define the real as
| |
| − | that whose characters are independent of what anybody
| |
| − | may think them to be.</p>
| |
| − |
| |
| − | <p class='c005'>But, however satisfactory such a definition may be found,
| |
| − | it would be a great mistake to suppose that it makes the
| |
| − | idea of reality perfectly clear. Here, then, let us apply
| |
| − | our rules. According to them, reality, like every other
| |
| − | quality, consists in the peculiar sensible effects which things
| |
| − | partaking of it produce. The only effect which real things
| |
| − | have is to cause belief, for all the sensations which they
| |
| − | <span class='pageno' id='Page_54'>54</span>excite emerge into consciousness in the form of beliefs.
| |
| − | The question, therefore, is, how is true belief (or belief in
| |
| − | the real) distinguished from false belief (or belief in fiction).
| |
| − | Now, as we have seen in the former paper, the
| |
| − | ideas of truth and falsehood, in their full development,
| |
| − | appertain exclusively to the scientific method of settling
| |
| − | opinion. A person who arbitrarily chooses the propositions
| |
| − | which he will adopt can use the word truth only to emphasize
| |
| − | the expression of his determination to hold on to his
| |
| − | choice. Of course, the method of tenacity never prevailed
| |
| − | exclusively; reason is too natural to men for that. But in
| |
| − | the literature of the dark ages we find some fine examples
| |
| − | of it. When Scotus Erigena is commenting upon a poetical
| |
| − | passage in which hellebore is spoken of as having caused
| |
| − | the death of Socrates, he does not hesitate to inform the
| |
| − | inquiring reader that Helleborus and Socrates were two
| |
| − | eminent Greek philosophers, and that the latter having been
| |
| − | overcome in argument by the former took the matter to
| |
| − | heart and died of it! What sort of an idea of truth could
| |
| − | a man have who could adopt and teach, without the qualification
| |
| − | of a perhaps, an opinion taken so entirely at random?
| |
| − | The real spirit of Socrates, who I hope would have
| |
| − | been delighted to have been “overcome in argument,” because
| |
| − | he would have learned something by it, is in curious
| |
| − | contrast with the naïve idea of the glossist, for whom discussion
| |
| − | would seem to have been simply a struggle. When
| |
| − | philosophy began to awake from its long slumber, and
| |
| − | before theology completely dominated it, the practice seems
| |
| − | to have been for each professor to seize upon any philosophical
| |
| − | position he found unoccupied and which seemed a
| |
| − | <span class='pageno' id='Page_55'>55</span>strong one, to intrench himself in it, and to sally forth from
| |
| − | time to time to give battle to the others. Thus, even the
| |
| − | scanty records we possess of those disputes enable us to
| |
| − | make out a dozen or more opinions held by different teachers
| |
| − | at one time concerning the question of nominalism and
| |
| − | realism. Read the opening part of the <i>Historia Calamitatum</i>
| |
| − | of Abelard, who was certainly as philosophical as
| |
| − | any of his contemporaries, and see the spirit of combat
| |
| − | which it breathes. For him, the truth is simply his particular
| |
| − | stronghold. When the method of authority prevailed,
| |
| − | the truth meant little more than the Catholic faith.
| |
| − | All the efforts of the scholastic doctors are directed toward
| |
| − | harmonizing their faith in Aristotle and their faith in the
| |
| − | Church, and one may search their ponderous folios through
| |
| − | without finding an argument which goes any further. It is
| |
| − | noticeable that where different faiths flourish side by side,
| |
| − | renegades are looked upon with contempt even by the party
| |
| − | whose belief they adopt; so completely has the idea of
| |
| − | loyalty replaced that of truth-seeking. Since the time of
| |
| − | Descartes, the defect in the conception of truth has been
| |
| − | less apparent. Still, it will sometimes strike a scientific
| |
| − | man that the philosophers have been less intent on finding
| |
| − | out what the facts are, than on inquiring what belief is
| |
| − | most in harmony with their system. It is hard to convince
| |
| − | a follower of the <i>a priori</i> method by adducing facts; but
| |
| − | show him that an opinion he is defending is inconsistent
| |
| − | with what he has laid down elsewhere, and he will be very
| |
| − | apt to retract it. These minds do not seem to believe that
| |
| − | disputation is ever to cease; they seem to think that the
| |
| − | opinion which is natural for one man is not so for another,
| |
| − | <span class='pageno' id='Page_56'>56</span>and that belief will, consequently, never be settled. In
| |
| − | contenting themselves with fixing their own opinions by a
| |
| − | method which would lead another man to a different result,
| |
| − | they betray their feeble hold of the conception of what
| |
| − | truth is.</p>
| |
| − |
| |
| − | <p class='c005'>On the other hand, all the followers of science are fully
| |
| − | persuaded that the processes of investigation, if only pushed
| |
| − | far enough, will give one certain solution to every question
| |
| − | to which they can be applied. One man may investigate
| |
| − | the velocity of light by studying the transits of Venus and
| |
| − | the aberration of the stars; another by the oppositions of
| |
| − | Mars and the eclipses of Jupiter’s satellites; a third by the
| |
| − | method of Fizeau; a fourth by that of Foucault; a fifth
| |
| − | by the motions of the curves of Lissajoux; a sixth, a seventh,
| |
| − | an eighth, and a ninth, may follow the different methods
| |
| − | of comparing the measures of statical and dynamical electricity.
| |
| − | They may at first obtain different results, but,
| |
| − | as each perfects his method and his processes, the results
| |
| − | will move steadily together toward a destined center. So
| |
| − | with all scientific research. Different minds may set out
| |
| − | with the most antagonistic views, but the progress of investigation
| |
| − | carries them by a force outside of themselves
| |
| − | to one and the same conclusion. This activity of thought
| |
| − | by which we are carried, not where we wish, but to a fore-ordained
| |
| − | goal, is like the operation of destiny. No modification
| |
| − | of the point of view taken, no selection of other
| |
| − | facts for study, no natural bent of mind even, can enable
| |
| − | a man to escape the predestinate opinion. This great law
| |
| − | is embodied in the conception of truth and reality. The
| |
| − | <span class='pageno' id='Page_57'>57</span>opinion which is fated<a id='r33' /><a href='#f33' class='c011'><sup>[33]</sup></a> to be ultimately agreed to by all
| |
| − | who investigate, is what we mean by the truth, and the object
| |
| − | represented in this opinion is the real. That is the way
| |
| − | I would explain reality.</p>
| |
| − |
| |
| − | <p class='c005'>But it may be said that this view is directly opposed
| |
| − | to the abstract definition which we have given of reality,
| |
| − | inasmuch as it makes the characters of the real depend
| |
| − | on what is ultimately thought about them. But the answer
| |
| − | to this is that, on the one hand, reality is independent, not
| |
| − | necessarily of thought in general, but only of what you or
| |
| − | I or any finite number of men may think about it; and that,
| |
| − | on the other hand, though the object of the final opinion
| |
| − | depends on what that opinion is, yet what that opinion is
| |
| − | does not depend on what you or I or any man thinks. Our
| |
| − | perversity and that of others may indefinitely postpone the
| |
| − | settlement of opinion; it might even conceivably cause an
| |
| − | arbitrary proposition to be universally accepted as long as
| |
| − | the human race should last. Yet even that would not change
| |
| − | the nature of the belief, which alone could be the result of
| |
| − | investigation carried sufficiently far; and if, after the extinction
| |
| − | of our race, another should arise with faculties and
| |
| − | disposition for investigation, that true opinion must be the
| |
| − | one which they would ultimately come to. “Truth crushed
| |
| − | to earth shall rise again,” and the opinion which would
| |
| − | finally result from investigation does not depend on how
| |
| − | anybody may actually think. But the reality of that which
| |
| − | is real does depend on the real fact that investigation is
| |
| − | <span class='pageno' id='Page_58'>58</span>destined to lead, at last, if continued long enough, to a
| |
| − | belief in it.</p>
| |
| − |
| |
| − | <p class='c005'>But I may be asked what I have to say to all the minute
| |
| − | facts of history, forgotten never to be recovered, to the lost
| |
| − | books of the ancients, to the buried secrets.</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'>“Full many a gem of purest ray serene</div>
| |
| − | <div class='line in2'>The dark, unfathomed caves of ocean bear;</div>
| |
| − | <div class='line'>Full many a flower is born to blush unseen,</div>
| |
| − | <div class='line in2'>And waste its sweetness on the desert air.”</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>Do these things not really exist because they are hopelessly
| |
| − | beyond the reach of our knowledge? And then, after the
| |
| − | universe is dead (according to the prediction of some scientists),
| |
| − | and all life has ceased forever, will not the shock
| |
| − | of atoms continue though there will be no mind to know it?
| |
| − | To this I reply that, though in no possible state of knowledge
| |
| − | can any number be great enough to express the relation
| |
| − | between the amount of what rests unknown to the
| |
| − | amount of the known, yet it is unphilosophical to suppose
| |
| − | that, with regard to any given question (which has any
| |
| − | clear meaning), investigation would not bring forth a solution
| |
| − | of it, if it were carried far enough. Who would have
| |
| − | said, a few years ago, that we could ever know of what
| |
| − | substances stars are made whose light may have been longer
| |
| − | in reaching us than the human race has existed? Who can
| |
| − | be sure of what we shall not know in a few hundred years?
| |
| − | Who can guess what would be the result of continuing the
| |
| − | pursuit of science for ten thousand years, with the activity
| |
| − | of the last hundred? And if it were to go on for a million,
| |
| − | or a billion, or any number of years you please, how is it
| |
| − | <span class='pageno' id='Page_59'>59</span>possible to say that there is any question which might not
| |
| − | ultimately be solved?</p>
| |
| − |
| |
| − | <p class='c005'>But it may be objected, “Why make so much of these
| |
| − | remote considerations, especially when it is your principle
| |
| − | that only practical distinctions have a meaning?” Well,
| |
| − | I must confess that it makes very little difference whether
| |
| − | we say that a stone on the bottom of the ocean, in complete
| |
| − | darkness, is brilliant or not—that is to say, that it <i>probably</i>
| |
| − | makes no difference, remembering always that that stone
| |
| − | <i>may</i> be fished up to-morrow. But that there are gems at
| |
| − | the bottom of the sea, flowers in the untraveled desert, etc.,
| |
| − | are propositions which, like that about a diamond being
| |
| − | hard when it is not pressed, concern much more the arrangement
| |
| − | of our language than they do the meaning of our ideas.</p>
| |
| − |
| |
| − | <p class='c005'>It seems to me, however, that we have, by the application
| |
| − | of our rule, reached so clear an apprehension of what we
| |
| − | mean by reality, and of the fact which the idea rests on,
| |
| − | that we should not, perhaps, be making a pretension so presumptuous
| |
| − | as it would be singular, if we were to offer a
| |
| − | metaphysical theory of existence for universal acceptance
| |
| − | among those who employ the scientific method of fixing belief.
| |
| − | However, as metaphysics is a subject much more
| |
| − | curious than useful, the knowledge of which, like that of a
| |
| − | sunken reef, serves chiefly to enable us to keep clear of it,
| |
| − | I will not trouble the reader with any more Ontology at
| |
| − | this moment. I have already been led much further into
| |
| − | that path than I should have desired; and I have given the
| |
| − | reader such a dose of mathematics, psychology, and all
| |
| − | that is most abstruse, that I fear he may already have left
| |
| − | me, and that what I am now writing is for the compositor
| |
| − | <span class='pageno' id='Page_60'>60</span>and proofreader exclusively. I trusted to the importance
| |
| − | of the subject. There is no royal road to logic, and really
| |
| − | valuable ideas can only be had at the price of close attention.
| |
| − | But I know that in the matter of ideas the public
| |
| − | prefer the cheap and nasty; and in my next paper I am
| |
| − | going to return to the easily intelligible, and not wander
| |
| − | from it again. The reader who has been at the pains of
| |
| − | wading through this paper, shall be rewarded in the next
| |
| − | one by seeing how beautifully what has been developed
| |
| − | in this tedious way can be applied to the ascertainment of
| |
| − | the rules of scientific reasoning.</p>
| |
| − |
| |
| − | <p class='c005'>We have, hitherto, not crossed the threshold of scientific
| |
| − | logic. It is certainly important to know how to make our
| |
| − | ideas clear, but they may be ever so clear without being
| |
| − | true. How to make them so, we have next to study. How
| |
| − | to give birth to those vital and procreative ideas which
| |
| − | multiply into a thousand forms and diffuse themselves
| |
| − | everywhere, advancing civilization and making the dignity
| |
| − | of man, is an art not yet reduced to rules, but of the secret
| |
| − | of which the history of science affords some hints.</p>
| |
| − |
| |
| − | <div>
| |
| − | <span class='pageno' id='Page_61'>61</span>
| |
| − | <h3 id='chap1-3' class='c001'>THIRD PAPER <br /> THE DOCTRINE OF CHANCES<a id='r34' /><a href='#f34' class='c011'><sup>[34]</sup></a></h3>
| |
| − | </div>
| |
| − | <h4 class='c012'>I</h4>
| |
| − | <p class='c006'>It is a common observation that a science first begins to be
| |
| − | exact when it is quantitatively treated. What are called
| |
| − | the exact sciences are no others than the mathematical ones.
| |
| − | Chemists reasoned vaguely until Lavoisier showed them
| |
| − | how to apply the balance to the verification of their theories,
| |
| − | when chemistry leaped suddenly into the position of the
| |
| − | most perfect of the classificatory sciences. It has thus
| |
| − | become so precise and certain that we usually think of it
| |
| − | along with optics, thermotics, and electrics. But these are
| |
| − | studies of general laws, while chemistry considers merely
| |
| − | the relations and classification of certain objects; and belongs,
| |
| − | in reality, in the same category as systematic botany
| |
| − | and zoölogy. Compare it with these last, however, and
| |
| − | the advantage that it derives from its quantitative treatment
| |
| − | is very evident.</p>
| |
| − |
| |
| − | <p class='c005'>The rudest numerical scales, such as that by which the
| |
| − | mineralogists distinguish the different degrees of hardness,
| |
| − | are found useful. The mere counting of pistils and stamens
| |
| − | sufficed to bring botany out of total chaos into some
| |
| − | kind of form. It is not, however, so much from <i>counting</i>
| |
| − | as from <i>measuring</i>, not so much from the conception of
| |
| − | <span class='pageno' id='Page_62'>62</span>number as from that of continuous quantity, that the advantage
| |
| − | of mathematical treatment comes. Number, after all,
| |
| − | only serves to pin us down to a precision in our thoughts
| |
| − | which, however beneficial, can seldom lead to lofty conceptions,
| |
| − | and frequently descends to pettiness. Of those two
| |
| − | faculties of which Bacon speaks, that which marks differences
| |
| − | and that which notes resemblances, the employment of
| |
| − | number can only aid the lesser one; and the excessive use
| |
| − | of it must tend to narrow the powers of the mind. But the
| |
| − | conception of continuous quantity has a great office to fulfill,
| |
| − | independently of any attempt at precision. Far from
| |
| − | tending to the exaggeration of differences, it is the direct
| |
| − | instrument of the finest generalizations. When a naturalist
| |
| − | wishes to study a species, he collects a considerable number
| |
| − | of specimens more or less similar. In contemplating
| |
| − | them, he observes certain ones which are more or less alike
| |
| − | in some particular respect. They all have, for instance,
| |
| − | a certain S-shaped marking. He observes that they are
| |
| − | not <i>precisely</i> alike, in this respect; the S has not precisely
| |
| − | the same shape, but the differences are such as to lead him
| |
| − | to believe that forms could be found intermediate between
| |
| − | any two of those he possesses. He, now, finds other forms
| |
| − | apparently quite dissimilar—say a marking in the form
| |
| − | of a C—and the question is, whether he can find intermediate
| |
| − | ones which will connect these latter with the others.
| |
| − | This he often succeeds in doing in cases where it would at
| |
| − | first be thought impossible; whereas he sometimes finds
| |
| − | those which differ, at first glance, much less, to be separated
| |
| − | in Nature by the non-occurrence of intermediaries. In
| |
| − | this way, he builds up from the study of Nature a new general
| |
| − | <span class='pageno' id='Page_63'>63</span>conception of the character in question. He obtains,
| |
| − | for example, an idea of a leaf which includes every part
| |
| − | of the flower, and an idea of a vertebra which includes the
| |
| − | skull. I surely need not say much to show what a logical
| |
| − | engine there is here. It is the essence of the method of the
| |
| − | naturalist.<a id='r35' /><a href='#f35' class='c011'><sup>[35]</sup></a> How he applies it first to one character, and
| |
| − | then to another, and finally obtains a notion of a species
| |
| − | of animals, the differences between whose members, however
| |
| − | great, are confined within limits, is a matter which does not
| |
| − | here concern us. The whole method of classification must
| |
| − | be considered later; but, at present, I only desire to point
| |
| − | out that it is by taking advantage of the idea of continuity,
| |
| − | or the passage from one form to another by insensible degrees,
| |
| − | that the naturalist builds his conceptions. Now, the
| |
| − | naturalists are the great builders of conceptions; there is
| |
| − | no other branch of science where so much of this work is
| |
| − | done as in theirs; and we must, in great measure, take them
| |
| − | for our teachers in this important part of logic. And it will
| |
| − | be found everywhere that the idea of continuity is a powerful
| |
| − | aid to the formation of true and fruitful conceptions.
| |
| − | By means of it, the greatest differences are broken down
| |
| − | and resolved into differences of degree, and the incessant
| |
| − | application of it is of the greatest value in broadening our
| |
| − | conceptions. I propose to make a great use of this idea in
| |
| − | the present series of papers; and the particular series of
| |
| − | important fallacies, which, arising from a neglect of it, have
| |
| − | desolated philosophy, must further on be closely studied.
| |
| − | <span class='pageno' id='Page_64'>64</span>At present, I simply call the reader’s attention to the utility
| |
| − | of this conception.</p>
| |
| − |
| |
| − | <p class='c005'>In studies of numbers, the idea of continuity is so indispensable,
| |
| − | that it is perpetually introduced even where
| |
| − | there is no continuity in fact, as where we say that there
| |
| − | are in the United States 10.7 inhabitants per square mile, or
| |
| − | that in New York 14.72 persons live in the average house.<a id='r36' /><a href='#f36' class='c011'><sup>[36]</sup></a>
| |
| − | Another example is that law of the distribution of errors
| |
| − | which Quetelet, Galton, and others, have applied with so
| |
| − | much success to the study of biological and social matters.
| |
| − | This application of continuity to cases where it does not
| |
| − | really exist illustrates, also, another point which will hereafter
| |
| − | demand a separate study, namely, the great utility
| |
| − | which fictions sometimes have in science.</p>
| |
| − | <h4 class='c012'>II</h4>
| |
| − | <p class='c006'>The theory of probabilities is simply the science of logic
| |
| − | quantitatively treated. There are two conceivable certainties
| |
| − | with reference to any hypothesis, the certainty of
| |
| − | its truth and the certainty of its falsity. The numbers <i>one</i>
| |
| − | and <i>zero</i> are appropriated, in this calculus, to marking these
| |
| − | extremes of knowledge; while fractions having values intermediate
| |
| − | between them indicate, as we may vaguely say, the
| |
| − | degrees in which the evidence leans toward one or the other.
| |
| − | The general problem of probabilities is, from a given state
| |
| − | <span class='pageno' id='Page_65'>65</span>of facts, to determine the numerical probability of a possible
| |
| − | fact. This is the same as to inquire how much the
| |
| − | given facts are worth, considered as evidence to prove the
| |
| − | possible fact. Thus the problem of probabilities is simply
| |
| − | the general problem of logic.</p>
| |
| − |
| |
| − | <p class='c005'>Probability is a continuous quantity, so that great advantages
| |
| − | may be expected from this mode of studying logic.
| |
| − | Some writers have gone so far as to maintain that, by means
| |
| − | of the calculus of chances, every solid inference may be
| |
| − | represented by legitimate arithmetical operations upon the
| |
| − | numbers given in the premises. If this be, indeed, true,
| |
| − | the great problem of logic, how it is that the observation
| |
| − | of one fact can give us knowledge of another independent
| |
| − | fact, is reduced to a mere question of arithmetic. It seems
| |
| − | proper to examine this pretension before undertaking any
| |
| − | more recondite solution of the paradox.</p>
| |
| − |
| |
| − | <p class='c005'>But, unfortunately, writers on probabilities are not agreed
| |
| − | in regard to this result. This branch of mathematics is the
| |
| − | only one, I believe, in which good writers frequently get
| |
| − | results entirely erroneous. In elementary geometry the
| |
| − | reasoning is frequently fallacious, but erroneous conclusions
| |
| − | are avoided; but it may be doubted if there is a single extensive
| |
| − | treatise on probabilities in existence which does not
| |
| − | contain solutions absolutely indefensible. This is partly
| |
| − | owing to the want of any regular method of procedure; for
| |
| − | the subject involves too many subtilties to make it easy to
| |
| − | put its problems into equations without such an aid. But,
| |
| − | beyond this, the fundamental principles of its calculus are
| |
| − | more or less in dispute. In regard to that class of questions
| |
| − | to which it is chiefly applied for practical purposes, there
| |
| − | <span class='pageno' id='Page_66'>66</span>is comparatively little doubt; but in regard to others to
| |
| − | which it has been sought to extend it, opinion is somewhat
| |
| − | unsettled.</p>
| |
| − |
| |
| − | <p class='c005'>This last class of difficulties can only be entirely overcome
| |
| − | by making the idea of probability perfectly clear in
| |
| − | our minds in the way set forth in our last paper.</p>
| |
| − | <h4 class='c012'>III</h4>
| |
| − | <p class='c006'>To get a clear idea of what we mean by probability, we
| |
| − | have to consider what real and sensible difference there is
| |
| − | between one degree of probability and another.</p>
| |
| − |
| |
| − | <p class='c005'>The character of probability belongs primarily, without
| |
| − | doubt, to certain inferences. Locke explains it as follows:
| |
| − | After remarking that the mathematician positively knows
| |
| − | that the sum of the three angles of a triangle is equal to
| |
| − | two right angles because he apprehends the geometrical
| |
| − | proof, he thus continues: “But another man who never took
| |
| − | the pains to observe the demonstration, hearing a mathematician,
| |
| − | a man of credit, affirm the three angles of a triangle
| |
| − | to be equal to two right ones, <i>assents</i> to it; i.e., receives
| |
| − | it for true. In which case the foundation of his assent
| |
| − | is the probability of the thing, the proof being such as,
| |
| − | for the most part, carries truth with it; the man on whose
| |
| − | testimony he receives it not being wont to affirm anything
| |
| − | contrary to, or besides his knowledge, especially in matters
| |
| − | of this kind.” The celebrated <i>Essay concerning Human
| |
| − | Understanding</i> contains many passages which, like this
| |
| − | one, make the first steps in profound analyses which are not
| |
| − | further developed. It was shown in the first of these papers
| |
| − | <span class='pageno' id='Page_67'>67</span>that the validity of an inference does not depend on any
| |
| − | tendency of the mind to accept it, however strong such tendency
| |
| − | may be; but consists in the real fact that, when
| |
| − | premises like those of the argument in question are true,
| |
| − | conclusions related to them like that of this argument are
| |
| − | also true. It was remarked that in a logical mind an argument
| |
| − | is always conceived as a member of a <i>genus</i> of
| |
| − | arguments all constructed in the same way, and such that,
| |
| − | when their premises are real facts, their conclusions are so
| |
| − | also. If the argument is demonstrative, then this is always
| |
| − | so; if it is only probable, then it is for the most part so.
| |
| − | As Locke says, the probable argument is “<i>such as</i> for the
| |
| − | most part carries truth with it.”</p>
| |
| − |
| |
| − | <p class='c005'>According to this, that real and sensible difference between
| |
| − | one degree of probability and another, in which the
| |
| − | meaning of the distinction lies, is that in the frequent employment
| |
| − | of two different modes of inference, one will carry
| |
| − | truth with it oftener than the other. It is evident that this
| |
| − | is the only difference there is in the existing fact. Having
| |
| − | certain premises, a man draws a certain conclusion, and as
| |
| − | far as this inference alone is concerned the only possible
| |
| − | practical question is whether that conclusion is true or not,
| |
| − | and between existence and non-existence there is no middle
| |
| − | term. “Being only is and nothing is altogether not,” said
| |
| − | Parmenides; and this is in strict accordance with the analysis
| |
| − | of the conception of reality given in the last paper. For
| |
| − | we found that the distinction of reality and fiction depends
| |
| − | on the supposition that sufficient investigation would cause
| |
| − | one opinion to be universally received and all others to be
| |
| − | rejected. That presupposition, involved in the very conceptions
| |
| − | <span class='pageno' id='Page_68'>68</span>of reality and figment, involves a complete sundering
| |
| − | of the two. It is the heaven-and-hell idea in the domain
| |
| − | of thought. But, in the long run, there is a real fact
| |
| − | which corresponds to the idea of probability, and it is that
| |
| − | a given mode of inference sometimes proves successful and
| |
| − | sometimes not, and that in a ratio ultimately fixed. As we
| |
| − | go on drawing inference after inference of the given kind,
| |
| − | during the first ten or hundred cases the ratio of successes
| |
| − | may be expected to show considerable fluctuations; but
| |
| − | when we come into the thousands and millions, these fluctuations
| |
| − | become less and less; and if we continue long
| |
| − | enough, the ratio will approximate toward a fixed limit.
| |
| − | We may, therefore, define the probability of a mode of
| |
| − | argument as the proportion of cases in which it carries truth
| |
| − | with it.</p>
| |
| − |
| |
| − | <p class='c005'>The inference from the premise, A, to the conclusion, B,
| |
| − | depends, as we have seen, on the guiding principle, that if
| |
| − | a fact of the class A is true, a fact of the class B is true.
| |
| − | The probability consists of the fraction whose numerator
| |
| − | is the number of times in which both A and B are true,
| |
| − | and whose denominator is the total number of times in
| |
| − | which A is true, whether B is so or not. Instead of speaking
| |
| − | of this as the probability of the inference, there is not
| |
| − | the slightest objection to calling it the probability that, if
| |
| − | A happens, B happens. But to speak of the probability
| |
| − | of the event B, without naming the condition, really has no
| |
| − | meaning at all. It is true that when it is perfectly obvious
| |
| − | what condition is meant, the ellipsis may be permitted. But
| |
| − | we should avoid contracting the habit of using language in
| |
| − | this way (universal as the habit is), because it gives rise
| |
| − | <span class='pageno' id='Page_69'>69</span>to a vague way of thinking, as if the action of causation
| |
| − | might either determine an event to happen or determine it
| |
| − | not to happen, or leave it more or less free to happen or
| |
| − | not, so as to give rise to an <i>inherent</i> chance in regard to its
| |
| − | occurrence.<a id='r37' /><a href='#f37' class='c011'><sup>[37]</sup></a> It is quite clear to me that some of the worst
| |
| − | and most persistent errors in the use of the doctrine of
| |
| − | chances have arisen from this vicious mode of expression.<a id='r38' /><a href='#f38' class='c011'><sup>[38]</sup></a></p>
| |
| − | <h4 class='c012'>IV</h4>
| |
| − | <p class='c006'>But there remains an important point to be cleared up.
| |
| − | According to what has been said, the idea of probability
| |
| − | essentially belongs to a kind of inference which is repeated
| |
| − | indefinitely. An individual inference must be either true
| |
| − | or false, and can show no effect of probability; and, therefore,
| |
| − | in reference to a single case considered in itself, probability
| |
| − | can have no meaning. Yet if a man had to choose
| |
| − | between drawing a card from a pack containing twenty-five
| |
| − | red cards and a black one, or from a pack containing
| |
| − | twenty-five black cards and a red one, and if the drawing
| |
| − | of a red card were destined to transport him to eternal
| |
| − | felicity, and that of a black one to consign him to everlasting
| |
| − | woe, it would be folly to deny that he ought to prefer the
| |
| − | pack containing the larger portion of red cards, although,
| |
| − | from the nature of the risk, it could not be repeated. It is
| |
| − | not easy to reconcile this with our analysis of the conception
| |
| − | <span class='pageno' id='Page_70'>70</span>of chance. But suppose he should choose the red pack,
| |
| − | and should draw the wrong card, what consolation would he
| |
| − | have? He might say that he had acted in accordance with
| |
| − | reason, but that would only show that his reason was absolutely
| |
| − | worthless. And if he should choose the right card,
| |
| − | how could he regard it as anything but a happy accident?
| |
| − | He could not say that if he had drawn from the other pack,
| |
| − | he might have drawn the wrong one, because an hypothetical
| |
| − | proposition such as, “if A, then B,” means nothing with
| |
| − | reference to a single case. Truth consists in the existence
| |
| − | of a real fact corresponding to the true proposition. Corresponding
| |
| − | to the proposition, “if A, then B,” there may be
| |
| − | the fact that <i>whenever</i> such an event as A happens such an
| |
| − | event as B happens. But in the case supposed, which has
| |
| − | no parallel as far as this man is concerned, there would be
| |
| − | no real fact whose existence could give any truth to the
| |
| − | statement that, if he had drawn from the other pack, he
| |
| − | might have drawn a black card. Indeed, since the validity
| |
| − | of an inference consists in the truth of the hypothetical
| |
| − | proposition that <i>if</i> the premises be true the conclusion will
| |
| − | also be true, and since the only real fact which can correspond
| |
| − | to such a proposition is that whenever the antecedent
| |
| − | is true the consequent is so also, it follows that there can
| |
| − | be no sense in reasoning in an isolated case, at all.</p>
| |
| − |
| |
| − | <p class='c005'>These considerations appear, at first sight, to dispose of
| |
| − | the difficulty mentioned. Yet the case of the other side is
| |
| − | not yet exhausted. Although probability will probably
| |
| − | manifest its effect in, say, a thousand risks, by a certain
| |
| − | proportion between the numbers of successes and failures,
| |
| − | yet this, as we have seen, is only to say that it certainly will,
| |
| − | <span class='pageno' id='Page_71'>71</span>at length, do so. Now the number of risks, the number of
| |
| − | probable inferences, which a man draws in his whole life,
| |
| − | is a finite one, and he cannot be absolutely <i>certain</i> that the
| |
| − | mean result will accord with the probabilities at all. Taking
| |
| − | all his risks collectively, then, it cannot be certain that
| |
| − | they will not fail, and his case does not differ, except in degree,
| |
| − | from the one last supposed. It is an indubitable result
| |
| − | of the theory of probabilities that every gambler, if he
| |
| − | continues long enough, must ultimately be ruined. Suppose
| |
| − | he tries the martingale, which some believe infallible, and
| |
| − | which is, as I am informed, disallowed in the gambling-houses.
| |
| − | In this method of playing, he first bets say $1;
| |
| − | if he loses it he bets $2; if he loses that he bets $4; if he
| |
| − | loses that he bets $8; if he then gains he has lost
| |
| − | 1 + 2 + 4 = 7, and he has gained $1 more; and no matter
| |
| − | how many bets he loses, the first one he gains will make
| |
| − | him $1 richer than he was in the beginning. In that way,
| |
| − | he will probably gain at first; but, at last, the time will
| |
| − | come when the run of luck is so against him that he will not
| |
| − | have money enough to double, and must, therefore, let his
| |
| − | bet go. This will <i>probably</i> happen before he has won as
| |
| − | much as he had in the first place, so that this run against
| |
| − | him will leave him poorer than he began; some time or other
| |
| − | it will be sure to happen. It is true that there is always a
| |
| − | possibility of his winning any sum the bank can pay, and
| |
| − | we thus come upon a celebrated paradox that, though he is
| |
| − | certain to be ruined, the value of his expectation calculated
| |
| − | according to the usual rules (which omit this consideration)
| |
| − | is large. But, whether a gambler plays in this way or any
| |
| − | other, the same thing is true, namely, that if he plays long
| |
| − | <span class='pageno' id='Page_72'>72</span>enough he will be sure some time to have such a run against
| |
| − | him as to exhaust his entire fortune. The same thing is
| |
| − | true of an insurance company. Let the directors take the
| |
| − | utmost pains to be independent of great conflagrations and
| |
| − | pestilences, their actuaries can tell them that, according
| |
| − | to the doctrine of chances, the time must come, at last, when
| |
| − | their losses will bring them to a stop. They may tide over
| |
| − | such a crisis by extraordinary means, but then they will
| |
| − | start again in a weakened state, and the same thing will
| |
| − | happen again all the sooner. An actuary might be inclined
| |
| − | to deny this, because he knows that the expectation of his
| |
| − | company is large, or perhaps (neglecting the interest upon
| |
| − | money) is infinite. But calculations of expectations leave
| |
| − | out of account the circumstance now under consideration,
| |
| − | which reverses the whole thing. However, I must not be
| |
| − | understood as saying that insurance is on this account unsound,
| |
| − | more than other kinds of business. All human affairs
| |
| − | rest upon probabilities, and the same thing is true
| |
| − | everywhere. If man were immortal he could be perfectly
| |
| − | sure of seeing the day when everything in which he had
| |
| − | trusted should betray his trust, and, in short, of coming
| |
| − | eventually to hopeless misery. He would break down, at
| |
| − | last, as every good fortune, as every dynasty, as every
| |
| − | civilization does. In place of this we have death.</p>
| |
| − |
| |
| − | <p class='c005'>But what, without death, would happen to every man,
| |
| − | with death must happen to some man. At the same time,
| |
| − | death makes the number of our risks, of our inferences,
| |
| − | finite, and so makes their mean result uncertain. The very
| |
| − | idea of probability and of reasoning rests on the assumption
| |
| − | that this number is indefinitely great. We are thus landed
| |
| − | <span class='pageno' id='Page_73'>73</span>in the same difficulty as before, and I can see but one solution
| |
| − | of it. It seems to me that we are driven to this, that
| |
| − | logicality inexorably requires that our interests shall <i>not</i>
| |
| − | be limited. They must not stop at our own fate, but must
| |
| − | embrace the whole community. This community, again,
| |
| − | must not be limited, but must extend to all races of beings
| |
| − | with whom we can come into immediate or mediate intellectual
| |
| − | relation. It must reach, however vaguely, beyond
| |
| − | this geological epoch, beyond all bounds. He who would
| |
| − | not sacrifice his own soul to save the whole world, is, as it
| |
| − | seems to me, illogical in all his inferences, collectively.
| |
| − | Logic is rooted in the social principle.</p>
| |
| − |
| |
| − | <p class='c005'>To be logical men should not be selfish; and, in point of
| |
| − | fact, they are not so selfish as they are thought. The willful
| |
| − | prosecution of one’s desires is a different thing from
| |
| − | selfishness. The miser is not selfish; his money does him
| |
| − | no good, and he cares for what shall become of it after his
| |
| − | death. We are constantly speaking of <i>our</i> possessions on
| |
| − | the Pacific, and of <i>our</i> destiny as a republic, where no personal
| |
| − | interests are involved, in a way which shows that we
| |
| − | have wider ones. We discuss with anxiety the possible exhaustion
| |
| − | of coal in some hundreds of years, or the cooling-off
| |
| − | of the sun in some millions, and show in the most popular
| |
| − | of all religious tenets that we can conceive the possibility of
| |
| − | a man’s descending into hell for the salvation of his fellows.</p>
| |
| − |
| |
| − | <p class='c005'>Now, it is not necessary for logicality that a man should
| |
| − | himself be capable of the heroism of self-sacrifice. It is
| |
| − | sufficient that he should recognize the possibility of it,
| |
| − | should perceive that only that man’s inferences who has it
| |
| − | are really logical, and should consequently regard his own
| |
| − | <span class='pageno' id='Page_74'>74</span>as being only so far valid as they would be accepted by
| |
| − | the hero. So far as he thus refers his inferences to that
| |
| − | standard, he becomes identified with such a mind.</p>
| |
| − |
| |
| − | <p class='c005'>This makes logicality attainable enough. Sometimes we
| |
| − | can personally attain to heroism. The soldier who runs to
| |
| − | scale a wall knows that he will probably be shot, but that
| |
| − | is not all he cares for. He also knows that if all the regiment,
| |
| − | with whom in feeling he identifies himself, rush forward
| |
| − | at once, the fort will be taken. In other cases we
| |
| − | can only imitate the virtue. The man whom we have supposed
| |
| − | as having to draw from the two packs, who if he is
| |
| − | not a logician will draw from the red pack from mere
| |
| − | habit, will see, if he is logician enough, that he cannot be
| |
| − | logical so long as he is concerned only with his own fate,
| |
| − | but that that man who should care equally for what was
| |
| − | to happen in all possible cases of the sort could act logically,
| |
| − | and would draw from the pack with the most red
| |
| − | cards, and thus, though incapable himself of such sublimity,
| |
| − | our logician would imitate the effect of that man’s
| |
| − | courage in order to share his logicality.</p>
| |
| − |
| |
| − | <p class='c005'>But all this requires a conceived identification of one’s
| |
| − | interests with those of an unlimited community. Now,
| |
| − | there exist no reasons, and a later discussion will show that
| |
| − | there can be no reasons, for thinking that the human race,
| |
| − | or any intellectual race, will exist forever. On the other
| |
| − | hand, there can be no reason against it;<a id='r39' /><a href='#f39' class='c011'><sup>[39]</sup></a> and, fortunately,
| |
| − | as the whole requirement is that we should have certain
| |
| − | <span class='pageno' id='Page_75'>75</span>sentiments, there is nothing in the facts to forbid our having
| |
| − | a <i>hope</i>, or calm and cheerful wish, that the community may
| |
| − | last beyond any assignable date.</p>
| |
| − |
| |
| − | <p class='c005'>It may seem strange that I should put forward three
| |
| − | sentiments, namely, interest in an indefinite community,
| |
| − | recognition of the possibility of this interest being made
| |
| − | supreme, and hope in the unlimited continuance of intellectual
| |
| − | activity, as indispensable requirements of logic. Yet,
| |
| − | when we consider that logic depends on a mere struggle to
| |
| − | escape doubt, which, as it terminates in action, must begin
| |
| − | in emotion, and that, furthermore, the only cause of our
| |
| − | planting ourselves on reason is that other methods of escaping
| |
| − | doubt fail on account of the social impulse, why should
| |
| − | we wonder to find social sentiment presupposed in
| |
| − | reasoning? As for the other two sentiments which I find
| |
| − | necessary, they are so only as supports and accessories of
| |
| − | that. It interests me to notice that these three sentiments
| |
| − | seem to be pretty much the same as that famous trio of
| |
| − | Charity, Faith, and Hope, which, in the estimation of St. Paul,
| |
| − | are the finest and greatest of spiritual gifts. Neither
| |
| − | Old nor New Testament is a textbook of the logic of science,
| |
| − | but the latter is certainly the highest existing authority in
| |
| − | regard to the dispositions of heart which a man ought
| |
| − | to have.</p>
| |
| − | <h4 class='c012'>V</h4>
| |
| − | <p class='c006'>Such average statistical numbers as the number of inhabitants
| |
| − | per square mile, the average number of deaths
| |
| − | per week, the number of convictions per indictment, or,
| |
| − | generally speaking, the numbers of <i>x</i>’s per <i>y</i>, where the <i>x</i>’s
| |
| − | <span class='pageno' id='Page_76'>76</span>are a class of things some or all of which are connected with
| |
| − | another class of things, their <i>y</i>’s, I term <i>relative numbers</i>.
| |
| − | Of the two classes of things to which a relative number
| |
| − | refers, that one of which it is a number may be called its
| |
| − | <i>relate</i>, and that one <i>per</i> which the numeration is made may
| |
| − | be called its <i>correlate</i>.</p>
| |
| − |
| |
| − | <p class='c005'>Probability is a kind of relative number; namely, it is
| |
| − | the ratio of the number of arguments of a certain genus
| |
| − | which carry truth with them to the total number of arguments
| |
| − | of that genus, and the rules for the calculation of
| |
| − | probabilities are very easily derived from this consideration.
| |
| − | They may all be given here, since they are extremely
| |
| − | simple, and it is sometimes convenient to know something
| |
| − | of the elementary rules of calculation of chances.</p>
| |
| − | <p class='c006'><span class='sc'>Rule I.</span> <i>Direct Calculation.</i>—To calculate, directly,
| |
| − | any relative number, say for instance the number of passengers
| |
| − | in the average trip of a street-car, we must proceed
| |
| − | as follows:</p>
| |
| − |
| |
| − | <p class='c005'>Count the number of passengers for each trip; add all
| |
| − | these numbers, and divide by the number of trips. There
| |
| − | are cases in which this rule may be simplified. Suppose
| |
| − | we wish to know the number of inhabitants to a dwelling
| |
| − | in New York. The same person cannot inhabit two dwellings.
| |
| − | If he divide his time between two dwellings he ought
| |
| − | to be counted a half-inhabitant of each. In this case we
| |
| − | have only to divide the total number of the inhabitants of
| |
| − | New York by the number of their dwellings, without the
| |
| − | necessity of counting separately those which inhabit each
| |
| − | one. A similar proceeding will apply wherever each individual
| |
| − | relate belongs to one individual correlate exclusively.
| |
| − | <span class='pageno' id='Page_77'>77</span>If we want the number of <i>x</i>’s per <i>y</i>, and no <i>x</i> belongs
| |
| − | to more than one <i>y</i>, we have only to divide the whole
| |
| − | number of <i>x</i>’s of <i>y</i>’s by the number of <i>y</i>’s. Such a method
| |
| − | would, of course, fail if applied to finding the average number
| |
| − | of street-car passengers per trip. We could not divide
| |
| − | the total number of travelers by the number of trips, since
| |
| − | many of them would have made many passages.</p>
| |
| − |
| |
| − | <p class='c005'>To find the probability that from a given class of premises,
| |
| − | A, a given class of conclusions, B, follow, it is simply
| |
| − | necessary to ascertain what proportion of the times in which
| |
| − | premises of that class are true, the appropriate conclusions
| |
| − | are also true. In other words, it is the number of cases
| |
| − | of the occurrence of both the events A and B, divided by
| |
| − | the total number of cases of the occurrence of the event A.</p>
| |
| − |
| |
| − | <p class='c006'><span class='sc'>Rule II.</span> <i>Addition of Relative Numbers.</i>—Given two
| |
| − | relative numbers having the same correlate, say the number
| |
| − | of <i>x</i>’s per <i>y</i>, and the number of <i>z</i>’s per <i>y</i>; it is required
| |
| − | to find the number of <i>x</i>’s and <i>z</i>’s together per <i>y</i>. If there
| |
| − | is nothing which is at once an <i>x</i> and a <i>z</i> to the same <i>y</i>, the
| |
| − | sum of the two given numbers would give the required
| |
| − | number. Suppose, for example, that we had given the average
| |
| − | number of friends that men have, and the average
| |
| − | number of enemies, the sum of these two is the average
| |
| − | number of persons interested in a man. On the other hand,
| |
| − | it plainly would not do to add the average number of
| |
| − | persons having constitutional diseases and over military
| |
| − | age, to the average number exempted by each special cause
| |
| − | from military service, in order to get the average number
| |
| − | exempt in any way, since many are exempt in two or more
| |
| − | ways at once.</p>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_78'>78</span>This rule applies directly to probabilities, given the
| |
| − | probability that two different and mutually exclusive events
| |
| − | will happen under the same supposed set of circumstances.
| |
| − | Given, for instance, the probability that if A then B, and
| |
| − | also the probability that if A then C, then the sum of these
| |
| − | two probabilities is the probability that if A then either B
| |
| − | or C, so long as there is no event which belongs at once to
| |
| − | the two classes B and C.</p>
| |
| − |
| |
| − | <p class='c006'><span class='sc'>Rule III.</span> <i>Multiplication of Relative Numbers.</i>—Suppose
| |
| − | that we have given the relative number of <i>x</i>’s per <i>y</i>;
| |
| − | also the relative number of <i>z</i>’s per <i>x</i> of <i>y</i>; or, to take a
| |
| − | concrete example, suppose that we have given, first, the
| |
| − | average number of children in families living in New York;
| |
| − | and, second, the average number of teeth in the head of a
| |
| − | New York child—then the product of these two numbers
| |
| − | would give the average number of children’s teeth in a
| |
| − | New York family. But this mode of reckoning will only
| |
| − | apply in general under two restrictions. In the first place,
| |
| − | it would not be true if the same child could belong to different
| |
| − | families, for in that case those children who belonged
| |
| − | to several different families might have an exceptionally
| |
| − | large or small number of teeth, which would affect the
| |
| − | average number of children’s teeth in a family more than
| |
| − | it would affect the average number of teeth in a child’s head.
| |
| − | In the second place, the rule would not be true if different
| |
| − | children could share the same teeth, the average number
| |
| − | of children’s teeth being in that case evidently something
| |
| − | different from the average number of teeth belonging to
| |
| − | a child.</p>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_79'>79</span>In order to apply this rule to probabilities, we must proceed
| |
| − | as follows: Suppose that we have given the probability
| |
| − | that the conclusion B follows from the premise A, B
| |
| − | and A representing as usual certain classes of propositions.
| |
| − | Suppose that we also knew the probability of an inference
| |
| − | in which B should be the premise, and a proposition of a
| |
| − | third kind, C, the conclusion. Here, then, we have the
| |
| − | materials for the application of this rule. We have, first,
| |
| − | the relative number of B’s per A. We next should have
| |
| − | the relative number of C’s per B following from A. But
| |
| − | the classes of propositions being so selected that the probability
| |
| − | of C following from any B in general is just the same
| |
| − | as the probability of C’s following from one of those B’s
| |
| − | which is deducible from an A, the two probabilities may
| |
| − | be multiplied together, in order to give the probability of
| |
| − | C following from A. The same restrictions exist as before.
| |
| − | It might happen that the probability that B follows from A
| |
| − | was affected by certain propositions of the class B following
| |
| − | from several different propositions of the class A. But,
| |
| − | practically speaking, all these restrictions are of very little
| |
| − | consequence, and it is usually recognized as a principle
| |
| − | universally true that the probability that, if A is true, B is,
| |
| − | multiplied by the probability that, if B is true, C is, gives
| |
| − | the probability that, if A is true, C is.</p>
| |
| − |
| |
| − | <p class='c005'>There is a rule supplementary to this, of which great use
| |
| − | is made. It is not universally valid, and the greatest caution
| |
| − | has to be exercised in making use of it—a double care,
| |
| − | first, never to use it when it will involve serious error; and,
| |
| − | second, never to fail to take advantage of it in cases in
| |
| − | which it can be employed. This rule depends upon the fact
| |
| − | <span class='pageno' id='Page_80'>80</span>that in very many cases the probability that C is true if
| |
| − | B is, is substantially the same as the probability that C is
| |
| − | true if A is. Suppose, for example, we have the average
| |
| − | number of males among the children born in New York;
| |
| − | suppose that we also have the average number of children
| |
| − | born in the winter months among those born in New York.
| |
| − | Now, we may assume without doubt, at least as a closely
| |
| − | approximate proposition (and no very nice calculation
| |
| − | would be in place in regard to probabilities), that the proportion
| |
| − | of males among all the children born in New York
| |
| − | is the same as the proportion of males born in summer in
| |
| − | New York; and, therefore, if the names of all the children
| |
| − | born during a year were put into an urn, we might multiply
| |
| − | the probability that any name drawn would be the name
| |
| − | of a male child by the probability that it would be the name
| |
| − | of a child born in summer, in order to obtain the probability
| |
| − | that it would be the name of a male child born in
| |
| − | summer. The questions of probability, in the treatises
| |
| − | upon the subject, have usually been such as relate to balls
| |
| − | drawn from urns, and games of cards, and so on, in which
| |
| − | the question of the <i>independence</i> of events, as it is called—that
| |
| − | is to say, the question of whether the probability of C,
| |
| − | under the hypothesis B, is the same as its probability under
| |
| − | the hypothesis A, has been very simple; but, in the application
| |
| − | of probabilities to the ordinary questions of life, it
| |
| − | is often an exceedingly nice question whether two events
| |
| − | may be considered as independent with sufficient accuracy
| |
| − | or not. In all calculations about cards it is assumed that
| |
| − | the cards are thoroughly shuffled, which makes one deal
| |
| − | quite independent of another. In point of fact the cards
| |
| − | <span class='pageno' id='Page_81'>81</span>seldom are, in practice, shuffled sufficiently to make this
| |
| − | true; thus, in a game of whist, in which the cards have
| |
| − | fallen in suits of four of the same suit, and are so gathered
| |
| − | up, they will lie more or less in sets of four of the same suit,
| |
| − | and this will be true even after they are shuffled. At least
| |
| − | some traces of this arrangement will remain, in consequence
| |
| − | of which the number of “short suits,” as they are called—that
| |
| − | is to say, the number of hands in which the cards
| |
| − | are very unequally divided in regard to suits—is smaller
| |
| − | than the calculation would make it to be; so that, when
| |
| − | there is a misdeal, where the cards, being thrown about the
| |
| − | table, get very thoroughly shuffled, it is a common saying
| |
| − | that in the hands next dealt out there are generally short
| |
| − | suits. A few years ago a friend of mine, who plays whist
| |
| − | a great deal, was so good as to count the number of spades
| |
| − | dealt to him in 165 hands, in which the cards had been, if
| |
| − | anything, shuffled better than usual. According to calculation,
| |
| − | there should have been 85 of these hands in which my
| |
| − | friend held either three or four spades, but in point of fact
| |
| − | there were 94, showing the influence of imperfect shuffling.</p>
| |
| − |
| |
| − | <p class='c005'>According to the view here taken, these are the only
| |
| − | fundamental rules for the calculation of chances. An additional
| |
| − | one, derived from a different conception of probability,
| |
| − | is given in some treatises, which if it be sound might
| |
| − | be made the basis of a theory of reasoning. Being, as I
| |
| − | believe it is, absolutely absurd, the consideration of it serves
| |
| − | to bring us to the true theory; and it is for the sake of this
| |
| − | discussion, which must be postponed to the next number,
| |
| − | that I have brought the doctrine of chances to the reader’s
| |
| − | attention at this early stage of our studies of the logic of
| |
| − | science.</p>
| |
| − |
| |
| − | <div>
| |
| − | <span class='pageno' id='Page_82'>82</span>
| |
| − | <h3 id='chap1-4' class='c001'>FOURTH PAPER <br /> THE PROBABILITY OF INDUCTION<a id='r40' /><a href='#f40' class='c011'><sup>[40]</sup></a></h3>
| |
| − | </div>
| |
| − | <h4 class='c012'>I</h4>
| |
| − | <p class='c006'>We have found that every argument derives its force from
| |
| − | the general truth of the class of inferences to which it belongs;
| |
| − | and that probability is the proportion of arguments
| |
| − | carrying truth with them among those of any <i>genus</i>. This
| |
| − | is most conveniently expressed in the nomenclature of the
| |
| − | medieval logicians. They called the fact expressed by a
| |
| − | premise an <i>antecedent</i>, and that which follows from it its
| |
| − | <i>consequent</i>; while the leading principle, that every (or
| |
| − | almost every) such antecedent is followed by such a consequent,
| |
| − | they termed the <i>consequence</i>. Using this language,
| |
| − | we may say that probability belongs exclusively to
| |
| − | <i>consequences</i>, and the probability of any consequence is
| |
| − | the number of times in which antecedent and consequent
| |
| − | both occur divided by the number of all the times in which
| |
| − | the antecedent occurs. From this definition are deduced
| |
| − | the following rules for the addition and multiplication of
| |
| − | probabilities:</p>
| |
| − |
| |
| − | <p class='c005'><i>Rule for the Addition of Probabilities.</i>—Given the separate
| |
| − | probabilities of two consequences having the same antecedent
| |
| − | and incompatible consequents. Then the sum of
| |
| − | these two numbers is the probability of the consequence,
| |
| − | <span class='pageno' id='Page_83'>83</span>that from the same antecedent one or other of those consequents
| |
| − | follows.</p>
| |
| − |
| |
| − | <p class='c005'><i>Rule for the Multiplication of Probabilities.</i>—Given the
| |
| − | separate probabilities of the two consequences, “If A then
| |
| − | B,” and “If both A and B, then C.” Then the product
| |
| − | of these two numbers is the probability of the consequence,
| |
| − | “If A, then both B and C.”</p>
| |
| − |
| |
| − | <p class='c005'><i>Special Rule for the Multiplication of Independent Probabilities.</i>—Given
| |
| − | the separate probabilities of two consequences
| |
| − | having the same antecedents, “If A, then B,” and
| |
| − | “If A, then C.” Suppose that these consequences are such
| |
| − | that the probability of the second is equal to the probability
| |
| − | of the consequence, “If both A and B, then C.” Then the
| |
| − | product of the two given numbers is equal to the probability
| |
| − | of the consequence, “If A, then both B and C.”</p>
| |
| − |
| |
| − | <p class='c005'>To show the working of these rules we may examine the
| |
| − | probabilities in regard to throwing dice. What is the probability
| |
| − | of throwing a six with one die? The antecedent
| |
| − | here is the event of throwing a die; the consequent, its
| |
| − | turning up a six. As the die has six sides, all of which are
| |
| − | turned up with equal frequency, the probability of turning
| |
| − | up any one is 1/6. Suppose two dice are thrown, what is
| |
| − | the probability of throwing sixes? The probability of either
| |
| − | coming up six is obviously the same when both are thrown
| |
| − | as when one is thrown—namely, 1/6. The probability that
| |
| − | either will come up six when the other does is also the same
| |
| − | as that of its coming up six whether the other does or not.
| |
| − | The probabilities are, therefore, independent; and, by our
| |
| − | rule, the probability that both events will happen together
| |
| − | is the product of their several probabilities, or 1/6 x 1/6. What
| |
| − | <span class='pageno' id='Page_84'>84</span>is the probability of throwing deuce-ace? The probability
| |
| − | that the first die will turn up ace and the second deuce is
| |
| − | the same as the probability that both will turn up sixes—namely,
| |
| − | 1/36; the probability that the <i>second</i> will turn up
| |
| − | ace and the <i>first</i> deuce is likewise 1/36; these two events—first,
| |
| − | ace; second, deuce; and, second, ace; first, deuce—are
| |
| − | incompatible. Hence the rule for addition holds, and
| |
| − | the probability that either will come up ace and the other
| |
| − | deuce is 1/36 + 1/36, or 1/18.</p>
| |
| − |
| |
| − | <p class='c005'>In this way all problems about dice, etc., may be solved.
| |
| − | When the number of dice thrown is supposed very large,
| |
| − | mathematics (which may be defined as the art of making
| |
| − | groups to facilitate numeration) comes to our aid with
| |
| − | certain devices to reduce the difficulties.</p>
| |
| − | <h4 class='c012'>II</h4>
| |
| − | <p class='c006'>The conception of probability as a matter of <i>fact</i>, i.e., as
| |
| − | the proportion of times in which an occurrence of one kind
| |
| − | is accompanied by an occurrence of another kind, is termed
| |
| − | by Mr. Venn the materialistic view of the subject. But
| |
| − | probability has often been regarded as being simply the
| |
| − | degree of belief which ought to attach to a proposition, and
| |
| − | this mode of explaining the idea is termed by Venn the
| |
| − | conceptualistic view. Most writers have mixed the two
| |
| − | conceptions together. They, first, define the probability of
| |
| − | an event as the reason we have to believe that it has taken
| |
| − | place, which is conceptualistic; but shortly after they state
| |
| − | that it is the ratio of the number of cases favorable to the
| |
| − | event to the total number of cases favorable or contrary,
| |
| − | <span class='pageno' id='Page_85'>85</span>and all equally possible. Except that this introduces the
| |
| − | thoroughly unclear idea of cases equally possible in place
| |
| − | of cases equally frequent, this is a tolerable statement of
| |
| − | the materialistic view. The pure conceptualistic theory has
| |
| − | been best expounded by Mr. De Morgan in his <i>Formal
| |
| − | Logic</i>: or, the <i>Calculus of Inference, Necessary and
| |
| − | Probable.</i></p>
| |
| − |
| |
| − | <p class='c005'>The great difference between the two analyses is, that
| |
| − | the conceptualists refer probability to an event, while the
| |
| − | materialists make it the ratio of frequency of events of a
| |
| − | <i>species</i> to those of a <i>genus</i> over that <i>species</i>, thus <i>giving it
| |
| − | two terms instead of one</i>. The opposition may be made to
| |
| − | appear as follows:</p>
| |
| − |
| |
| − | <p class='c005'>Suppose that we have two rules of inference, such that,
| |
| − | of all the questions to the solution of which both can be
| |
| − | applied, the first yields correct answers to 81/100, and incorrect
| |
| − | answers to the remaining 19/100; while the second
| |
| − | yields correct answers to 93/100, and incorrect answers to the
| |
| − | remaining 7/100. Suppose, further, that the two rules are
| |
| − | entirely independent as to their truth, so that the second
| |
| − | answers correctly 93/100 of the questions which the first answers
| |
| − | correctly, and also 93/100 of the questions which the
| |
| − | first answers incorrectly, and answers incorrectly the remaining
| |
| − | 7/100 of the questions which the first answers
| |
| − | correctly, and also the remaining 7/100 of the questions which
| |
| − | the first answers incorrectly. Then, of all the questions to
| |
| − | the solution of which both rules can be applied—</p>
| |
| − |
| |
| − | <p class='c007'><span class='pageno' id='Page_86'>86</span>both answer correctly 93/100 of 81/100 or 93/100 x 81/100;</p>
| |
| − |
| |
| − | <p class='c008'>the second answers correctly and the first incorrectly 93/100 of 19/100 or 93/100 x 19/100;</p>
| |
| − |
| |
| − | <p class='c008'>the second answers incorrectly and the first correctly 7/100 of 81/100 or 7/100 x 81/100;</p>
| |
| − |
| |
| − | <p class='c008'>and both answer incorrectly 7/100 of 19/100 or 7/100 x 19/100;</p>
| |
| − |
| |
| − | <p class='c014'>Suppose, now, that, in reference to any question, both
| |
| − | give the same answer. Then (the questions being always
| |
| − | such as are to be answered by <i>yes</i> or <i>no</i>), those in reference
| |
| − | to which their answers agree are the same as those which
| |
| − | both answer correctly together with those which both answer
| |
| − | falsely, or 93/100 x 81/100 + 7/100 x 19/100 of all. The
| |
| − | proportion of those which both answer correctly out of those
| |
| − | their answers to which agree is, therefore—</p>
| |
| − |
| |
| − | <p class='c007'>((93 × 81)/(100 × 100))/((93 × 81)/(100 × 100)) + ((7 × 19)/(100 × 100)) or (93 × 81)/((93 × 81) + (7 × 19)).</p>
| |
| − |
| |
| − | <p class='c014'>This is, therefore, the probability that, if both modes of
| |
| − | inference yield the same result, that result is correct. We
| |
| − | may here conveniently make use of another mode of expression.
| |
| − | <i>Probability</i> is the ratio of the favorable cases to
| |
| − | all the cases. Instead of expressing our result in terms of
| |
| − | this ratio, we may make use of another—the ratio of
| |
| − | favorable to unfavorable cases. This last ratio may be
| |
| − | called the <i>chance</i> of an event. Then the chance of a true
| |
| − | answer by the first mode of inference is 81/19 and by the
| |
| − | second is 93/7; and the chance of a correct answer from both,
| |
| − | when they agree, is—</p>
| |
| − |
| |
| − | <p class='c007'><span class='pageno' id='Page_87'>87</span>(81 × 93)/(19 × 7) or 81/19 × 93/7,</p>
| |
| − |
| |
| − | <p class='c014'>or the product of the chances of each singly yielding a true
| |
| − | answer.</p>
| |
| − |
| |
| − | <p class='c005'>It will be seen that a chance is a quantity which may have
| |
| − | any magnitude, however great. An event in whose favor
| |
| − | there is an even chance, or 1/1, has a probability of 1/2. An
| |
| − | argument having an even chance can do nothing toward re-enforcing
| |
| − | others, since according to the rule its combination
| |
| − | with another would only multiply the chance of the latter
| |
| − | by 1.</p>
| |
| − |
| |
| − | <p class='c005'>Probability and chance undoubtedly belong primarily to
| |
| − | consequences, and are relative to premises; but we may,
| |
| − | nevertheless, speak of the chance of an event absolutely,
| |
| − | meaning by that the chance of the combination of all arguments
| |
| − | in reference to it which exist for us in the given state
| |
| − | of our knowledge. Taken in this sense it is incontestable
| |
| − | that the chance of an event has an intimate connection with
| |
| − | the degree of our belief in it. Belief is certainly something
| |
| − | more than a mere feeling; yet there is a feeling of believing,
| |
| − | and this feeling does and ought to vary with the chance of
| |
| − | the thing believed, as deduced from all the arguments.
| |
| − | Any quantity which varies with the chance might, therefore,
| |
| − | it would seem, serve as a thermometer for the proper intensity
| |
| − | of belief. Among all such quantities there is one
| |
| − | which is peculiarly appropriate. When there is a very great
| |
| − | chance, the feeling of belief ought to be very intense. Absolute
| |
| − | certainty, or an infinite chance, can never be attained
| |
| − | by mortals, and this may be represented appropriately by
| |
| − | an infinite belief. As the chance diminishes the feeling of
| |
| − | <span class='pageno' id='Page_88'>88</span>believing should diminish, until an even chance is reached,
| |
| − | where it should completely vanish and not incline either
| |
| − | toward or away from the proposition. When the chance
| |
| − | becomes less, then a contrary belief should spring up and
| |
| − | should increase in intensity as the chance diminishes, and
| |
| − | as the chance almost vanishes (which it can never quite do)
| |
| − | the contrary belief should tend toward an infinite intensity.
| |
| − | Now, there is one quantity which, more simply than any
| |
| − | other, fulfills these conditions; it is the <i>logarithm</i> of the
| |
| − | chance. But there is another consideration which must,
| |
| − | if admitted, fix us to this choice for our thermometer. It
| |
| − | is that our belief ought to be proportional to the weight of
| |
| − | evidence, in this sense, that two arguments which are entirely
| |
| − | independent, neither weakening nor strengthening
| |
| − | each other, ought, when they concur, to produce a belief
| |
| − | equal to the sum of the intensities of belief which either
| |
| − | would produce separately. Now, we have seen that the
| |
| − | chances of independent concurrent arguments are to be
| |
| − | multiplied together to get the chance of their combination,
| |
| − | and, therefore, the quantities which best express the intensities
| |
| − | of belief should be such that they are to be <i>added</i>
| |
| − | when the <i>chances</i> are multiplied in order to produce the
| |
| − | quantity which corresponds to the combined chance. Now,
| |
| − | the logarithm is the only quantity which fulfills this condition.
| |
| − | There is a general law of sensibility, called Fechner’s
| |
| − | psychophysical law. It is that the intensity of any sensation
| |
| − | is proportional to the logarithm of the external force
| |
| − | which produces it. It is entirely in harmony with this law
| |
| − | that the feeling of belief should be as the logarithm of the
| |
| − | chance, this latter being the expression of the state of facts
| |
| − | which produces the belief.</p>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_89'>89</span>The rule for the combination of independent concurrent
| |
| − | arguments takes a very simple form when expressed in
| |
| − | terms of the intensity of belief, measured in the proposed
| |
| − | way. It is this: Take the sum of all the feelings of belief
| |
| − | which would be produced separately by all the arguments
| |
| − | <i>pro</i>, subtract from that the similar sum for arguments <i>con</i>,
| |
| − | and the remainder is the feeling of belief which we ought
| |
| − | to have on the whole. This is a proceeding which men
| |
| − | often resort to, under the name of <i>balancing reasons</i>.</p>
| |
| − |
| |
| − | <p class='c005'>These considerations constitute an argument in favor of
| |
| − | the conceptualistic view. The kernel of it is that the conjoint
| |
| − | probability of all the arguments in our possession,
| |
| − | with reference to any fact, must be intimately connected
| |
| − | with the just degree of our belief in that fact; and this point
| |
| − | is supplemented by various others showing the consistency
| |
| − | of the theory with itself and with the rest of our knowledge.</p>
| |
| − |
| |
| − | <p class='c005'>But probability, to have any value at all, must express a
| |
| − | fact. It is, therefore, a thing to be inferred upon evidence.
| |
| − | Let us, then, consider for a moment the formation of a belief
| |
| − | of probability. Suppose we have a large bag of beans
| |
| − | from which one has been secretly taken at random and
| |
| − | hidden under a thimble. We are now to form a probable
| |
| − | judgment of the color of that bean, by drawing others singly
| |
| − | from the bag and looking at them, each one to be thrown
| |
| − | back, and the whole well mixed up after each drawing.
| |
| − | Suppose the first drawing is white and the next black. We
| |
| − | conclude that there is not an immense preponderance of
| |
| − | either color, and that there is something like an even chance
| |
| − | that the bean under the thimble is black. But this judgment
| |
| − | may be altered by the next few drawings. When we
| |
| − | <span class='pageno' id='Page_90'>90</span>have drawn ten times, if 4, 5, or 6, are white, we have more
| |
| − | confidence that the chance is even. When we have drawn
| |
| − | a thousand times, if about half have been white, we have
| |
| − | great confidence in this result. We now feel pretty sure
| |
| − | that, if we were to make a large number of bets upon the
| |
| − | color of single beans drawn from the bag, we could approximately
| |
| − | insure ourselves in the long run by betting each time
| |
| − | upon the white, a confidence which would be entirely wanting
| |
| − | if, instead of sampling the bag by 1,000 drawings, we
| |
| − | had done so by only two. Now, as the whole utility of
| |
| − | probability is to insure us in the long run, and as that assurance
| |
| − | depends, not merely on the value of the chance, but
| |
| − | also on the accuracy of the evaluation, it follows that we
| |
| − | ought not to have the same feeling of belief in reference
| |
| − | to all events of which the chance is even. In short, to express
| |
| − | the proper state of our belief, not <i>one</i> number but <i>two</i>
| |
| − | are requisite, the first depending on the inferred probability,
| |
| − | the second on the amount of knowledge on which
| |
| − | that probability is based.<a id='r41' /><a href='#f41' class='c011'><sup>[41]</sup></a> It is true that when our knowledge
| |
| − | is very precise, when we have made many drawings
| |
| − | from the bag, or, as in most of the examples in the books,
| |
| − | when the total contents of the bag are absolutely known,
| |
| − | the number which expresses the uncertainty of the assumed
| |
| − | probability and its liability to be changed by further experience
| |
| − | may become insignificant, or utterly vanish. But,
| |
| − | when our knowledge is very slight, this number may be even
| |
| − | more important than the probability itself; and when we
| |
| − | have no knowledge at all this completely overwhelms the
| |
| − | <span class='pageno' id='Page_91'>91</span>other, so that there is no sense in saying that the chance
| |
| − | of the totally unknown event is even (for what expresses
| |
| − | absolutely no fact has absolutely no meaning), and what
| |
| − | ought to be said is that the chance is entirely indefinite.
| |
| − | We thus perceive that the conceptualistic view, though
| |
| − | answering well enough in some cases, is quite inadequate.</p>
| |
| − |
| |
| − | <p class='c005'>Suppose that the first bean which we drew from our
| |
| − | bag were black. That would constitute an argument, no
| |
| − | matter how slender, that the bean under the thimble was
| |
| − | also black. If the second bean were also to turn out black,
| |
| − | that would be a second independent argument reënforcing
| |
| − | the first. If the whole of the first twenty beans drawn
| |
| − | should prove black, our confidence that the hidden bean
| |
| − | was black would justly attain considerable strength. But
| |
| − | suppose the twenty-first bean were to be white and that
| |
| − | we were to go on drawing until we found that we had drawn
| |
| − | 1,010 black beans and 990 white ones. We should conclude
| |
| − | that our first twenty beans being black was simply an
| |
| − | extraordinary accident, and that in fact the proportion of
| |
| − | white beans to black was sensibly equal, and that it was an
| |
| − | even chance that the hidden bean was black. Yet according
| |
| − | to the rule of <i>balancing reasons</i>, since all the drawings
| |
| − | of black beans are so many independent arguments in favor
| |
| − | of the one under the thimble being black, and all the white
| |
| − | drawings so many against it, an excess of twenty black
| |
| − | beans ought to produce the same degree of belief that the
| |
| − | hidden bean was black, whatever the total number drawn.</p>
| |
| − |
| |
| − | <p class='c005'>In the conceptualistic view of probability, complete ignorance,
| |
| − | where the judgment ought not to swerve either toward
| |
| − | or away from the hypothesis, is represented by the probability
| |
| − | 1/2.<a id='r42' /><a href='#f42' class='c011'><sup>[42]</sup></a></p>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_92'>92</span>But let us suppose that we are totally ignorant what
| |
| − | colored hair the inhabitants of Saturn have. Let us, then,
| |
| − | take a color-chart in which all possible colors are shown
| |
| − | shading into one another by imperceptible degrees. In
| |
| − | such a chart the relative areas occupied by different classes
| |
| − | of colors are perfectly arbitrary. Let us inclose such an
| |
| − | area with a closed line, and ask what is the chance on conceptualistic
| |
| − | principles that the color of the hair of the
| |
| − | inhabitants of Saturn falls within that area? The answer
| |
| − | cannot be indeterminate because we must be in some state
| |
| − | of belief; and, indeed, conceptualistic writers do not admit
| |
| − | indeterminate probabilities. As there is no certainty in
| |
| − | the matter, the answer lies between <i>zero</i> and <i>unity</i>. As no
| |
| − | numerical value is afforded by the data, the number must
| |
| − | be determined by the nature of the scale of probability
| |
| − | itself, and not by calculation from the data. The answer
| |
| − | can, therefore, only be one-half, since the judgment should
| |
| − | neither favor nor oppose the hypothesis. What is true of
| |
| − | this area is true of any other one; and it will equally be
| |
| − | true of a third area which embraces the other two. But
| |
| − | the probability for each of the smaller areas being one-half,
| |
| − | that for the larger should be at least unity, which is absurd.</p>
| |
| − | <h4 class='c012'>III</h4>
| |
| − | <p class='c006'>All our reasonings are of two kinds: 1. <i>Explicative</i>, <i>analytic</i>,
| |
| − | or <i>deductive</i>; 2. <i>Amplifiative</i>, <i>synthetic</i>, or (loosely
| |
| − | speaking) <i>inductive</i>. In explicative reasoning, certain facts
| |
| − | are first laid down in the premises. These facts are, in
| |
| − | every case, an inexhaustible multitude, but they may often
| |
| − | <span class='pageno' id='Page_93'>93</span>be summed up in one simple proposition by means of some
| |
| − | regularity which runs through them all. Thus, take the
| |
| − | proposition that Socrates was a man; this implies (to go no
| |
| − | further) that during every fraction of a second of his whole
| |
| − | life (or, if you please, during the greater part of them) he
| |
| − | was a man. He did not at one instant appear as a tree
| |
| − | and at another as a dog; he did not flow into water, or appear
| |
| − | in two places at once; you could not put your finger
| |
| − | through him as if he were an optical image, etc. Now,
| |
| − | the facts being thus laid down, some order among some of
| |
| − | them, not particularly made use of for the purpose of stating
| |
| − | them, may perhaps be discovered; and this will enable
| |
| − | us to throw part or all of them into a new statement, the
| |
| − | possibility of which might have escaped attention. Such
| |
| − | a statement will be the conclusion of an analytic inference.
| |
| − | Of this sort are all mathematical demonstrations. But synthetic
| |
| − | reasoning is of another kind. In this case the facts
| |
| − | summed up in the conclusion are not among those stated
| |
| − | in the premises. They are different facts, as when one
| |
| − | sees that the tide rises <i>m</i> times and concludes that it will
| |
| − | rise the next time. These are the only inferences which
| |
| − | increase our real knowledge, however useful the others
| |
| − | may be.</p>
| |
| − |
| |
| − | <p class='c005'>In any problem in probabilities, we have given the relative
| |
| − | frequency of certain events, and we perceive that in
| |
| − | these facts the relative frequency of another event is given
| |
| − | in a hidden way. This being stated makes the solution.
| |
| − | This is, therefore, mere explicative reasoning, and is evidently
| |
| − | entirely inadequate to the representation of synthetic
| |
| − | reasoning, which goes out beyond the facts given in the
| |
| − | <span class='pageno' id='Page_94'>94</span>premises. There is, therefore, a manifest impossibility in
| |
| − | so tracing out any probability for a synthetic conclusion.</p>
| |
| − |
| |
| − | <p class='c005'>Most treatises on probability contain a very different
| |
| − | doctrine. They state, for example, that if one of the
| |
| − | ancient denizens of the shores of the Mediterranean, who
| |
| − | had never heard of tides, had gone to the bay of Biscay,
| |
| − | and had there seen the tide rise, say <i>m</i> times, he could know
| |
| − | that there was a probability equal to</p>
| |
| − |
| |
| − | <p class='c007'>(m + 1)/(m + 2)</p>
| |
| − |
| |
| − | <p class='c014'>that it would rise the next time. In a well-known work
| |
| − | by Quetelet, much stress is laid on this, and it is made the
| |
| − | foundation of a theory of inductive reasoning.</p>
| |
| − |
| |
| − | <p class='c005'>But this solution betrays its origin if we apply it to the
| |
| − | case in which the man has never seen the tide rise at all;
| |
| − | that is, if we put <i>m</i> = 0. In this case, the probability that
| |
| − | it will rise the next time comes out 1/2, or, in other words,
| |
| − | the solution involves the conceptualistic principle that there
| |
| − | is an even chance of a totally unknown event. The manner
| |
| − | in which it has been reached has been by considering a
| |
| − | number of urns all containing the same number of balls,
| |
| − | part white and part black. One urn contains all white
| |
| − | balls, another one black and the rest white, a third two
| |
| − | black and the rest white, and so on, one urn for each proportion,
| |
| − | until an urn is reached containing only black balls.
| |
| − | But the only possible reason for drawing any analogy between
| |
| − | such an arrangement and that of Nature is the principle
| |
| − | that alternatives of which we know nothing must be
| |
| − | considered as equally probable. But this principle is absurd.
| |
| − | There is an indefinite variety of ways of enumerating
| |
| − | <span class='pageno' id='Page_95'>95</span>the different possibilities, which, on the application of
| |
| − | this principle, would give different results. If there be any
| |
| − | way of enumerating the possibilities so as to make them
| |
| − | all equal, it is not that from which this solution is derived,
| |
| − | but is the following: Suppose we had an immense granary
| |
| − | filled with black and white balls well mixed up; and suppose
| |
| − | each urn were filled by taking a fixed number of balls
| |
| − | from this granary quite at random. The relative number
| |
| − | of white balls in the granary might be anything, say one in
| |
| − | three. Then in one-third of the urns the first ball would
| |
| − | be white, and in two-thirds black. In one-third of those
| |
| − | urns of which the first ball was white, and also in one-third
| |
| − | of those in which the first ball was black, the second ball
| |
| − | would be white. In this way, we should have a distribution
| |
| − | like that shown in the following table, where <i>w</i> stands
| |
| − | for a white ball and <i>b</i> for a black one. The reader can,
| |
| − | if he chooses, verify the table for himself.</p>
| |
| − |
| |
| − | <div class='lg-container-l c015'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'>wwww.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'>wwwb. wwbw. wbww. bwww.</div>
| |
| − | <div class='line'>wwwb. wwbw. wbww. bwww.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'>wwbb. wbwb. bwwb. wbbw. bwbw. bbww.</div>
| |
| − | <div class='line'>wwbb. wbwb. bwwb. wbbw. bwbw. bbww.</div>
| |
| − | <div class='line'>wwbb. wbwb. bwwb. wbbw. bwbw. bbww.</div>
| |
| − | <div class='line'>wwbb. wbwb. bwwb. wbbw. bwbw. bbww.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'>wbbb. bwbb. bbwb. bbbw.</div>
| |
| − | <div class='line'>wbbb. bwbb. bbwb. bbbw.</div>
| |
| − | <div class='line'>wbbb. bwbb. bbwb. bbbw.</div>
| |
| − | <div class='line'>wbbb. bwbb. bbwb. bbbw.</div>
| |
| − | <div class='line'><span class='pageno' id='Page_96'>96</span>wbbb. bwbb. bbwb. bbbw.</div>
| |
| − | <div class='line'>wbbb. bwbb. bbwb. bbbw.</div>
| |
| − | <div class='line'>wbbb. bwbb. bbwb. bbbw.</div>
| |
| − | <div class='line'>wbbb. bwbb. bbwb. bbbw.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'>bbbb.</div>
| |
| − | <div class='line'>bbbb.</div>
| |
| − | <div class='line'>bbbb.</div>
| |
| − | <div class='line'>bbbb.</div>
| |
| − | <div class='line'>bbbb.</div>
| |
| − | <div class='line'>bbbb.</div>
| |
| − | <div class='line'>bbbb.</div>
| |
| − | <div class='line'>bbbb.</div>
| |
| − | <div class='line'>bbbb.</div>
| |
| − | <div class='line'>bbbb.</div>
| |
| − | <div class='line'>bbbb.</div>
| |
| − | <div class='line'>bbbb.</div>
| |
| − | <div class='line'>bbbb.</div>
| |
| − | <div class='line'>bbbb.</div>
| |
| − | <div class='line'>bbbb.</div>
| |
| − | <div class='line'>bbbb.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c005'>In the second group, where there is one b, there
| |
| − | are two sets just alike; in the third there are 4, in
| |
| − | the fourth 8, and in the fifth 16, doubling every
| |
| − | time. This is because we have supposed twice as
| |
| − | many black balls in the granary as white ones; had
| |
| − | we supposed 10 times as many, instead of</p>
| |
| − |
| |
| − | <p class='c007'> 1, 2, 4, 8, 16</p>
| |
| − |
| |
| − | <p class='c014'>sets we should have had</p>
| |
| − |
| |
| − | <p class='c007'> 1, 10, 100, 1000, 10000</p>
| |
| − |
| |
| − | <p class='c014'>sets; on the other hand, had the numbers of black
| |
| − | and white balls in the granary been even, there
| |
| − | would have been but one set in each group. Now
| |
| − | suppose two balls were drawn from one of these urns and
| |
| − | were found to be both white, what would be the probability
| |
| − | of the next one being white? If the two drawn out were
| |
| − | the first two put into the urns, and the next to be drawn
| |
| − | out were the third put in, then the probability of this third
| |
| − | being white would be the same whatever the colors of the
| |
| − | first two, for it has been supposed that just the same proportion
| |
| − | of urns has the third ball white among those which
| |
| − | have the first two <i>white-white</i>, <i>white-black</i>, <i>black-white</i>,
| |
| − | <span class='pageno' id='Page_97'>97</span>and <i>black-black</i>. Thus, in this case, the chance of the third
| |
| − | ball being white would be the same whatever the first two
| |
| − | were. But, by inspecting the table, the reader can see that
| |
| − | in each group all orders of the balls occur with equal frequency,
| |
| − | so that it makes no difference whether they are
| |
| − | drawn out in the order they were put in or not. Hence the
| |
| − | colors of the balls already drawn have no influence on the
| |
| − | probability of any other being white or black.</p>
| |
| − |
| |
| − | <p class='c005'>Now, if there be any way of enumerating the possibilities
| |
| − | of Nature so as to make them equally probable, it is clearly
| |
| − | one which should make one arrangement or combination
| |
| − | of the elements of Nature as probable as another, that is,
| |
| − | a distribution like that we have supposed, and it, therefore,
| |
| − | appears that the assumption that any such thing can be
| |
| − | done, leads simply to the conclusion that reasoning from
| |
| − | past to future experience is absolutely worthless. In fact,
| |
| − | the moment that you assume that the chances in favor of
| |
| − | that of which we are totally ignorant are even, the problem
| |
| − | about the tides does not differ, in any arithmetical particular,
| |
| − | from the case in which a penny (known to be equally
| |
| − | likely to come up heads and tails) should turn up heads
| |
| − | <i>m</i> times successively. In short, it would be to assume that
| |
| − | Nature is a pure chaos, or chance combination of independent
| |
| − | elements, in which reasoning from one fact to another
| |
| − | would be impossible; and since, as we shall hereafter
| |
| − | see, there is no judgment of pure observation without reasoning,
| |
| − | it would be to suppose all human cognition illusory
| |
| − | and no real knowledge possible. It would be to suppose
| |
| − | that if we have found the order of Nature more or less
| |
| − | regular in the past, this has been by a pure run of luck which
| |
| − | <span class='pageno' id='Page_98'>98</span>we may expect is now at an end. Now, it may be we have
| |
| − | no scintilla of proof to the contrary, but reason is unnecessary
| |
| − | in reference to that belief which is of all the most
| |
| − | settled, which nobody doubts or can doubt, and which he
| |
| − | who should deny would stultify himself in so doing.</p>
| |
| − |
| |
| − | <p class='c005'>The relative probability of this or that arrangement of
| |
| − | Nature is something which we should have a right to talk
| |
| − | about if universes were as plenty as blackberries, if we
| |
| − | could put a quantity of them in a bag, shake them well up,
| |
| − | draw out a sample, and examine them to see what proportion
| |
| − | of them had one arrangement and what proportion
| |
| − | another. But, even in that case, a higher universe would
| |
| − | contain us, in regard to whose arrangements the conception
| |
| − | of probability could have no applicability.</p>
| |
| − | <h4 class='c012'>IV</h4>
| |
| − | <p class='c006'>We have examined the problem proposed by the conceptualists,
| |
| − | which, translated into clear language, is this:
| |
| − | Given a synthetic conclusion; required to know out of all
| |
| − | possible states of things how many will accord, to any assigned
| |
| − | extent, with this conclusion; and we have found
| |
| − | that it is only an absurd attempt to reduce synthetic to
| |
| − | analytic reason, and that no definite solution is possible.</p>
| |
| − |
| |
| − | <p class='c005'>But there is another problem in connection with this subject.
| |
| − | It is this: Given a certain state of things, required
| |
| − | to know what proportion of all synthetic inferences relating
| |
| − | to it will be true within a given degree of approximation.
| |
| − | Now, there is no difficulty about this problem (except for
| |
| − | its mathematical complication); it has been much studied,
| |
| − | <span class='pageno' id='Page_99'>99</span>and the answer is perfectly well known. And is not this,
| |
| − | after all, what we want to know much rather than the other?
| |
| − | Why should we want to know the probability that the fact
| |
| − | will accord with our conclusion? That implies that we
| |
| − | are interested in all possible worlds, and not merely the one
| |
| − | in which we find ourselves placed. Why is it not much
| |
| − | more to the purpose to know the probability that our conclusion
| |
| − | will accord with the fact? One of these questions
| |
| − | is the first above stated and the other the second, and I
| |
| − | ask the reader whether, if people, instead of using the word
| |
| − | probability without any clear apprehension of their own
| |
| − | meaning, had always spoken of relative frequency, they
| |
| − | could have failed to see that what they wanted was not to
| |
| − | follow along the synthetic procedure with an analytic one,
| |
| − | in order to find the probability of the conclusion; but, on
| |
| − | the contrary, to begin with the fact at which the synthetic
| |
| − | inference aims, and follow back to the facts it uses for
| |
| − | premises in order to see the probability of their being such
| |
| − | as will yield the truth.</p>
| |
| − |
| |
| − | <p class='c005'>As we cannot have an urn with an infinite number of
| |
| − | balls to represent the inexhaustibleness of Nature, let us
| |
| − | suppose one with a finite number, each ball being thrown
| |
| − | back into the urn after being drawn out, so that there is
| |
| − | no exhaustion of them. Suppose one ball out of three is
| |
| − | white and the rest black, and that four balls are drawn.
| |
| − | Then the table on pages <a href='#Page_95'>95</a>-96 represents the relative frequency
| |
| − | of the different ways in which these balls might
| |
| − | be drawn. It will be seen that if we should judge by these
| |
| − | four balls of the proportion in the urn, 32 times out of 81
| |
| − | we should find it 1/4, and 24 times out of 81 we should find it
| |
| − | <span class='pageno' id='Page_100'>100</span>1/2, the truth being 1/3. To extend this table to high numbers
| |
| − | would be great labor, but the mathematicians have found
| |
| − | some ingenious ways of reckoning what the numbers would
| |
| − | be. It is found that, if the true proportion of white balls
| |
| − | is <i>p</i>, and <i>s</i> balls are drawn, then the error of the proportion
| |
| − | obtained by the induction will be—</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'>half the time within 0.477 √((2p(1-p))/s)</div>
| |
| − | <div class='line'>9 times out of 10 within 1.163 √((2p(1-p))/s)</div>
| |
| − | <div class='line'>99 times out of 100 within 1.821 √((2p(1-p))/s)</div>
| |
| − | <div class='line'>999 times out of 1,000 within 2.328 √((2p(1-p))/s)</div>
| |
| − | <div class='line'>9,999 times out of 10,000 within 2.751 √((2p(1-p))/s)</div>
| |
| − | <div class='line'>9,999,999,999 times out of 10,000,000,000 within 4.77 √((2p(1-p))/s)</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>The use of this may be illustrated by an example. By
| |
| − | the census of 1870, it appears that the proportion of males
| |
| − | among native white children under one year old was 0.5082,
| |
| − | while among colored children of the same age the proportion
| |
| − | was only 0.4977. The difference between these is 0.0105,
| |
| − | or about one in a 100. Can this be attributed to chance,
| |
| − | or would the difference always exist among a great number
| |
| − | of white and colored children under like circumstances?
| |
| − | Here <i>p</i> may be taken at 1/2; hence 2<i>p</i>(1-<i>p</i>) is also 1/2. The
| |
| − | number of white children counted was near 1,000,000;
| |
| − | hence the fraction whose square-root is to be taken is about
| |
| − | 1/2000000. The root is about 1/1400, and this multiplied by
| |
| − | 0.477 gives about 0.0003 as the probable error in the ratio
| |
| − | <span class='pageno' id='Page_101'>101</span>of males among the whites as obtained from the induction.
| |
| − | The number of black children was about 150,000, which
| |
| − | gives 0.0008 for the probable error. We see that the actual
| |
| − | discrepancy is ten times the sum of these, and such a result
| |
| − | would happen, according to our table, only once out of
| |
| − | 10,000,000,000 censuses, in the long run.</p>
| |
| − |
| |
| − | <p class='c005'>It may be remarked that when the real value of the probability
| |
| − | sought inductively is either very large or very small,
| |
| − | the reasoning is more secure. Thus, suppose there were
| |
| − | in reality one white ball in 100 in a certain urn, and we
| |
| − | were to judge of the number by 100 drawings. The probability
| |
| − | of drawing no white ball would be 366/1000; that of
| |
| − | drawing one white ball would be 370/1000; that of drawing two
| |
| − | would be 185/1000; that of drawing three would be 61/1000;
| |
| − | that of drawing four would be 15/1000; that of drawing five
| |
| − | would be only 3/1000, etc. Thus we should be tolerably certain
| |
| − | of not being in error by more than one ball in 100.</p>
| |
| − |
| |
| − | <p class='c005'>It appears, then, that in one sense we can, and in another
| |
| − | we cannot, determine the probability of synthetic inference.
| |
| − | When I reason in this way:</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'>Ninety-nine Cretans in a hundred are liars;</div>
| |
| − | <div class='line'>But Epimenides is a Cretan;</div>
| |
| − | <div class='line'>Therefore, Epimenides is a liar:—</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>I know that reasoning similar to that would carry truth 99
| |
| − | times in 100. But when I reason in the opposite direction:</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'>Minos, Sarpedon, Rhadamanthus, Deucalion, and Epimenides,</div>
| |
| − | <div class='line'>are all the Cretans I can think of;</div>
| |
| − | <div class='line'>But these were all atrocious liars,</div>
| |
| − | <div class='line'>Therefore, pretty much all Cretans must have been liars;</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>I do not in the least know how often such reasoning would
| |
| − | <span class='pageno' id='Page_102'>102</span>carry me right. On the other hand, what I do know is
| |
| − | that some definite proportion of Cretans must have been
| |
| − | liars, and that this proportion can be probably approximated
| |
| − | to by an induction from five or six instances. Even in the
| |
| − | worst case for the probability of such an inference, that
| |
| − | in which about half the Cretans are liars, the ratio so obtained
| |
| − | would probably not be in error by more than 1/6. So
| |
| − | much I know; but, then, in the present case the inference
| |
| − | is that pretty much all Cretans are liars, and whether there
| |
| − | may not be a special improbability in that I do not know.</p>
| |
| − | <h4 class='c012'>V</h4>
| |
| − | <p class='c006'>Late in the last century, Immanuel Kant asked the question,
| |
| − | “How are synthetical judgments <i>a priori</i> possible?”
| |
| − | By synthetical judgments he meant such as assert positive
| |
| − | fact and are not mere affairs of arrangement; in short,
| |
| − | judgments of the kind which synthetical reasoning produces,
| |
| − | and which analytic reasoning cannot yield. By <i>a priori</i>
| |
| − | judgments he meant such as that all outward objects are in
| |
| − | space, every event has a cause, etc., propositions which
| |
| − | according to him can never be inferred from experience.
| |
| − | Not so much by his answer to this question as by the mere
| |
| − | asking of it, the current philosophy of that time was shattered
| |
| − | and destroyed, and a new epoch in its history was
| |
| − | begun. But before asking <i>that</i> question he ought to have
| |
| − | asked the more general one, “How are any synthetical
| |
| − | judgments at all possible?” How is it that a man can observe
| |
| − | one fact and straightway pronounce judgment concerning
| |
| − | another different fact not involved in the first?
| |
| − | <span class='pageno' id='Page_103'>103</span>Such reasoning, as we have seen, has, at least in the usual
| |
| − | sense of the phrase, no definite probability; how, then,
| |
| − | can it add to our knowledge? This is a strange paradox;
| |
| − | the Abbé Gratry says it is a miracle, and that every true
| |
| − | induction is an immediate inspiration from on high.<a id='r43' /><a href='#f43' class='c011'><sup>[43]</sup></a> I
| |
| − | respect this explanation far more than many a pedantic
| |
| − | attempt to solve the question by some juggle with probabilities,
| |
| − | with the forms of syllogism, or what not. I respect
| |
| − | it because it shows an appreciation of the depth of
| |
| − | the problem, because it assigns an adequate cause, and because
| |
| − | it is intimately connected—as the true account
| |
| − | should be—with a general philosophy of the universe.
| |
| − | At the same time, I do not accept this explanation, because
| |
| − | an explanation should tell <i>how</i> a thing is done, and to assert
| |
| − | a perpetual miracle seems to be an abandonment of all
| |
| − | hope of doing that, without sufficient justification.</p>
| |
| − |
| |
| − | <p class='c005'>It will be interesting to see how the answer which Kant
| |
| − | gave to his question about synthetical judgments <i>a priori</i>
| |
| − | will appear if extended to the question of synthetical judgments
| |
| − | in general. That answer is, that synthetical judgments
| |
| − | <i>a priori</i> are possible because whatever is universally
| |
| − | true is involved in the conditions of experience. Let us
| |
| − | apply this to a general synthetical reasoning. I take from
| |
| − | a bag a handful of beans; they are all purple, and I infer
| |
| − | that all the beans in the bag are purple. How can I do
| |
| − | that? Why, upon the principle that whatever is universally
| |
| − | true of my experience (which is here the appearance
| |
| − | <span class='pageno' id='Page_104'>104</span>of these different beans) is involved in the condition of
| |
| − | experience. The condition of this special experience is
| |
| − | that all these beans were taken from that bag. According
| |
| − | to Kant’s principle, then, whatever is found true of all the
| |
| − | beans drawn from the bag must find its explanation in
| |
| − | some peculiarity of the contents of the bag. This is a
| |
| − | satisfactory statement of the principle of induction.</p>
| |
| − |
| |
| − | <p class='c005'>When we draw a deductive or analytic conclusion, our
| |
| − | rule of inference is that facts of a certain general character
| |
| − | are either invariably or in a certain proportion of cases
| |
| − | accompanied by facts of another general character. Then
| |
| − | our premise being a fact of the former class, we infer with
| |
| − | certainty or with the appropriate degree of probability
| |
| − | the existence of a fact of the second class. But the rule
| |
| − | for synthetic inference is of a different kind. When we
| |
| − | sample a bag of beans we do not in the least assume that
| |
| − | the fact of some beans being purple involves the necessity
| |
| − | or even the probability of other beans being so. On the
| |
| − | contrary, the conceptualistic method of treating probabilities,
| |
| − | which really amounts simply to the deductive treatment
| |
| − | of them, when rightly carried out leads to the result
| |
| − | that a synthetic inference has just an even chance in its
| |
| − | favor, or in other words is absolutely worthless. The color
| |
| − | of one bean is entirely independent of that of another. But
| |
| − | synthetic inference is founded upon a classification of facts,
| |
| − | not according to their characters, but according to the manner
| |
| − | of obtaining them. Its rule is, that a number of facts
| |
| − | obtained in a given way will in general more or less resemble
| |
| − | other facts obtained in the same way; or, <i>experiences
| |
| − | whose conditions are the same will have the same
| |
| − | general characters</i>.</p>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_105'>105</span>In the former case, we know that premises precisely
| |
| − | similar in form to those of the given ones will yield true
| |
| − | conclusions, just once in a calculable number of times. In
| |
| − | the latter case, we only know that premises obtained under
| |
| − | circumstances similar to the given ones (though perhaps
| |
| − | themselves very different) will yield true conclusions, at
| |
| − | least once in a calculable number of times. We may express
| |
| − | this by saying that in the case of analytic inference
| |
| − | we know the probability of our conclusion (if the premises
| |
| − | are true), but in the case of synthetic inferences we only
| |
| − | know the degree of trustworthiness of our proceeding. As
| |
| − | all knowledge comes from synthetic inference, we must
| |
| − | equally infer that all human certainty consists merely in
| |
| − | our knowing that the processes by which our knowledge
| |
| − | has been derived are such as must generally have led to
| |
| − | true conclusions.</p>
| |
| − |
| |
| − | <p class='c005'>Though a synthetic inference cannot by any means be
| |
| − | reduced to deduction, yet that the rule of induction will
| |
| − | hold good in the long run may be deduced from the principle
| |
| − | that reality is only the object of the final opinion to which
| |
| − | sufficient investigation would lead. That belief gradually
| |
| − | tends to fix itself under the influence of inquiry is, indeed,
| |
| − | one of the facts with which logic sets out.</p>
| |
| − |
| |
| − | <div>
| |
| − | <span class='pageno' id='Page_106'>106</span>
| |
| − | <h3 id='chap1-5' class='c001'>FIFTH PAPER <br /> THE ORDER OF NATURE<a id='r44' /><a href='#f44' class='c011'><sup>[44]</sup></a></h3>
| |
| − | </div>
| |
| − | <h4 class='c012'>I</h4>
| |
| − | <p class='c006'>Any proposition whatever concerning the order of Nature
| |
| − | must touch more or less upon religion. In our day, belief,
| |
| − | even in these matters, depends more and more upon the
| |
| − | observation of facts. If a remarkable and universal orderliness
| |
| − | be found in the universe, there must be some cause
| |
| − | for this regularity, and science has to consider what hypotheses
| |
| − | might account for the phenomenon. One way of
| |
| − | accounting for it, certainly, would be to suppose that the
| |
| − | world is ordered by a superior power. But if there is
| |
| − | nothing in the universal subjection of phenomena to laws,
| |
| − | nor in the character of those laws themselves (as being
| |
| − | benevolent, beautiful, economical, etc.), which goes to prove
| |
| − | the existence of a governor of the universe, it is hardly to
| |
| − | be anticipated that any other sort of evidence will be found
| |
| − | to weigh very much with minds emancipated from the tyranny
| |
| − | of tradition.</p>
| |
| − |
| |
| − | <p class='c005'>Nevertheless, it cannot truly be said that even an absolutely
| |
| − | negative decision of that question could altogether
| |
| − | destroy religion, inasmuch as there are faiths in which,
| |
| − | however much they differ from our own, we recognize those
| |
| − | essential characters which make them worthy to be called
| |
| − | religions, and which, nevertheless, do not postulate an
| |
| − | <span class='pageno' id='Page_107'>107</span>actually existing Deity. That one, for instance, which has
| |
| − | had the most numerous and by no means the least intelligent
| |
| − | following of any on earth, teaches that the Divinity in his
| |
| − | highest perfection is wrapped away from the world in a
| |
| − | state of profound and eternal sleep, which really does not
| |
| − | differ from non-existence, whether it be called by that name
| |
| − | or not. No candid mind who has followed the writings of
| |
| − | M. Vacherot can well deny that his religion is as earnest
| |
| − | as can be. He worships the Perfect, the Supreme Ideal;
| |
| − | but he conceives that the very notion of the Ideal is repugnant
| |
| − | to its real existence.<a id='r45' /><a href='#f45' class='c011'><sup>[45]</sup></a> In fact, M. Vacherot finds
| |
| − | it agreeable to his reason to assert that non-existence
| |
| − | is an essential character of the perfect, just as St.
| |
| − | Anselm and Descartes found it agreeable to theirs to assert
| |
| − | the extreme opposite. I confess that there is one respect in
| |
| − | which either of these positions seems to me more congruous
| |
| − | with the religious attitude than that of a theology which
| |
| − | stands upon evidences; for as soon as the Deity presents
| |
| − | himself to either Anselm or Vacherot, and manifests his
| |
| − | glorious attributes, whether it be in a vision of the night
| |
| − | or day, either of them recognizes his adorable God, and
| |
| − | sinks upon his knees at once; whereas the theologian of
| |
| − | evidences will first demand that the divine apparition shall
| |
| − | identify himself, and only after having scrutinized his credentials
| |
| − | and weighed the probabilities of his being found
| |
| − | among the totality of existences, will he finally render his
| |
| − | circumspect homage, thinking that no characters can be
| |
| − | adorable but those which belong to a real thing.</p>
| |
| − |
| |
| − | <p class='c005'>If we could find out any general characteristic of the
| |
| − | <span class='pageno' id='Page_108'>108</span>universe, any mannerism in the ways of Nature, any law
| |
| − | everywhere applicable and universally valid, such a discovery
| |
| − | would be of such singular assistance to us in all our
| |
| − | future reasoning, that it would deserve a place almost at
| |
| − | the head of the principles of logic. On the other hand,
| |
| − | if it can be shown that there is nothing of the sort to find
| |
| − | out, but that every discoverable regularity is of limited
| |
| − | range, this again will be of logical importance. What sort
| |
| − | of a conception we ought to have of the universe, how to
| |
| − | think of the <i>ensemble</i> of things, is a fundamental problem
| |
| − | in the theory of reasoning.</p>
| |
| − | <h4 class='c012'>II</h4>
| |
| − | <p class='c006'>It is the legitimate endeavor of scientific men now, as it
| |
| − | was twenty-three hundred years ago, to account for the
| |
| − | formation of the solar system and of the cluster of stars
| |
| − | which forms the galaxy, by the fortuitous concourse of
| |
| − | atoms. The greatest expounder of this theory, when asked
| |
| − | how he could write an immense book on the system of the
| |
| − | world without one mention of its author, replied, very
| |
| − | logically, “Je n’avais pas besoin de cette hypothèse-là.”
| |
| − | But, in truth, there is nothing atheistical in the theory,
| |
| − | any more than there was in this answer. Matter is supposed
| |
| − | to be composed of molecules which obey the laws of
| |
| − | mechanics and exert certain attractions upon one another;
| |
| − | and it is to these regularities (which there is no attempt to
| |
| − | account for) that general arrangement of the solar system
| |
| − | would be due, and not to hazard.</p>
| |
| − |
| |
| − | <p class='c005'>If any one has ever maintained that the universe is a
| |
| − | pure throw of the dice, the theologians have abundantly
| |
| − | <span class='pageno' id='Page_109'>109</span>refuted him. “How often,” says Archbishop Tillotson,
| |
| − | “might a man, after he had jumbled a set of letters in a
| |
| − | bag, fling them out upon the ground before they would
| |
| − | fall into an exact poem, yea, or so much as make a good
| |
| − | discourse in prose! And may not a little book be as easily
| |
| − | made by chance as this great volume of the world?” The
| |
| − | chance world here shown to be so different from that in
| |
| − | which we live would be one in which there were no laws,
| |
| − | the characters of different things being entirely independent;
| |
| − | so that, should a sample of any kind of objects ever
| |
| − | show a prevalent character, it could only be by accident,
| |
| − | and no general proposition could ever be established.
| |
| − | Whatever further conclusions we may come to in regard
| |
| − | to the order of the universe, thus much may be regarded
| |
| − | as solidly established, that the world is not a mere chance-medley.</p>
| |
| − |
| |
| − | <p class='c005'>But whether the world makes an exact poem or not, is
| |
| − | another question. When we look up at the heavens at
| |
| − | night, we readily perceive that the stars are not simply
| |
| − | splashed on to the celestial vault; but there does not seem
| |
| − | to be any precise system in their arrangement either. It
| |
| − | will be worth our while, then, to inquire into the degree of
| |
| − | orderliness in the universe; and, to begin, let us ask whether
| |
| − | the world we live in is any more orderly than a purely
| |
| − | chance-world would be.</p>
| |
| − |
| |
| − | <p class='c005'>Any uniformity, or law of Nature, may be stated in the
| |
| − | form, “Every A is B”; as, every ray of light is a non-curved
| |
| − | line, every body is accelerated toward the earth’s
| |
| − | center, etc. This is the same as to say, “There does not
| |
| − | exist any A which is not B”; there is no curved ray; there
| |
| − | <span class='pageno' id='Page_110'>110</span>is no body not accelerated toward the earth; so that the
| |
| − | uniformity consists in the non-occurrence in Nature of a
| |
| − | certain combination of characters (in this case, the combination
| |
| − | of being A with being non-B).<a id='r46' /><a href='#f46' class='c011'><sup>[46]</sup></a> And, conversely,
| |
| − | every case of the non-occurrence of a combination of characters
| |
| − | would constitute a uniformity in Nature. Thus, suppose
| |
| − | the quality A is never found in combination with the
| |
| − | quality C: for example, suppose the quality of idiocy is
| |
| − | never found in combination with that of having a well-developed
| |
| − | brain. Then nothing of the sort A is of the sort
| |
| − | C, or everything of the sort A is of the sort non-C (or say,
| |
| − | every idiot has an ill-developed brain), which, being something
| |
| − | universally true of the A’s, is a uniformity in the
| |
| − | world. Thus we see that, in a world where there were no
| |
| − | uniformities, no logically possible combination of characters
| |
| − | would be excluded, but every combination would exist in
| |
| − | some object. But two objects not identical must differ in
| |
| − | some of their characters, though it be only in the character
| |
| − | of being in such-and-such a place. Hence, precisely the
| |
| − | same combination of characters could not be found in two
| |
| − | different objects; and, consequently, in a chance-world every
| |
| − | combination involving either the positive or negative of
| |
| − | every character would belong to just one thing. Thus, if
| |
| − | there were but five simple characters in such a world,<a id='r47' /><a href='#f47' class='c011'><sup>[47]</sup></a> we
| |
| − | might denote them by A, B, C, D, E, and their negatives
| |
| − | <span class='pageno' id='Page_111'>111</span>by a, b, c, d, e; and then, as there would be 2<sup>5</sup> or 32 different
| |
| − | combinations of these characters, completely determinate
| |
| − | in reference to each of them, that world would have just 32
| |
| − | objects in it, their characters being as in the following
| |
| − | table:</p>
| |
| − | <p class='c006'><span class='sc'>Table I.</span></p>
| |
| − |
| |
| − | <div class='lg-container-l c015'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'>ABCDE AbCDE aBCDE abCDE</div>
| |
| − | <div class='line'>ABCDe AbCDe aBCDe abCDe</div>
| |
| − | <div class='line'>ABCdE AbCdE aBCdE abCdE</div>
| |
| − | <div class='line'>ABCde AbCde aBCde abCde</div>
| |
| − | <div class='line'>ABcDE AbcDE aBcDE abcDE</div>
| |
| − | <div class='line'>ABcDe AbcDe aBcDe abcDe</div>
| |
| − | <div class='line'>ABcdE AbcdE aBcdE abcdE</div>
| |
| − | <div class='line'>ABcde Abcde aBcde abcde</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c005'>For example, if the five primary characters were <i>hard</i>,
| |
| − | <i>sweet</i>, <i>fragrant</i>, <i>green</i>, <i>bright</i>, there would be one object
| |
| − | which reunited all these qualities, one which was hard,
| |
| − | sweet, fragrant, and green, but not bright; one which was
| |
| − | hard, sweet, fragrant, and bright, but not green; one which
| |
| − | was hard, sweet, and fragrant, but neither green nor bright;
| |
| − | and so on through all the combinations.</p>
| |
| − |
| |
| − | <p class='c005'>This is what a thoroughly chance-world would be like,
| |
| − | and certainly nothing could be imagined more systematic.
| |
| − | When a quantity of letters are poured out of a bag, the
| |
| − | appearance of disorder is due to the circumstance that the
| |
| − | phenomena are only partly fortuitous. The laws of space
| |
| − | are supposed, in that case, to be rigidly preserved, and
| |
| − | there is also a certain amount of regularity in the formation
| |
| − | of the letters. The result is that some elements are
| |
| − | <span class='pageno' id='Page_112'>112</span>orderly and some are disorderly, which is precisely what
| |
| − | we observe in the actual world. Tillotson, in the passage
| |
| − | of which a part has been quoted, goes on to ask, “How long
| |
| − | might 20,000 blind men which should be sent out from
| |
| − | the several remote parts of England, wander up and down
| |
| − | before they would all meet upon Salisbury Plains, and fall
| |
| − | into rank and file in the exact order of an army? And yet
| |
| − | this is much more easy to be imagined than how the innumerable
| |
| − | blind parts of matter should rendezvous themselves
| |
| − | into a world.” This is very true, but in the actual
| |
| − | world the <i>blind men</i> are, as far as we can see, <i>not</i> drawn up
| |
| − | in any particular order at all. And, in short, while a certain
| |
| − | amount of order exists in the world, it would seem that
| |
| − | the world is not so orderly as it might be, and, for instance,
| |
| − | not so much so as a world of pure chance would be.</p>
| |
| − |
| |
| − | <p class='c005'>But we can never get to the bottom of this question until
| |
| − | we take account of a highly-important logical principle<a id='r48' /><a href='#f48' class='c011'><sup>[48]</sup></a>
| |
| − | which I now proceed to enounce. This principle is that
| |
| − | any plurality or lot of objects whatever have some character
| |
| − | in common (no matter how insignificant) which is peculiar
| |
| − | to them and not shared by anything else. The word
| |
| − | “character” here is taken in such a sense as to include
| |
| − | negative characters, such as incivility, inequality, etc., as
| |
| − | well as their positives, civility, equality, etc. To prove the
| |
| − | theorem, I will show what character any two things, A and
| |
| − | B, have in common, not shared by anything else. The
| |
| − | things, A and B, are each distinguished from all other
| |
| − | things by the possession of certain characters which may be
| |
| − | named A-ness and B-ness. Corresponding to these positive
| |
| − | <span class='pageno' id='Page_113'>113</span>characters, are the negative characters un-A-ness, which
| |
| − | is possessed by everything except A, and un-B-ness, which
| |
| − | is possessed by everything except B. These two characters
| |
| − | are united in everything except A and B; and this union
| |
| − | of the characters un-A-ness and un-B-ness makes a compound
| |
| − | character which may be termed A-B-lessness. This
| |
| − | is not possessed by either A or B, but it is possessed by
| |
| − | everything else. This character, like every other, has its
| |
| − | corresponding negative un-A-B-lessness, and this last is the
| |
| − | character possessed by both A and B, and by nothing else.
| |
| − | It is obvious that what has thus been shown true of two
| |
| − | things is <i>mutatis mutandis</i>, true of any number of things.
| |
| − | Q. E. D.</p>
| |
| − |
| |
| − | <p class='c005'>In any world whatever, then, there must be a character
| |
| − | peculiar to each possible group of objects. If, as a matter
| |
| − | of nomenclature, characters peculiar to the same group be
| |
| − | regarded as only different aspects of the same character,
| |
| − | then we may say that there will be precisely one character
| |
| − | for each possible group of objects. Thus, suppose a world
| |
| − | to contain five things, α, β, γ, δ, ε. Then it will have a
| |
| − | separate character for each of the 31 groups (with <i>non-existence</i>
| |
| − | making up 32 or 2<sup>5</sup>) shown in the following table:</p>
| |
| − | <p class='c006'><span class='sc'>Table II.</span></p>
| |
| − |
| |
| − | <div class='lg-container-l c015'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line in5'>αβ αβγ αβγδ αβγδε</div>
| |
| − | <div class='line'>α αγ αβδ αβγε</div>
| |
| − | <div class='line'>β αδ αβε αβδε</div>
| |
| − | <div class='line'>γ αε αγδ αγδε</div>
| |
| − | <div class='line'>δ βγ αγε βγδε</div>
| |
| − | <div class='line'>ε βδ αδε</div>
| |
| − | <div class='line in5'>βε βγδ</div>
| |
| − | <div class='line in5'>γδ βγε</div>
| |
| − | <div class='line in5'>γε βδε</div>
| |
| − | <div class='line in5'>δε γδε</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_114'>114</span>This shows that a contradiction is involved in the very
| |
| − | idea<a id='r49' /><a href='#f49' class='c011'><sup>[49]</sup></a> of a chance-world, for in a world of 32 things, instead
| |
| − | of there being only 3<sup>5</sup> or 243 characters, as we have
| |
| − | seen that the notion of a chance-world requires, there would,
| |
| − | in fact, be no less than 2<sup>32</sup>, or 4,294,967,296 characters,
| |
| − | which would not be all independent, but would have all
| |
| − | possible relations with one another.</p>
| |
| − |
| |
| − | <p class='c005'>We further see that so long as we regard characters
| |
| − | abstractly, without regard to their relative importance, etc.,
| |
| − | there is no possibility of a more or less degree of orderliness
| |
| − | in the world, the whole system of relationship between
| |
| − | the different characters being given by mere logic; that is,
| |
| − | being implied in those facts which are tacitly admitted as
| |
| − | soon as we admit that there is any such thing as reasoning.</p>
| |
| − |
| |
| − | <p class='c005'>In order to descend from this abstract point of view, it
| |
| − | is requisite to consider the characters of things as relative
| |
| − | to the perceptions and active powers of living beings. Instead,
| |
| − | then, of attempting to imagine a world in which there
| |
| − | should be no uniformities, let us suppose one in which none
| |
| − | of the uniformities should have reference to characters
| |
| − | interesting or important to us. In the first place, there
| |
| − | would be nothing to puzzle us in such a world. The small
| |
| − | number of qualities which would directly meet the senses
| |
| − | would be the ones which would afford the key to everything
| |
| − | which could possibly interest us. The whole universe
| |
| − | would have such an air of system and perfect regularity
| |
| − | that there would be nothing to ask. In the next
| |
| − | place, no action of ours, and no event of Nature, would have
| |
| − | important consequences in such a world. We should be
| |
| − | <span class='pageno' id='Page_115'>115</span>perfectly free from all responsibility, and there would be
| |
| − | nothing to do but to enjoy or suffer whatever happened to
| |
| − | come along. Thus there would be nothing to stimulate or
| |
| − | develop either the mind or the will, and we consequently
| |
| − | should neither act nor think. We should have no memory,
| |
| − | because that depends on a law of our organization. Even
| |
| − | if we had any senses, we should be situated toward such a
| |
| − | world precisely as inanimate objects are toward the present
| |
| − | one, provided we suppose that these objects have an absolutely
| |
| − | transitory and instantaneous consciousness without
| |
| − | memory—a supposition which is a mere mode of speech,
| |
| − | for that would be no consciousness at all. We may, therefore,
| |
| − | say that a world of chance is simply our actual world
| |
| − | viewed from the standpoint of an animal at the very vanishing-point
| |
| − | of intelligence. The actual world is almost a
| |
| − | chance-medley to the mind of a polyp. The interest which
| |
| − | the uniformities of Nature have for an animal measures
| |
| − | his place in the scale of intelligence.</p>
| |
| − |
| |
| − | <p class='c005'>Thus, nothing can be made out from the orderliness of
| |
| − | Nature in regard to the existence of a God, unless it be
| |
| − | maintained that the existence of a finite mind proves the
| |
| − | existence of an infinite one.</p>
| |
| − | <h4 class='c012'>III</h4>
| |
| − | <p class='c006'>In the last of these papers we examined the nature of
| |
| − | inductive or synthetic reasoning. We found it to be a
| |
| − | process of sampling. A number of specimens of a class
| |
| − | are taken, not by selection within that class, but at random.
| |
| − | These specimens will agree in a great number of respects.
| |
| − | If, now, it were likely that a second lot would agree with
| |
| − | <span class='pageno' id='Page_116'>116</span>the first in the majority of these respects, we might base
| |
| − | on this consideration an inference in regard to any one of
| |
| − | these characters. But such an inference would neither be
| |
| − | of the nature of induction, nor would it (except in special
| |
| − | cases) be valid, because the vast majority of points of
| |
| − | agreement in the first sample drawn would generally be
| |
| − | entirely accidental, as well as insignificant. To illustrate
| |
| − | this, I take the ages at death of the first five poets given in
| |
| − | Wheeler’s <i>Biographical Dictionary</i>. They are:</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'>Aagard, 48.</div>
| |
| − | <div class='line'>Abeille, 70.</div>
| |
| − | <div class='line'>Abulola, 84.</div>
| |
| − | <div class='line'>Abunowas, 48.</div>
| |
| − | <div class='line'>Accords, 45.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>These five ages have the following characters in common:</p>
| |
| − |
| |
| − | <p class='c005'>1. The difference of the two digits composing the number,
| |
| − | divided by three, leaves a remainder of <i>one</i>.</p>
| |
| − |
| |
| − | <p class='c005'>2. The first digit raised to the power indicated by the
| |
| − | second, and divided by three, leaves a remainder of <i>one</i>.</p>
| |
| − |
| |
| − | <p class='c005'>3. The sum of the prime factors of each age, including
| |
| − | one, is divisible by three.</p>
| |
| − |
| |
| − | <p class='c005'>It is easy to see that the number of accidental agreements
| |
| − | of this sort would be quite endless. But suppose
| |
| − | that, instead of considering a character because of its prevalence
| |
| − | in the sample, we designate a character before
| |
| − | taking the sample, selecting it for its importance, obviousness,
| |
| − | or other point of interest. Then two considerable
| |
| − | samples drawn at random are extremely likely to agree
| |
| − | <span class='pageno' id='Page_117'>117</span>approximately in regard to the proportion of occurrences
| |
| − | of a character so chosen. <i>The inference that a previously
| |
| − | designated character has nearly the same frequency of
| |
| − | occurrence in the whole of a class that it has in a sample
| |
| − | drawn at random out of that class is induction.</i> If the character
| |
| − | be not previously designated, then a sample in which
| |
| − | it is found to be prevalent can only serve to suggest that
| |
| − | it <i>may be</i> prevalent in the whole class. We may consider
| |
| − | this surmise as an inference if we please—an inference
| |
| − | of possibility; but a second sample must be drawn to test
| |
| − | the question of whether the character actually is prevalent.
| |
| − | Instead of designating beforehand a single character in
| |
| − | reference to which we will examine a sample, we may designate
| |
| − | two, and use the same sample to determine the relative
| |
| − | frequencies of both. This will be making two inductive
| |
| − | inferences at once; and, of course, we are less certain that
| |
| − | both will yield correct conclusions than we should be that
| |
| − | either separately would do so. What is true of two characters
| |
| − | is true of any limited number. Now, the number
| |
| − | of characters which have any considerable interest for us
| |
| − | in reference to any class of objects is more moderate than
| |
| − | might be supposed. As we shall be sure to examine any
| |
| − | sample with reference to these characters, they may be
| |
| − | regarded not exactly as predesignated, but as predetermined
| |
| − | (which amounts to the same thing); and we may
| |
| − | infer that the sample represents the class in all these respects
| |
| − | if we please, remembering only that this is not so
| |
| − | secure an inference as if the particular quality to be looked
| |
| − | for had been fixed upon beforehand.</p>
| |
| − |
| |
| − | <p class='c005'>The demonstration of this theory of induction rests upon
| |
| − | <span class='pageno' id='Page_118'>118</span>principles and follows methods which are accepted by all
| |
| − | those who display in other matters the particular knowledge
| |
| − | and force of mind which qualify them to judge of this. The
| |
| − | theory itself, however, quite unaccountably seems never to
| |
| − | have occurred to any of the writers who have undertaken
| |
| − | to explain synthetic reasoning. The most widely-spread
| |
| − | opinion in the matter is one which was much promoted by
| |
| − | Mr. John Stuart Mill—namely, that induction depends
| |
| − | for its validity upon the uniformity of Nature—that is,
| |
| − | on the principle that what happens once will, under a sufficient
| |
| − | degree of similarity of circumstances, happen again
| |
| − | as often as the same circumstances recur. The application
| |
| − | is this: The fact that different things belong to the same
| |
| − | class constitutes the similarity of circumstances, and the
| |
| − | induction is good, provided this similarity is “sufficient.”
| |
| − | What happens once is, that a number of these things are
| |
| − | found to have a certain character; what may be expected,
| |
| − | then, to happen again as often as the circumstances recur
| |
| − | consists in this, that all things belonging to the same class
| |
| − | should have the same character.</p>
| |
| − |
| |
| − | <p class='c005'>This analysis of induction has, I venture to think, various
| |
| − | imperfections, to some of which it may be useful to
| |
| − | call attention. In the first place, when I put my hand in
| |
| − | a bag and draw out a handful of beans, and, finding three-quarters
| |
| − | of them black, infer that about three-quarters of
| |
| − | all in the bag are black, my inference is obviously of the
| |
| − | same kind as if I had found any larger proportion, or the
| |
| − | whole, of the sample black, and had assumed that it represented
| |
| − | in that respect the rest of the contents of the bag.
| |
| − | But the analysis in question hardly seems adapted to the
| |
| − | <span class='pageno' id='Page_119'>119</span>explanation of this <i>proportionate</i> induction, where the conclusion,
| |
| − | instead of being that a certain event uniformly
| |
| − | happens under certain circumstances, is precisely that it
| |
| − | does not uniformly occur, but only happens in a certain
| |
| − | proportion of cases. It is true that the whole sample may
| |
| − | be regarded as a single object, and the inference may be
| |
| − | brought under the formula proposed by considering the
| |
| − | conclusion to be that any similar sample will show a similar
| |
| − | proportion among its constituents. But this is to treat the
| |
| − | induction as if it rested on a single instance, which gives
| |
| − | a very false idea of its probability.</p>
| |
| − |
| |
| − | <p class='c005'>In the second place, if the uniformity of Nature were the
| |
| − | sole warrant of induction, we should have no right to draw
| |
| − | one in regard to a character whose constancy we knew
| |
| − | nothing about. Accordingly, Mr. Mill says that, though
| |
| − | none but white swans were known to Europeans for thousands
| |
| − | of years, yet the inference that all swans were white
| |
| − | was “not a good induction,” because it was not known
| |
| − | that color was a usual generic character (it, in fact, not
| |
| − | being so by any means). But it is mathematically demonstrable
| |
| − | that an inductive inference may have as high a degree
| |
| − | of probability as you please independent of any antecedent
| |
| − | knowledge of the constancy of the character inferred.
| |
| − | Before it was known that color is not usually a character
| |
| − | of <i>genera</i>, there was certainly a considerable probability
| |
| − | that all swans were white. But the further study of the
| |
| − | <i>genera</i> of animals led to the induction of their non-uniformity
| |
| − | in regard to color. A deductive application of
| |
| − | this general proposition would have gone far to overcome
| |
| − | the probability of the universal whiteness of swans before
| |
| − | <span class='pageno' id='Page_120'>120</span>the black species was discovered. When we do know anything
| |
| − | in regard to the general constancy or inconstancy of
| |
| − | a character, the application of that general knowledge to
| |
| − | the particular class to which any induction relates, though
| |
| − | it serves to increase or diminish the force of the induction,
| |
| − | is, like every application of general knowledge to particular
| |
| − | cases, deductive in its nature and not inductive.</p>
| |
| − |
| |
| − | <p class='c005'>In the third place, to say that inductions are true because
| |
| − | similar events happen in similar circumstances—or, what
| |
| − | is the same thing, because objects similar in some respects
| |
| − | are likely to be similar in others—is to overlook those
| |
| − | conditions which really are essential to the validity of inductions.
| |
| − | When we take all the characters into account,
| |
| − | any pair of objects resemble one another in just as many
| |
| − | particulars as any other pair. If we limit ourselves to such
| |
| − | characters as have for us any importance, interest, or
| |
| − | obviousness, then a synthetic conclusion may be drawn,
| |
| − | but only on condition that the specimens by which we
| |
| − | judge have been taken at random from the class in regard
| |
| − | to which we are to form a judgment, and not selected as
| |
| − | belonging to any sub-class. The induction only has its full
| |
| − | force when the character concerned has been designated
| |
| − | before examining the sample. These are the essentials of
| |
| − | induction, and they are not recognized in attributing the
| |
| − | validity of induction to the uniformity of Nature. The
| |
| − | explanation of induction by the doctrine of probabilities,
| |
| − | given in the last of these papers, is not a mere metaphysical
| |
| − | formula, but is one from which all the rules of synthetic
| |
| − | reasoning can be deduced systematically and with mathematical
| |
| − | cogency. But the account of the matter by a principle
| |
| − | <span class='pageno' id='Page_121'>121</span>of Nature, even if it were in other respects satisfactory,
| |
| − | presents the fatal disadvantage of leaving us quite as much
| |
| − | afloat as before in regard to the proper method of induction.
| |
| − | It does not surprise me, therefore, that those who
| |
| − | adopt this theory have given erroneous rules for the conduct
| |
| − | of reasoning, nor that the greater number of examples
| |
| − | put forward by Mr. Mill in his first edition, as models of
| |
| − | what inductions should be, proved in the light of further
| |
| − | scientific progress so particularly unfortunate that they had
| |
| − | to be replaced by others in later editions. One would have
| |
| − | supposed that Mr. Mill might have based an induction on
| |
| − | <i>this</i> circumstance, especially as it is his avowed principle
| |
| − | that, if the conclusion of an induction turns out false, it
| |
| − | cannot have been a good induction. Nevertheless, neither
| |
| − | he nor any of his scholars seem to have been led to suspect,
| |
| − | in the least, the perfect solidity of the framework which he
| |
| − | devised for securely supporting the mind in its passage
| |
| − | from the known to the unknown, although at its first trial
| |
| − | it did not answer quite so well as had been expected.</p>
| |
| − | <h4 class='c012'>IV</h4>
| |
| − | <p class='c006'>When we have drawn any statistical induction—such,
| |
| − | for instance, as that one-half of all births are of male children—it
| |
| − | is always possible to discover, by investigation
| |
| − | sufficiently prolonged, a class of which the same predicate
| |
| − | may be affirmed universally; to find out, for instance, <i>what
| |
| − | sort of</i> births are of male children. The truth of this principle
| |
| − | follows immediately from the theorem that there is a
| |
| − | character peculiar to every possible group of objects. The
| |
| − | <span class='pageno' id='Page_122'>122</span>form in which the principle is usually stated is, that <i>every
| |
| − | event must have a cause</i>.</p>
| |
| − |
| |
| − | <p class='c005'>But, though there exists a cause for every event, and
| |
| − | that of a kind which is capable of being discovered, yet if
| |
| − | there be nothing to guide us to the discovery; if we have
| |
| − | to hunt among all the events in the world without any
| |
| − | scent; if, for instance, the sex of a child might equally be
| |
| − | supposed to depend on the configuration of the planets, on
| |
| − | what was going on at the antipodes, or on anything else—then
| |
| − | the discovery would have no chance of ever getting
| |
| − | made.</p>
| |
| − |
| |
| − | <p class='c005'>That we ever do discover the precise causes of things,
| |
| − | that any induction whatever is absolutely without exception,
| |
| − | is what we have no right to assume. On the contrary,
| |
| − | it is an easy corollary, from the theorem just referred to,
| |
| − | that every empirical rule has an exception.<a id='r50' /><a href='#f50' class='c011'><sup>[50]</sup></a> But there are
| |
| − | certain of our inductions which present an approach to
| |
| − | universality so extraordinary that, even if we are to suppose
| |
| − | that they are not strictly universal truths, we cannot
| |
| − | possibly think that they have been reached merely by
| |
| − | accident. The most remarkable laws of this kind are those
| |
| − | of <i>time</i> and <i>space</i>. With reference to space, Bishop
| |
| − | Berkeley first showed, in a very conclusive manner, that
| |
| − | it was not a thing <i>seen</i>, but a thing <i>inferred</i>. Berkeley
| |
| − | chiefly insists on the impossibility of directly seeing the
| |
| − | third dimension of space, since the retina of the eye is a
| |
| − | surface. But, in point of fact, the retina is not even a
| |
| − | surface; it is a conglomeration of nerve-needles directed
| |
| − | <span class='pageno' id='Page_123'>123</span>toward the light and having only their extreme points sensitive,
| |
| − | these points lying at considerable distances from one
| |
| − | another compared with their areas. Now, of these points,
| |
| − | certainly the excitation of no one singly can produce the
| |
| − | perception of a surface, and consequently not the aggregate
| |
| − | of all the sensations can amount to this. But certain relations
| |
| − | subsist between the excitations of different nerve-points,
| |
| − | and these constitute the premises upon which the
| |
| − | hypothesis of space is founded, and from which it is inferred.
| |
| − | That space is not immediately perceived is now
| |
| − | universally admitted; and a mediate cognition is what is
| |
| − | called an inference, and is subject to the criticism of logic.
| |
| − | But what are we to say to the fact of every chicken as soon
| |
| − | as it is hatched solving a problem whose data are of a complexity
| |
| − | sufficient to try the greatest mathematical powers?
| |
| − | It would be insane to deny that the tendency to light upon
| |
| − | the conception of space is inborn in the mind of the chicken
| |
| − | and of every animal. The same thing is equally true of
| |
| − | time. That time is not directly perceived is evident, since
| |
| − | no lapse of time is present, and we only perceive what is
| |
| − | present. That, not having the idea of time, we should
| |
| − | never be able to perceive the flow in our sensations without
| |
| − | some particular aptitude for it, will probably also be admitted.
| |
| − | The idea of force—at least, in its rudiments—is
| |
| − | another conception so early arrived at, and found in
| |
| − | animals so low in the scale of intelligence, that it must be
| |
| − | supposed innate. But the innateness of an idea admits
| |
| − | of degree, for it consists in the tendency of that idea to
| |
| − | present itself to the mind. Some ideas, like that of space,
| |
| − | do so present themselves irresistibly at the very dawn of
| |
| − | <span class='pageno' id='Page_124'>124</span>intelligence, and take possession of the mind on small provocation,
| |
| − | while of other conceptions we are prepossessed,
| |
| − | indeed, but not so strongly, down a scale which is greatly
| |
| − | extended. The tendency to personify every thing, and to
| |
| − | attribute human characters to it, may be said to be innate;
| |
| − | but it is a tendency which is very soon overcome by civilized
| |
| − | man in regard to the greater part of the objects about him.
| |
| − | Take such a conception as that of gravitation varying inversely
| |
| − | as the square of the distance. It is a very simple
| |
| − | law. But to say that it is simple is merely to say that it
| |
| − | is one which the mind is particularly adapted to apprehend
| |
| − | with facility. Suppose the idea of a quantity multiplied
| |
| − | into another had been no more easy to the mind than that
| |
| − | of a quantity raised to the power indicated by itself—should
| |
| − | we ever have discovered the law of the solar system?</p>
| |
| − |
| |
| − | <p class='c005'>It seems incontestable, therefore, that the mind of man
| |
| − | is strongly adapted to the comprehension of the world; at
| |
| − | least, so far as this goes, that certain conceptions, highly
| |
| − | important for such a comprehension, naturally arise in his
| |
| − | mind; and, without such a tendency, the mind could never
| |
| − | have had any development at all.</p>
| |
| − |
| |
| − | <p class='c005'>How are we to explain this adaptation? The great
| |
| − | utility and indispensableness of the conceptions of time,
| |
| − | space, and force, even to the lowest intelligence, are such
| |
| − | as to suggest that they are the results of natural selection.
| |
| − | Without something like geometrical, kinetical, and mechanical
| |
| − | conceptions, no animal could seize his food or do anything
| |
| − | which might be necessary for the preservation of the
| |
| − | species. He might, it is true, be provided with an instinct
| |
| − | which would generally have the same effect; that is to say,
| |
| − | <span class='pageno' id='Page_125'>125</span>he might have conceptions different from those of time,
| |
| − | space, and force, but which coincided with them in regard
| |
| − | to the ordinary cases of the animal’s experience. But, as
| |
| − | that animal would have an immense advantage in the
| |
| − | struggle for life whose mechanical conceptions did not break
| |
| − | down in a novel situation (such as development must bring
| |
| − | about), there would be a constant selection in favor of
| |
| − | more and more correct ideas of these matters. Thus would
| |
| − | be attained the knowledge of that fundamental law upon
| |
| − | which all science rolls; namely, that forces depend upon
| |
| − | relations of time, space, and mass. When this idea was
| |
| − | once sufficiently clear, it would require no more than a
| |
| − | comprehensible degree of genius to discover the exact nature
| |
| − | of these relations. Such an hypothesis naturally suggests
| |
| − | itself, but it must be admitted that it does not seem
| |
| − | sufficient to account for the extraordinary accuracy with
| |
| − | which these conceptions apply to the phenomena of Nature,
| |
| − | and it is probable that there is some secret here which
| |
| − | remains to be discovered.</p>
| |
| − | <h4 class='c012'>V</h4>
| |
| − | <p class='c006'>Some important questions of logic depend upon whether
| |
| − | we are to consider the material universe as of limited extent
| |
| − | and finite age, or quite boundless in space and in time.
| |
| − | In the former case, it is conceivable that a general plan
| |
| − | or design embracing the whole universe should be discovered,
| |
| − | and it would be proper to be on the alert for some
| |
| − | traces of such a unity. In the latter case, since the proportion
| |
| − | of the world of which we can have any experience
| |
| − | is less than the smallest assignable fraction, it follows that
| |
| − | <span class='pageno' id='Page_126'>126</span>we never could discover any <i>pattern</i> in the universe except
| |
| − | a repeating one; any design embracing the whole would be
| |
| − | beyond our powers to discern, and beyond the united powers
| |
| − | of all intellects during all time. Now, what is absolutely
| |
| − | incapable of being known is, as we have seen in a former
| |
| − | paper, not real at all. An absolutely incognizable existence
| |
| − | is a nonsensical phrase. If, therefore, the universe is infinite,
| |
| − | the attempt to find in it any design embracing it as a whole
| |
| − | is futile, and involves a false way of looking at the subject.
| |
| − | If the universe never had any beginning, and if in space
| |
| − | world stretches beyond world without limit, there is no
| |
| − | <i>whole</i> of material things, and consequently no general character
| |
| − | to the universe, and no need or possibility of any
| |
| − | governor for it. But if there was a time before which
| |
| − | absolutely no matter existed, if there are certain absolute
| |
| − | bounds to the region of things outside of which there is a
| |
| − | mere void, then we naturally seek for an explanation of it,
| |
| − | and, since we cannot look for it among material things,
| |
| − | the hypothesis of a great disembodied animal, the creator
| |
| − | and governor of the world, is natural enough.</p>
| |
| − |
| |
| − | <p class='c005'>The actual state of the evidence as to the limitation of
| |
| − | the universe is as follows: As to time, we find on our earth
| |
| − | a constant progress of development since the planet was a
| |
| − | red-hot ball; the solar system seems to have resulted from
| |
| − | the condensation of a nebula, and the process appears to
| |
| − | be still going on. We sometimes see stars (presumably
| |
| − | with systems of worlds) destroyed and apparently resolved
| |
| − | back into the nebulous condition, but we have no evidence
| |
| − | of any existence of the world previous to the nebulous stage
| |
| − | from which it seems to have been evolved. All this rather
| |
| − | <span class='pageno' id='Page_127'>127</span>favors the idea of a beginning than otherwise. As for
| |
| − | limits in space, we cannot be sure that we see anything
| |
| − | outside of the system of the Milky Way. Minds of theological
| |
| − | predilections have therefore no need of distorting the
| |
| − | facts to reconcile them with their views.</p>
| |
| − |
| |
| − | <p class='c005'>But the only scientific presumption is, that the unknown
| |
| − | parts of space and time are like the known parts, occupied;
| |
| − | that, as we see cycles of life and death in all development
| |
| − | which we can trace out to the end, the same holds good in
| |
| − | regard to solar systems; that as enormous distances lie between
| |
| − | the different planets of our solar system, relatively
| |
| − | to their diameters, and as still more enormous distances lie
| |
| − | between our system relatively to its diameter and other
| |
| − | systems, so it may be supposed that other galactic clusters
| |
| − | exist so remote from ours as not to be recognized as such
| |
| − | with certainty. I do not say that these are strong inductions;
| |
| − | I only say that they are the presumptions which,
| |
| − | in our ignorance of the facts, should be preferred to hypotheses
| |
| − | which involve conceptions of things and occurrences
| |
| − | totally different in their character from any of which
| |
| − | we have had any experience, such as disembodied spirits,
| |
| − | the creation of matter, infringements of the laws of mechanics,
| |
| − | etc.</p>
| |
| − |
| |
| − | <p class='c005'>The universe ought to be presumed too vast to have any
| |
| − | character. When it is claimed that the arrangements of
| |
| − | Nature are benevolent, or just, or wise, or of any other
| |
| − | peculiar kind, we ought to be prejudiced against such
| |
| − | opinions, as being the offspring of an ill-founded notion
| |
| − | of the finitude of the world. And examination has hitherto
| |
| − | shown that such beneficences, justice, etc., are of a most
| |
| − | limited kind—limited in degree and limited in range.</p>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_128'>128</span>In like manner, if any one claims to have discovered a
| |
| − | plan in the structure of organized beings, or a scheme in
| |
| − | their classification, or a regular arrangement among natural
| |
| − | objects, or a system of proportionality in the human form,
| |
| − | or an order of development, or a correspondence between
| |
| − | conjunctions of the planets and human events, or a significance
| |
| − | in numbers, or a key to dreams, the first thing we
| |
| − | have to ask is whether such relations are susceptible of
| |
| − | explanation on mechanical principles, and if not they should
| |
| − | be looked upon with disfavor as having already a strong
| |
| − | presumption against them; and examination has generally
| |
| − | exploded all such theories.</p>
| |
| − |
| |
| − | <p class='c005'>There are minds to whom every prejudice, every presumption,
| |
| − | seems unfair. It is easy to say what minds these
| |
| − | are. They are those who never have known what it is to
| |
| − | draw a well-grounded induction, and who imagine that
| |
| − | other people’s knowledge is as nebulous as their own. That
| |
| − | all science rolls upon presumption (not of a formal but of
| |
| − | a real kind) is no argument with them, because they cannot
| |
| − | imagine that there is anything solid in human knowledge.
| |
| − | These are the people who waste their time and
| |
| − | money upon perpetual motions and other such rubbish.</p>
| |
| − |
| |
| − | <p class='c005'>But there are better minds who take up mystical theories
| |
| − | (by which I mean all those which have no possibility of
| |
| − | being mechanically explained). These are persons who are
| |
| − | strongly prejudiced in favor of such theories. We all have
| |
| − | natural tendencies to believe in such things; our education
| |
| − | often strengthens this tendency; and the result is, that to
| |
| − | many minds nothing seems so antecedently probable as
| |
| − | a theory of this kind. Such persons find evidence enough
| |
| − | <span class='pageno' id='Page_129'>129</span>in favor of their views, and in the absence of any recognized
| |
| − | logic of induction they cannot be driven from their belief.</p>
| |
| − |
| |
| − | <p class='c005'>But to the mind of a physicist there ought to be a strong
| |
| − | presumption against every mystical theory; and, therefore,
| |
| − | it seems to me that those scientific men who have sought
| |
| − | to make out that science was not hostile to theology have
| |
| − | not been so clear-sighted as their opponents.</p>
| |
| − |
| |
| − | <p class='c005'>It would be extravagant to say that science can at present
| |
| − | disprove religion; but it does seem to me that the spirit of
| |
| − | science is hostile to any religion except such a one as that
| |
| − | of M. Vacherot. Our appointed teachers inform us that
| |
| − | Buddhism is a miserable and atheistical faith, shorn of the
| |
| − | most glorious and needful attributes of a religion; that its
| |
| − | priests can be of no use to agriculture by praying for rain,
| |
| − | nor to war by commanding the sun to stand still. We also
| |
| − | hear the remonstrances of those who warn us that to shake
| |
| − | the general belief in the living God would be to shake the
| |
| − | general morals, public and private. This, too, must be admitted;
| |
| − | such a revolution of thought could no more be
| |
| − | accomplished without waste and desolation than a plantation
| |
| − | of trees could be transferred to new ground, however
| |
| − | wholesome in itself, without all of them languishing for a
| |
| − | time, and many of them dying. Nor is it, by-the-way, a
| |
| − | thing to be presumed that a man would have taken part
| |
| − | in a movement having a possible atheistical issue without
| |
| − | having taken serious and adequate counsel in regard to that
| |
| − | responsibility. But, let the consequences of such a belief
| |
| − | be as dire as they may, one thing is certain: that the state
| |
| − | of the facts, whatever it may be, will surely get found out,
| |
| − | and no human prudence can long arrest the triumphal car
| |
| − | <span class='pageno' id='Page_130'>130</span>of truth—no, not if the discovery were such as to drive
| |
| − | every individual of our race to suicide!</p>
| |
| − |
| |
| − | <p class='c005'>But it would be folly to suppose that any metaphysical
| |
| − | theory in regard to the mode of being of the perfect is to
| |
| − | destroy that aspiration toward the perfect which constitutes
| |
| − | the essence of religion. It is true that, if the priests of
| |
| − | any particular form of religion succeed in making it generally
| |
| − | believed that religion cannot exist without the acceptance
| |
| − | of certain formulas, or if they succeed in so interweaving
| |
| − | certain dogmas with the popular religion that the
| |
| − | people can see no essential analogy between a religion
| |
| − | which accepts these points of faith and one which rejects
| |
| − | them, the result may very well be to render those who cannot
| |
| − | believe these things irreligious. Nor can we ever hope
| |
| − | that any body of priests should consider themselves more
| |
| − | teachers of religion in general than of the particular system
| |
| − | of theology advocated by their own party. But no man
| |
| − | need be excluded from participation in the common feelings,
| |
| − | nor from so much of the public expression of them as is
| |
| − | open to all the laity, by the unphilosophical narrowness of
| |
| − | those who guard the mysteries of worship. Am I to be
| |
| − | prevented from joining in that common joy at the revelation
| |
| − | of enlightened principles of religion, which we celebrate
| |
| − | at Easter and Christmas, because I think that certain scientific,
| |
| − | logical, and metaphysical ideas which have been mixed
| |
| − | up with these principles are untenable? No; to do so
| |
| − | would be to estimate those errors as of more consequence
| |
| − | than the truth—an opinion which few would admit.
| |
| − | People who do not believe what are really the fundamental
| |
| − | principles of Christianity are rare to find, and all but these
| |
| − | few ought to feel at home in the churches.</p>
| |
| − |
| |
| − | <div>
| |
| − | <span class='pageno' id='Page_131'>131</span>
| |
| − | <h3 id='chap1-6' class='c001'>SIXTH PAPER <br /> DEDUCTION, INDUCTION, AND HYPOTHESIS<a id='r51' /><a href='#f51' class='c011'><sup>[51]</sup></a></h3>
| |
| − | </div>
| |
| − | <h4 class='c012'>I</h4>
| |
| − | <p class='c006'>The chief business of the logician is to classify arguments;
| |
| − | for all testing clearly depends on classification. The classes
| |
| − | of the logicians are defined by certain typical forms called
| |
| − | syllogisms. For example, the syllogism called <i>Barbara</i> is
| |
| − | as follows:</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'>S is M; M is P:</div>
| |
| − | <div class='line'>Hence, S is P.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>Or, to put words for letters—</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'>Enoch and Elijah were men; all men die:</div>
| |
| − | <div class='line'>Hence, Enoch and Elijah must have died.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>The “is P” of the logicians stands for any verb, active
| |
| − | or neuter. It is capable of strict proof (with which, however,
| |
| − | I will not trouble the reader) that all arguments
| |
| − | whatever can be put into this form; but only under the
| |
| − | condition that the <i>is</i> shall mean “<i>is</i> for the purposes of the
| |
| − | argument” or “is represented by.” Thus, an induction
| |
| − | will appear in this form something like this:</p>
| |
| − |
| |
| − | <p class='c005'>These beans are two-thirds white;</p>
| |
| − |
| |
| − | <p class='c005'>But, the beans in this bag are (represented by) these
| |
| − | beans;</p>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_132'>132</span>∴ The beans in the bag are two-thirds white.</p>
| |
| − |
| |
| − | <p class='c005'>But, because all inference may be reduced in some way
| |
| − | to <i>Barbara</i>, it does not follow that this is the most appropriate
| |
| − | form in which to represent every kind of inference.
| |
| − | On the contrary, to show the distinctive characters of different
| |
| − | sorts of inference, they must clearly be exhibited in
| |
| − | different forms peculiar to each. <i>Barbara</i> particularly
| |
| − | typifies deductive reasoning; and so long as the <i>is</i> is taken
| |
| − | literally, no inductive reasoning can be put into this form.
| |
| − | <i>Barbara</i> is, in fact, nothing but the application of a rule.
| |
| − | The so-called major premise lays down this rule; as, for
| |
| − | example, <i>All men are mortal.</i> The other or minor premise
| |
| − | states a case under the rule; as, <i>Enoch was a man.</i> The
| |
| − | conclusion applies the rule to the case and states the result:
| |
| − | <i>Enoch is mortal.</i> All deduction is of this character; it is
| |
| − | merely the application of general rules to particular cases.
| |
| − | Sometimes this is not very evident, as in the following:</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'>All quadrangles are figures,</div>
| |
| − | <div class='line'>But no triangle is a quadrangle;</div>
| |
| − | <div class='line'>Therefore, some figures are not triangles.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>But here the reasoning is really this:</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>Rule.</i>—Every quadrangle is other than a triangle.</div>
| |
| − | <div class='line'><i>Case.</i>—Some figures are quadrangles.</div>
| |
| − | <div class='line'><i>Result.</i>—Some figures are not triangles.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>Inductive or synthetic reasoning, being something more
| |
| − | than the mere application of a general rule to a particular
| |
| − | case, can never be reduced to this form.</p>
| |
| − |
| |
| − | <p class='c005'>If, from a bag of beans of which we know that 2/3 are
| |
| − | white, we take one at random, it is a deductive inference
| |
| − | <span class='pageno' id='Page_133'>133</span>that this bean is probably white, the probability being 2/3.
| |
| − | We have, in effect, the following syllogism:</p>
| |
| − |
| |
| − | <p class='c005'><i>Rule.</i>—The beans in this bag are 2/3 white.</p>
| |
| − |
| |
| − | <p class='c005'><i>Case.</i>—This bean has been drawn in such a way that
| |
| − | in the long run the relative number of white beans so drawn
| |
| − | would be equal to the relative number in the bag.</p>
| |
| − |
| |
| − | <p class='c005'><i>Result.</i>—This bean has been drawn in such a way that
| |
| − | in the long run it would turn out white 2/3 of the time.</p>
| |
| − |
| |
| − | <p class='c005'>If instead of drawing one bean we draw a handful at
| |
| − | random and conclude that about 2/3 of the handful are probably
| |
| − | white, the reasoning is of the same sort. If, however,
| |
| − | not knowing what proportion of white beans there are in
| |
| − | the bag, we draw a handful at random and, finding 2/3 of
| |
| − | the beans in the handful white, conclude that about 2/3 of
| |
| − | those in the bag are white, we are rowing up the current
| |
| − | of deductive sequence, and are concluding a rule from the
| |
| − | observation of a result in a certain case. This is particularly
| |
| − | clear when all the handful turn out one color. The
| |
| − | induction then is:</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line in4'>These beans were in this bag.———————-</div>
| |
| − | <div class='line in4'>These beans are white.—————————</div>
| |
| − | <div class='line in4'>All the beans in the bag were white. | |</div>
| |
| − | <div class='line in51'>| | |</div>
| |
| − | <div class='line'>Which is but an inversion of the deductive | | |</div>
| |
| − | <div class='line in2'>syllogism. | | |</div>
| |
| − | <div class='line in51'>| | |</div>
| |
| − | <div class='line in4'><i>Rule.</i>—All the beans in the bag were white.—+ | |</div>
| |
| − | <div class='line in4'><i>Case.</i>—These beans were in the bag.——————+-+</div>
| |
| − | <div class='line in4'><i>Result.</i>—These beans are white.————————+</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>So that induction is the inference of the <i>rule</i> from the <i>case</i>
| |
| − | and <i>result</i>.</p>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_134'>134</span>But this is not the only way of inverting a deductive
| |
| − | syllogism so as to produce a synthetic inference. Suppose
| |
| − | I enter a room and there find a number of bags, containing
| |
| − | different kinds of beans. On the table there is a handful
| |
| − | of white beans; and, after some searching, I find one of the
| |
| − | bags contains white beans only. I at once infer as a probability,
| |
| − | or as a fair guess, that this handful was taken out
| |
| − | of that bag. This sort of inference is called <i>making an
| |
| − | hypothesis</i>.<a id='r52' /><a href='#f52' class='c011'><sup>[52]</sup></a> It is the inference of a <i>case</i> from a <i>rule</i> and
| |
| − | <i>result</i>. We have, then—</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'><span class='sc'>Deduction.</span></div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>Rule.</i>—All the beans from this bag are white.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>Case.</i>—These beans are from this bag.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'>∴ <i>Result.</i>—These beans are white.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'><span class='sc'>Induction.</span></div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>Case.</i>—These beans are from this bag.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>Result.</i>—These beans are white.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'>∴ <i>Rule.</i>—All the beans from this bag are white.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'><span class='sc'>Hypothesis.</span></div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>Rule.</i>—All the beans from this bag are white.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>Result.</i>—These beans are white.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'>∴ <i>Case.</i>—These beans are from this bag.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>We, accordingly, classify all inference as follows:</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line in17'>Inference.</div>
| |
| − | <div class='line in11'>/———————<sup>—</sup>——————-|</div>
| |
| − | <div class='line'>Deductive or Analytic. Synthetic.</div>
| |
| − | <div class='line in27'>/————<sup>—</sup>————|</div>
| |
| − | <div class='line in22'>Induction. Hypothesis.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'><span class='pageno' id='Page_135'>135</span>Induction is where we generalize from a number of cases
| |
| − | of which something is true, and infer that the same thing
| |
| − | is true of a whole class. Or, where we find a certain thing
| |
| − | to be true of a certain proportion of cases and infer that it
| |
| − | is true of the same proportion of the whole class. Hypothesis
| |
| − | is where we find some very curious circumstance,
| |
| − | which would be explained by the supposition that it was
| |
| − | a case of a certain general rule, and thereupon adopt that
| |
| − | supposition. Or, where we find that in certain respects
| |
| − | two objects have a strong resemblance, and infer that they
| |
| − | resemble one another strongly in other respects.</p>
| |
| − |
| |
| − | <p class='c005'>I once landed at a seaport in a Turkish province; and,
| |
| − | as I was walking up to the house which I was to visit, I
| |
| − | met a man upon horseback, surrounded by four horsemen
| |
| − | holding a canopy over his head. As the governor of the
| |
| − | province was the only personage I could think of who would
| |
| − | be so greatly honored, I inferred that this was he. This
| |
| − | was an hypothesis.</p>
| |
| − |
| |
| − | <p class='c005'>Fossils are found; say, remains like those of fishes, but
| |
| − | far in the interior of the country. To explain the phenomenon,
| |
| − | we suppose the sea once washed over this land.
| |
| − | This is another hypothesis.</p>
| |
| − |
| |
| − | <p class='c005'>Numberless documents and monuments refer to a conqueror
| |
| − | called Napoleon Bonaparte. Though we have not
| |
| − | seen the man, yet we cannot explain what we have seen,
| |
| − | namely, all these documents and monuments, without supposing
| |
| − | that he really existed. Hypothesis again.</p>
| |
| − |
| |
| − | <p class='c005'>As a general rule, hypothesis is a weak kind of argument.
| |
| − | It often inclines our judgment so slightly toward its conclusion
| |
| − | that we cannot say that we believe the latter to
| |
| − | <span class='pageno' id='Page_136'>136</span>be true; we only surmise that it may be so. But there is no
| |
| − | difference except one of degree between such an inference
| |
| − | and that by which we are led to believe that we remember
| |
| − | the occurrences of yesterday from our feeling as if we did so.</p>
| |
| − | <h4 class='c012'>II</h4>
| |
| − | <p class='c006'>Besides the way just pointed out of inverting a deductive
| |
| − | syllogism to produce an induction or hypothesis, there is
| |
| − | another. If from the truth of a certain premise the truth
| |
| − | of a certain conclusion would necessarily follow, then from
| |
| − | the falsity of the conclusion the falsity of the premise would
| |
| − | follow. Thus, take the following syllogism in <i>Barbara</i>:</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>Rule.</i>—All men are mortal.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>Case.</i>—Enoch and Elijah were men.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'>∴ <i>Result.</i>—Enoch and Elijah were mortal.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>Now, a person who denies this result may admit the rule,
| |
| − | and, in that case, he must deny the case. Thus:</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>Denial of Result.</i>—Enoch and Elijah were not mortal.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>Rule.</i>—All men are mortal.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'>∴ <i>Denial of Case.</i>—Enoch and Elijah were not men.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>This kind of syllogism is called <i>Baroco</i>, which is the typical
| |
| − | mood of the second figure. On the other hand, the
| |
| − | person who denies the result may admit the case, and in
| |
| − | that case he must deny the rule. Thus:</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>Denial of the Result.</i>—Enoch and Elijah were not mortal.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>Case.</i>—Enoch and Elijah were men.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'>∴ <i>Denial of the Rule.</i>—Some men are not mortal.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'><span class='pageno' id='Page_137'>137</span>This kind of syllogism is called <i>Bocardo</i>, which is the
| |
| − | typical mood of the third figure.</p>
| |
| − |
| |
| − | <p class='c005'><i>Baroco</i> and <i>Bocardo</i> are, of course, deductive syllogisms;
| |
| − | but of a very peculiar kind. They are called by logicians
| |
| − | indirect moods, because they need some transformation to
| |
| − | appear as the application of a rule to a particular case.
| |
| − | But if, instead of setting out as we have here done with a
| |
| − | necessary deduction in <i>Barbara</i>, we take a probable deduction
| |
| − | of similar form, the indirect moods which we shall
| |
| − | obtain will be—</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line in5'>Corresponding to <i>Baroco</i>, an hypothesis;</div>
| |
| − | <div class='line'>and, Corresponding to <i>Bocardo</i>, an induction.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>For example, let us begin with this probable deduction
| |
| − | in <i>Barbara</i>:</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>Rule.</i>—Most of the beans in this bag are white.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>Case.</i>—This handful of beans are from this bag.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'>∴ <i>Result.</i>—Probably, most of this handful of beans are white.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>Now, deny the result, but accept the rule:</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>Denial of Result.</i>—Few beans of this handful are white.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>Rule.</i>—Most beans in this bag are white.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'>∴ <i>Denial of Case.</i>—Probably, these beans were taken from another bag.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>This is an hypothetical inference. Next, deny the result,
| |
| − | but accept the case:</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>Denial of Result.</i>—Few beans of this handful are white.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>Case.</i>—These beans came from this bag.</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line'><span class='pageno' id='Page_138'>138</span>∴ <i>Denial of Rule.</i>—Probably, few beans in the bag are white.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>This is an induction.</p>
| |
| − |
| |
| − | <p class='c005'>The relation thus exhibited between synthetic and deductive
| |
| − | reasoning is not without its importance. When we
| |
| − | adopt a certain hypothesis, it is not alone because it will
| |
| − | explain the observed facts, but also because the contrary
| |
| − | hypothesis would probably lead to results contrary to those
| |
| − | observed. So, when we make an induction, it is drawn not
| |
| − | only because it explains the distribution of characters in
| |
| − | the sample, but also because a different rule would probably
| |
| − | have led to the sample being other than it is.</p>
| |
| − |
| |
| − | <p class='c005'>But the advantage of this way of considering the subject
| |
| − | might easily be overrated. An induction is really the inference
| |
| − | of a rule, and to consider it as the denial of a rule
| |
| − | is an artificial conception, only admissible because, when
| |
| − | statistical or proportional propositions are considered as
| |
| − | rules, the denial of a rule is itself a rule. So, an hypothesis
| |
| − | is really a subsumption of a case under a class and not the
| |
| − | denial of it, except for this, that to deny a subsumption
| |
| − | under one class is to admit a subsumption under another.</p>
| |
| − |
| |
| − | <p class='c005'><i>Bocardo</i> may be considered as an induction, so timid as
| |
| − | to lose its amplificative character entirely. Enoch and Elijah
| |
| − | are specimens of a certain kind of men. All that kind
| |
| − | of men are shown by these instances to be immortal. But
| |
| − | instead of boldly concluding that all very pious men, or all
| |
| − | men favorites of the Almighty, etc., are immortal, we refrain
| |
| − | from specifying the description of men, and rest in
| |
| − | the merely explicative inference that <i>some</i> men are immortal.
| |
| − | <span class='pageno' id='Page_139'>139</span>So <i>Baroco</i> might be considered as a very timid
| |
| − | hypothesis. Enoch and Elijah are not mortal. Now, we
| |
| − | might boldly suppose them to be gods or something of that
| |
| − | sort, but instead of that we limit ourselves to the inference
| |
| − | that they are of <i>some</i> nature different from that of man.</p>
| |
| − |
| |
| − | <p class='c005'>But, after all, there is an immense difference between the
| |
| − | relation of <i>Baroco</i> and <i>Bocardo</i> to <i>Barbara</i> and that of
| |
| − | Induction and Hypothesis to Deduction. <i>Baroco</i> and <i>Bocardo</i>
| |
| − | are based upon the fact that if the truth of a conclusion
| |
| − | necessarily follows from the truth of a premise, then
| |
| − | the falsity of the premise follows from the falsity of the
| |
| − | conclusion. This is always true. It is different when the
| |
| − | inference is only probable. It by no means follows that,
| |
| − | because the truth of a certain premise would render the
| |
| − | truth of a conclusion probable, therefore the falsity of the
| |
| − | conclusion renders the falsity of the premise probable. At
| |
| − | least, this is only true, as we have seen in a former paper,
| |
| − | when the word probable is used in one sense in the antecedent
| |
| − | and in another in the consequent.</p>
| |
| − | <h4 class='c012'>III</h4>
| |
| − | <p class='c006'>A certain anonymous writing is upon a torn piece of
| |
| − | paper. It is suspected that the author is a certain person.
| |
| − | His desk, to which only he has had access, is searched, and
| |
| − | in it is found a piece of paper, the torn edge of which exactly
| |
| − | fits, in all its irregularities, that of the paper in question.
| |
| − | It is a fair hypothetic inference that the suspected
| |
| − | man was actually the author. The ground of this inference
| |
| − | evidently is that two torn pieces of paper are extremely
| |
| − | <span class='pageno' id='Page_140'>140</span>unlikely to fit together by accident. Therefore, of a great
| |
| − | number of inferences of this sort, but a very small proportion
| |
| − | would be deceptive. The analogy of hypothesis with
| |
| − | induction is so strong that some logicians have confounded
| |
| − | them. Hypothesis has been called an induction of characters.
| |
| − | A number of characters belonging to a certain class
| |
| − | are found in a certain object; whence it is inferred that all
| |
| − | the characters of that class belong to the object in question.
| |
| − | This certainly involves the same principle as induction;
| |
| − | yet in a modified form. In the first place, characters are
| |
| − | not susceptible of simple enumeration like objects; in the
| |
| − | next place, characters run in categories. When we make
| |
| − | an hypothesis like that about the piece of paper, we only
| |
| − | examine a single line of characters, or perhaps two or three,
| |
| − | and we take no specimen at all of others. If the hypothesis
| |
| − | were nothing but an induction, all that we should be justified
| |
| − | in concluding, in the example above, would be that the
| |
| − | two pieces of paper which matched in such irregularities
| |
| − | as have been examined would be found to match in other,
| |
| − | say slighter, irregularities. The inference from the shape
| |
| − | of the paper to its ownership is precisely what distinguishes
| |
| − | hypothesis from induction, and makes it a bolder and more
| |
| − | perilous step.</p>
| |
| − |
| |
| − | <p class='c005'>The same warnings that have been given against imagining
| |
| − | that induction rests upon the uniformity of Nature
| |
| − | might be repeated in regard to hypothesis. Here, as there,
| |
| − | such a theory not only utterly fails to account for the
| |
| − | validity of the inference, but it also gives rise to methods
| |
| − | of conducting it which are absolutely vicious. There are,
| |
| − | no doubt, certain uniformities in Nature, the knowledge of
| |
| − | <span class='pageno' id='Page_141'>141</span>which will fortify an hypothesis very much. For example,
| |
| − | we suppose that iron, titanium, and other metals exist in
| |
| − | the sun, because we find in the solar spectrum many lines
| |
| − | coincident in position with those which these metals would
| |
| − | produce; and this hypothesis is greatly strengthened by
| |
| − | our knowledge of the remarkable distinctiveness of the particular
| |
| − | line of characters observed. But such a fortification
| |
| − | of hypothesis is of a deductive kind, and hypothesis may
| |
| − | still be probable when such reënforcement is wanting.</p>
| |
| − |
| |
| − | <p class='c005'>There is no greater nor more frequent mistake in practical
| |
| − | logic than to suppose that things which resemble one
| |
| − | another strongly in some respects are any the more likely
| |
| − | for that to be alike in others. That this is absolutely false,
| |
| − | admits of rigid demonstration; but, inasmuch as the
| |
| − | reasoning is somewhat severe and complicated (requiring,
| |
| − | like all such reasoning, the use of A, B, C, etc., to set it
| |
| − | forth), the reader would probably find it distasteful, and
| |
| − | I omit it. An example, however, may illustrate the proposition:
| |
| − | The comparative mythologists occupy themselves
| |
| − | with finding points of resemblance between solar phenomena
| |
| − | and the careers of the heroes of all sorts of traditional
| |
| − | stories; and upon the basis of such resemblances they infer
| |
| − | that these heroes are impersonations of the sun. If
| |
| − | there be anything more in their reasonings, it has never
| |
| − | been made clear to me. An ingenious logician, to show how
| |
| − | futile all that is, wrote a little book, in which he pretended
| |
| − | to prove, in the same manner, that Napoleon Bonaparte
| |
| − | is only an impersonation of the sun. It was really wonderful
| |
| − | to see how many points of resemblance he made out.
| |
| − | The truth is, that any two things resemble one another
| |
| − | <span class='pageno' id='Page_142'>142</span>just as strongly as any two others, if recondite resemblances
| |
| − | are admitted. But, in order that the process of making an
| |
| − | hypothesis should lead to a probable result, the following
| |
| − | rules must be followed:</p>
| |
| − |
| |
| − | <p class='c005'>1. The hypothesis should be distinctly put as a question,
| |
| − | before making the observations which are to test its truth.
| |
| − | In other words, we must try to see what the result of predictions
| |
| − | from the hypothesis will be.</p>
| |
| − |
| |
| − | <p class='c005'>2. The respect in regard to which the resemblances are
| |
| − | noted must be taken at random. We must not take a particular
| |
| − | kind of predictions for which the hypothesis is known
| |
| − | to be good.</p>
| |
| − |
| |
| − | <p class='c005'>3. The failures as well as the successes of the predictions
| |
| − | must be honestly noted. The whole proceeding must be
| |
| − | fair and unbiased.</p>
| |
| − |
| |
| − | <p class='c005'>Some persons fancy that bias and counter-bias are favorable
| |
| − | to the extraction of truth—that hot and partisan debate
| |
| − | is the way to investigate. This is the theory of our
| |
| − | atrocious legal procedure. But Logic puts its heel upon
| |
| − | this suggestion. It irrefragably demonstrates that knowledge
| |
| − | can only be furthered by the real desire for it, and
| |
| − | that the methods of obstinacy, of authority, and every mode
| |
| − | of trying to reach a foregone conclusion, are absolutely of
| |
| − | no value. These things are proved. The reader is at liberty
| |
| − | to think so or not as long as the proof is not set forth,
| |
| − | or as long as he refrains from examining it. Just so, he
| |
| − | can preserve, if he likes, his freedom of opinion in regard
| |
| − | to the propositions of geometry; only, in that case, if he
| |
| − | takes a fancy to read Euclid, he will do well to skip whatever
| |
| − | he finds with A, B, C, etc., for, if he reads attentively
| |
| − | <span class='pageno' id='Page_143'>143</span>that disagreeable matter, the freedom of his opinion about
| |
| − | geometry may unhappily be lost forever.</p>
| |
| − |
| |
| − | <p class='c005'>How many people there are who are incapable of putting
| |
| − | to their own consciences this question, “Do I want to know
| |
| − | how the fact stands, or not?”</p>
| |
| − |
| |
| − | <p class='c005'>The rules which have thus far been laid down for induction
| |
| − | and hypothesis are such as are absolutely essential.
| |
| − | There are many other maxims expressing particular contrivances
| |
| − | for making synthetic inferences strong, which are
| |
| − | extremely valuable and should not be neglected. Such
| |
| − | are, for example, Mr. Mill’s four methods. Nevertheless,
| |
| − | in the total neglect of these, inductions and hypotheses
| |
| − | may and sometimes do attain the greatest force.</p>
| |
| − | <h4 class='c012'>IV</h4>
| |
| − | <p class='c006'>Classifications in all cases perfectly satisfactory hardly
| |
| − | exist. Even in regard to the great distinction between explicative
| |
| − | and ampliative inferences, examples could be found
| |
| − | which seem to lie upon the border between the two classes,
| |
| − | and to partake in some respects of the characters of either.
| |
| − | The same thing is true of the distinction between induction
| |
| − | and hypothesis. In the main, it is broad and decided. By
| |
| − | induction, we conclude that facts, similar to observed facts,
| |
| − | are true in cases not examined. By hypothesis, we conclude
| |
| − | the existence of a fact quite different from anything
| |
| − | observed, from which, according to known laws, something
| |
| − | observed would necessarily result. The former, is reasoning
| |
| − | from particulars to the general law; the latter, from
| |
| − | effect to cause. The former classifies, the latter explains.
| |
| − | <span class='pageno' id='Page_144'>144</span>It is only in some special cases that there can be more than
| |
| − | a momentary doubt to which category a given inference
| |
| − | belongs. One exception is where we observe, not facts similar
| |
| − | under similar circumstances, but facts different under
| |
| − | different circumstances—the difference of the former having,
| |
| − | however, a definite relation to the difference of the
| |
| − | latter. Such inferences, which are really inductions, sometimes
| |
| − | present nevertheless some indubitable resemblances
| |
| − | to hypotheses.</p>
| |
| − |
| |
| − | <p class='c005'>Knowing that water expands by heat, we make a number
| |
| − | of observations of the volume of a constant mass of water
| |
| − | at different temperatures. The scrutiny of a few of these
| |
| − | suggests a form of algebraical formula which will approximately
| |
| − | express the relation of the volume to the temperature.
| |
| − | It may be, for instance, that <i>v</i> being the relative
| |
| − | volume, and <i>t</i> the temperature, a few observations examined
| |
| − | indicate a relation of the form—</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>v</i> = 1 + <i>at</i> + <i>bt</i><sup>2</sup> + <i>ct</i><sup>3</sup>.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>Upon examining observations at other temperatures taken
| |
| − | at random, this idea is confirmed; and we draw the inductive
| |
| − | conclusion that all observations within the limits of
| |
| − | temperature from which we have drawn our observations
| |
| − | could equally be so satisfied. Having once ascertained that
| |
| − | such a formula is possible, it is a mere affair of arithmetic
| |
| − | to find the values of <i>a</i>, <i>b</i>, and <i>c</i>, which will make the formula
| |
| − | satisfy the observations best. This is what physicists call
| |
| − | an empirical formula, because it rests upon mere induction,
| |
| − | and is not explained by any hypothesis.</p>
| |
| − |
| |
| − | <p class='c005'>Such formulæ, though very useful as means of describing
| |
| − | <span class='pageno' id='Page_145'>145</span>in general terms the results of observations, do not take
| |
| − | any high rank among scientific discoveries. The induction
| |
| − | which they embody, that expansion by heat (or whatever
| |
| − | other phenomenon is referred to) takes place in a perfectly
| |
| − | gradual manner without sudden leaps or inummerable fluctuations,
| |
| − | although really important, attracts no attention,
| |
| − | because it is what we naturally anticipate. But the defects
| |
| − | of such expressions are very serious. In the first place, as
| |
| − | long as the observations are subject to error, as all observations
| |
| − | are, the formula cannot be expected to satisfy the
| |
| − | observations exactly. But the discrepancies cannot be due
| |
| − | solely to the errors of the observations, but must be partly
| |
| − | owing to the error of the formula which has been deducted
| |
| − | from erroneous observations. Moreover, we have no right
| |
| − | to suppose that the real facts, if they could be had free
| |
| − | from error, could be expressed by such a formula at all.
| |
| − | They might, perhaps, be expressed by a similar formula
| |
| − | with an infinite number of terms; but of what use would
| |
| − | that be to us, since it would require an infinite number of
| |
| − | coefficients to be written down? When one quantity varies
| |
| − | with another, if the corresponding values are exactly known,
| |
| − | it is a mere matter of mathematical ingenuity to find some
| |
| − | way of expressing their relation in a simple manner. If
| |
| − | one quantity is of one kind—say, a specific gravity—and
| |
| − | the other of another kind—say, a temperature—we do
| |
| − | not desire to find an expression for their relation which is
| |
| − | wholly free from numerical constants, since if it were free
| |
| − | from them when, say, specific gravity as compared with
| |
| − | water, and temperature as expressed by the Centigrade thermometer,
| |
| − | were in question, numbers would have to be introduced
| |
| − | <span class='pageno' id='Page_146'>146</span>when the scales of measurement were changed.
| |
| − | We may, however, and do desire to find formulas expressing
| |
| − | the relations of physical phenomena which shall contain
| |
| − | no more arbitrary numbers than changes in the scales of
| |
| − | measurement might require.</p>
| |
| − |
| |
| − | <p class='c005'>When a formula of this kind is discovered, it is no longer
| |
| − | called an empirical formula, but a law of Nature; and is
| |
| − | sooner or later made the basis of an hypothesis which is
| |
| − | to explain it. These simple formulæ are not usually, if
| |
| − | ever, exactly true, but they are none the less important for
| |
| − | that; and the great triumph of the hypothesis comes when
| |
| − | it explains not only the formula, but also the deviations
| |
| − | from the formula. In the current language of the physicists,
| |
| − | an hypothesis of this importance is called a theory,
| |
| − | while the term hypothesis is restricted to suggestions which
| |
| − | have little evidence in their favor. There is some justice
| |
| − | in the contempt which clings to the word hypothesis. To
| |
| − | think that we can strike out of our own minds a true preconception
| |
| − | of how Nature acts, in a vain fancy. As Lord
| |
| − | Bacon well says: “The subtlety of Nature far exceeds the
| |
| − | subtlety of sense and intellect: so that these fine meditations,
| |
| − | and speculations, and reasonings of men are a sort
| |
| − | of insanity, only there is no one at hand to remark it.”
| |
| − | The successful theories are not pure guesses, but are guided
| |
| − | by reasons.</p>
| |
| − |
| |
| − | <p class='c005'>The kinetical theory of gases is a good example of this.
| |
| − | This theory is intended to explain certain simple formulæ,
| |
| − | the chief of which is called the law of Boyle. It is, that if
| |
| − | air or any other gas be placed in a cylinder with a piston,
| |
| − | and if its volume be measured under the pressure of the
| |
| − | <span class='pageno' id='Page_147'>147</span>atmosphere, say fifteen pounds on the square inch, and if
| |
| − | then another fifteen pounds per square inch be placed on
| |
| − | the piston, the gas will be compressed to one-half its bulk,
| |
| − | and in similar inverse ratio for other pressures. The
| |
| − | hypothesis which has been adopted to account for this law
| |
| − | is that the molecules of a gas are small, solid particles at
| |
| − | great distances from each other (relatively to their dimensions),
| |
| − | and moving with great velocity, without sensible
| |
| − | attractions or repulsions, until they happen to approach
| |
| − | one another very closely. Admit this, and it follows that
| |
| − | when a gas is under pressure what prevents it from collapsing
| |
| − | is not the incompressibility of the separate molecules,
| |
| − | which are under no pressure at all, since they do not
| |
| − | touch, but the pounding of the molecules against the piston.
| |
| − | The more the piston falls, and the more the gas is compressed,
| |
| − | the nearer together the molecules will be; the
| |
| − | greater number there will be at any moment within a given
| |
| − | distance of the piston, the shorter the distance which any
| |
| − | one will go before its course is changed by the influence of
| |
| − | another, the greater number of new courses of each in a
| |
| − | given time, and the oftener each, within a given distance
| |
| − | of the piston, will strike it. This explains Boyle’s law. The
| |
| − | law is not exact; but the hypothesis does not lead us to it
| |
| − | exactly. For, in the first place, if the molecules are large,
| |
| − | they will strike each other oftener when their mean distances
| |
| − | are diminished, and will consequently strike the
| |
| − | piston oftener, and will produce more pressure upon it. On
| |
| − | the other hand, if the molecules have an attraction for one
| |
| − | another, they will remain for a sensible time within one
| |
| − | another’s influence, and consequently they will not strike
| |
| − | <span class='pageno' id='Page_148'>148</span>the wall so often as they otherwise would, and the pressure
| |
| − | will be less increased by compression.</p>
| |
| − |
| |
| − | <p class='c005'>When the kinetical theory of gases was first proposed by
| |
| − | Daniel Bernoulli, in 1738, it rested only on the law of
| |
| − | Boyle, and was therefore pure hypothesis. It was accordingly
| |
| − | quite naturally and deservedly neglected. But,
| |
| − | at present, the theory presents quite another aspect; for,
| |
| − | not to speak of the considerable number of observed facts
| |
| − | of different kinds with which it has been brought into relation,
| |
| − | it is supported by the mechanical theory of heat.
| |
| − | That bringing together bodies which attract one another, or
| |
| − | separating bodies which repel one another, when sensible
| |
| − | motion is not produced nor destroyed, is always accompanied
| |
| − | by the evolution of heat, is little more than an induction.
| |
| − | Now, it has been shown by experiment that, when a gas is
| |
| − | allowed to expand without doing work, a very small amount
| |
| − | of heat disappears. This proves that the particles of the
| |
| − | gas attract one another slightly, and but very slightly. It
| |
| − | follows that, when a gas is under pressure, what prevents
| |
| − | it from collapsing is not any repulsion between the particles,
| |
| − | since there is none. Now, there are only two modes
| |
| − | of force known to us, force of position or attractions and
| |
| − | repulsions, and force of motion. Since, therefore, it is not
| |
| − | the force of position which gives a gas its expansive force,
| |
| − | it must be the force of motion. In this point of view, the
| |
| − | kinetical theory of gases appears as a deduction from the
| |
| − | mechanical theory of heat. It is to be observed, however,
| |
| − | that it supposes the same law of mechanics (that there are
| |
| − | only those two modes of force) which holds in regard to
| |
| − | bodies such as we can see and examine, to hold also for
| |
| − | <span class='pageno' id='Page_149'>149</span>what are very different, the molecules of bodies. Such a
| |
| − | supposition has but a slender support from induction. Our
| |
| − | belief in it is greatly strengthened by its connection with the
| |
| − | law of Boyle, and it is, therefore, to be considered as an
| |
| − | hypothetical inference. Yet it must be admitted that the
| |
| − | kinetical theory of gases would deserve little credence if it
| |
| − | had not been connected with the principles of mechanics.</p>
| |
| − |
| |
| − | <p class='c005'>The great difference between induction and hypothesis is,
| |
| − | that the former infers the existence of phenomena such as
| |
| − | we have observed in cases which are similar, while hypothesis
| |
| − | supposes something of a different kind from what we
| |
| − | have directly observed, and frequently something which
| |
| − | it would be impossible for us to observe directly. Accordingly,
| |
| − | when we stretch an induction quite beyond the limits
| |
| − | of our observation, the inference partakes of the nature of
| |
| − | hypothesis. It would be absurd to say that we have no
| |
| − | inductive warrant for a generalization extending a little
| |
| − | beyond the limits of experience, and there is no line to be
| |
| − | drawn beyond which we cannot push our inference; only
| |
| − | it becomes weaker the further it is pushed. Yet, if an induction
| |
| − | be pushed very far, we cannot give it much credence
| |
| − | unless we find that such an extension explains some fact
| |
| − | which we can and do observe. Here, then, we have a kind
| |
| − | of mixture of induction and hypothesis supporting one another;
| |
| − | and of this kind are most of the theories of physics.</p>
| |
| − | <div>
| |
| − | <span class='pageno' id='Page_150'>150</span>
| |
| − | <h4 class='c012'>V</h4>
| |
| − | </div>
| |
| − | <p class='c006'>That synthetic inferences may be divided into induction
| |
| − | and hypothesis in the manner here proposed,<a id='r53' /><a href='#f53' class='c011'><sup>[53]</sup></a> admits of no
| |
| − | question. The utility and value of the distinction are to
| |
| − | be tested by their applications.</p>
| |
| − |
| |
| − | <p class='c005'>Induction is, plainly, a much stronger kind of inference
| |
| − | than hypothesis; and this is the first reason for distinguishing
| |
| − | between them. Hypotheses are sometimes regarded as
| |
| − | provisional resorts, which in the progress of science are to
| |
| − | be replaced by inductions. But this is a false view of the
| |
| − | subject. Hypothetic reasoning infers very frequently a fact
| |
| − | not capable of direct observation. It is an hypothesis that
| |
| − | Napoleon Bonaparte once existed. How is that hypothesis
| |
| − | ever to be replaced by an induction? It may be said that
| |
| − | from the premise that such facts as we have observed are
| |
| − | as they would be if Napoleon existed, we are to infer by
| |
| − | induction that <i>all</i> facts that are hereafter to be observed
| |
| − | will be of the same character. There is no doubt that every
| |
| − | hypothetic inference may be distorted into the appearance
| |
| − | of an induction in this way. But the essence of an induction
| |
| − | is that it infers from one set of facts another set of
| |
| − | similar facts, whereas hypothesis infers from facts of one
| |
| − | kind to facts of another. Now, the facts which serve as
| |
| − | grounds for our belief in the historic reality of Napoleon
| |
| − | are not by any means necessarily the only kind of facts
| |
| − | which are explained by his existence. It may be that, at
| |
| − | <span class='pageno' id='Page_151'>151</span>the time of his career, events were being recorded in some
| |
| − | way not now dreamed of, that some ingenious creature on
| |
| − | a neighboring planet was photographing the earth, and that
| |
| − | these pictures on a sufficiently large scale may some time
| |
| − | come into our possession, or that some mirror upon a distant
| |
| − | star will, when the light reaches it, reflect the whole
| |
| − | story back to earth. Never mind how improbable these
| |
| − | suppositions are; everything which happens is infinitely
| |
| − | improbable. I am not saying that <i>these</i> things are likely
| |
| − | to occur, but that <i>some</i> effect of Napoleon’s existence which
| |
| − | now seems impossible is certain nevertheless to be brought
| |
| − | about. The hypothesis asserts that such facts, when they
| |
| − | do occur, will be of a nature to confirm, and not to refute,
| |
| − | the existence of the man. We have, in the impossibility of
| |
| − | inductively inferring hypothetical conclusions, a second
| |
| − | reason for distinguishing between the two kinds of inference.</p>
| |
| − |
| |
| − | <p class='c005'>A third merit of the distinction is, that it is associated
| |
| − | with an important psychological or rather physiological
| |
| − | difference in the mode of apprehending facts. Induction
| |
| − | infers a rule. Now, the belief of a rule is a habit. That
| |
| − | a habit is a rule active in us, is evident. That every belief
| |
| − | is of the nature of a habit, in so far as it is of a general
| |
| − | character, has been shown in the earlier papers of this
| |
| − | series. Induction, therefore, is the logical formula which
| |
| − | expresses the physiological process of formation of a habit.
| |
| − | Hypothesis substitutes, for a complicated tangle of predicates
| |
| − | attached to one subject, a single conception. Now,
| |
| − | there is a peculiar sensation belonging to the act of thinking
| |
| − | that each of these predicates inheres in the subject. In
| |
| − | hypothetic inference this complicated feeling so produced
| |
| − | <span class='pageno' id='Page_152'>152</span>is replaced by a single feeling of greater intensity, that
| |
| − | belonging to the act of thinking the hypothetic conclusion.
| |
| − | Now, when our nervous system is excited in a complicated
| |
| − | way, there being a relation between the elements of the
| |
| − | excitation, the result is a single harmonious disturbance
| |
| − | which I call an emotion. Thus, the various sounds made
| |
| − | by the instruments of an orchestra strike upon the ear,
| |
| − | and the result is a peculiar musical emotion, quite distinct
| |
| − | from the sounds themselves. This emotion is essentially
| |
| − | the same thing as an hypothetic inference, and every hypothetic
| |
| − | inference involves the formation of such an emotion.
| |
| − | We may say, therefore, that hypothesis produces the <i>sensuous</i>
| |
| − | element of thought, and induction the <i>habitual</i> element.
| |
| − | As for deduction, which adds nothing to the premises, but
| |
| − | only out of the various facts represented in the premises
| |
| − | selects one and brings the attention down to it, this may
| |
| − | be considered as the logical formula for paying attention,
| |
| − | which is the <i>volitional</i> element of thought, and corresponds
| |
| − | to nervous discharge in the sphere of physiology.</p>
| |
| − |
| |
| − | <p class='c005'>Another merit of the distinction between induction and
| |
| − | hypothesis is, that it leads to a very natural classification
| |
| − | of the sciences and of the minds which prosecute them.
| |
| − | What must separate different kinds of scientific men more
| |
| − | than anything else are the differences of their <i>techniques</i>.
| |
| − | We cannot expect men who work with books chiefly to
| |
| − | have much in common with men whose lives are passed in
| |
| − | laboratories. But, after differences of this kind, the next
| |
| − | most important are differences in the modes of reasoning.
| |
| − | Of the natural sciences, we have, first, the classificatory
| |
| − | sciences, which are purely inductive—systematic botany
| |
| − | <span class='pageno' id='Page_153'>153</span>and zoölogy, mineralogy, and chemistry. Then, we have
| |
| − | the sciences of theory, as above explained—astronomy,
| |
| − | pure physics, etc. Then, we have sciences of hypothesis—geology,
| |
| − | biology, etc.</p>
| |
| − |
| |
| − | <p class='c005'>There are many other advantages of the distinction in
| |
| − | question which I shall leave the reader to find out by experience.
| |
| − | If he will only take the custom of considering
| |
| − | whether a given inference belongs to one or other of the
| |
| − | two forms of synthetic inference given on page <a href='#Page_134'>134</a>, I can
| |
| − | promise him that he will find his advantage in it, in
| |
| − | various ways.</p>
| |
| − |
| |
| − | <div class='chapter'>
| |
| − | <span class='pageno' id='Page_155'>155</span>
| |
| − | <h2 id='part2' class='c009'>PART II <br /> LOVE AND CHANCE</h2>
| |
| − | </div>
| |
| − | <div>
| |
| − | <span class='pageno' id='Page_157'>157</span>
| |
| − | <h3 id='chap2-1' class='c001'>I. THE ARCHITECTURE OF THEORIES<a id='r54' /><a href='#f54' class='c011'><sup>[54]</sup></a></h3>
| |
| − | </div>
| |
| − | <p class='c006'>Of the fifty or hundred systems of philosophy that have
| |
| − | been advanced at different times of the world’s history,
| |
| − | perhaps the larger number have been, not so much results
| |
| − | of historical evolution, as happy thoughts which have accidently
| |
| − | occurred to their authors. An idea which has been
| |
| − | found interesting and fruitful has been adopted, developed,
| |
| − | and forced to yield explanations of all sorts of phenomena.
| |
| − | The English have been particularly given to this way of
| |
| − | philosophizing; witness, Hobbes, Hartley, Berkeley, James
| |
| − | Mill. Nor has it been by any means useless labor; it
| |
| − | shows us what the true nature and value of the ideas developed
| |
| − | are, and in that way affords serviceable materials
| |
| − | for philosophy. Just as if a man, being seized with the
| |
| − | conviction that paper was a good material to make things
| |
| − | of, were to go to work to build a <i>papier mâché</i> house, with
| |
| − | roof of roofing-paper, foundations of pasteboard, windows
| |
| − | of paraffined paper, chimneys, bath tubs, locks, etc., all of
| |
| − | different forms of paper, his experiment would probably
| |
| − | afford valuable lessons to builders, while it would certainly
| |
| − | make a detestable house, so those one-idea’d philosophies
| |
| − | are exceedingly interesting and instructive, and yet are quite
| |
| − | unsound.</p>
| |
| − |
| |
| − | <p class='c005'>The remaining systems of philosophy have been of the
| |
| − | nature of reforms, sometimes amounting to radical revolutions,
| |
| − | suggested by certain difficulties which have been found
| |
| − | <span class='pageno' id='Page_158'>158</span>to beset systems previously in vogue; and such ought certainly
| |
| − | to be in large part the motive of any new theory.
| |
| − | This is like partially rebuilding a house. The faults that
| |
| − | have been committed are, first, that the repairs of the
| |
| − | dilapidations have generally not been sufficiently thorough-going,
| |
| − | and second, that not sufficient pains had been taken
| |
| − | to bring the additions into deep harmony with the really
| |
| − | sound parts of the old structure.</p>
| |
| − |
| |
| − | <p class='c005'>When a man is about to build a house, what a power of
| |
| − | thinking he has to do, before he can safely break ground!
| |
| − | With what pains he has to excogitate the precise wants that
| |
| − | are to be supplied! What a study to ascertain the most
| |
| − | available and suitable materials, to determine the mode
| |
| − | of construction to which those materials are best adapted,
| |
| − | and to answer a hundred such questions! Now without
| |
| − | riding the metaphor too far, I think we may safely say
| |
| − | that the studies preliminary to the construction of a great
| |
| − | theory should be at least as deliberate and thorough as
| |
| − | those that are preliminary to the building of a dwelling-house.</p>
| |
| − |
| |
| − | <p class='c005'>That systems ought to be constructed architectonically
| |
| − | has been preached since Kant, but I do not think the full
| |
| − | import of the maxim has by any means been apprehended.
| |
| − | What I would recommend is that every person who wishes
| |
| − | to form an opinion concerning fundamental problems, should
| |
| − | first of all make a complete survey of human knowledge,
| |
| − | should take note of all the valuable ideas in each branch of
| |
| − | science, should observe in just what respect each has been
| |
| − | successful and where it has failed, in order that in the light
| |
| − | of the thorough acquaintance so attained of the available
| |
| − | <span class='pageno' id='Page_159'>159</span>materials for a philosophical theory and of the nature and
| |
| − | strength of each, he may proceed to the study of what the
| |
| − | problem of philosophy consists in, and of the proper way
| |
| − | of solving it. I must not be understood as endeavoring
| |
| − | to state fully all that these preparatory studies should embrace;
| |
| − | on the contrary, I purposely slur over many points,
| |
| − | in order to give emphasis to one special recommendation,
| |
| − | namely, to make a systematic study of the conceptions out
| |
| − | of which a philosophical theory may be built, in order to
| |
| − | ascertain what place each conception may fitly occupy in
| |
| − | such a theory, and to what uses it is adapted.</p>
| |
| − |
| |
| − | <p class='c005'>The adequate treatment of this single point would fill a
| |
| − | volume, but I shall endeavor to illustrate my meaning by
| |
| − | glancing at several sciences and indicating conceptions in
| |
| − | them serviceable for philosophy. As to the results to which
| |
| − | long studies thus commenced have led me, I shall just give
| |
| − | a hint at their nature.</p>
| |
| − |
| |
| − | <p class='c005'>We may begin with dynamics,—field in our day of
| |
| − | perhaps the grandest conquest human science has ever
| |
| − | made,—I mean the law of the conservation of energy.
| |
| − | But let us revert to the first step taken by modern scientific
| |
| − | thought,—and a great stride it was,—the inauguration of
| |
| − | dynamics by Galileo. A modern physicist on examining
| |
| − | Galileo’s works is surprised to find how little experiment
| |
| − | had to do with the establishment of the foundations of
| |
| − | mechanics. His principal appeal is to common sense and
| |
| − | <i>il lume naturale</i>. He always assumes that the true theory
| |
| − | will be found to be a simple and natural one. And we can
| |
| − | see why it should indeed be so in dynamics. For instance,
| |
| − | a body left to its own inertia, moves in a straight line, and
| |
| − | <span class='pageno' id='Page_160'>160</span>a straight line appears to us the simplest of curves. In
| |
| − | <i>itself</i>, no curve is simpler than another. A system of
| |
| − | straight lines has intersections precisely corresponding to
| |
| − | those of a system of like parabolas similarly placed, or to
| |
| − | those of any one of an infinity of systems of curves. But
| |
| − | the straight line appears to us simple, because, as Euclid
| |
| − | says, it lies evenly between its extremities; that is, because
| |
| − | viewed endwise it appears as a point. That is, again, because
| |
| − | light moves in straight lines. Now, light moves in
| |
| − | straight lines because of the part which the straight line
| |
| − | plays in the laws of dynamics. Thus it is that our minds
| |
| − | having been formed under the influence of phenomena
| |
| − | governed by the laws of mechanics, certain conceptions
| |
| − | entering into those laws become implanted in our minds,
| |
| − | so that we readily guess at what the laws are. Without
| |
| − | such a natural prompting, having to search blindfold for
| |
| − | a law which would suit the phenomena, our chance of finding
| |
| − | it would be as one to infinity. The further physical
| |
| − | studies depart from phenomena which have directly influenced
| |
| − | the growth of the mind, the less we can expect to
| |
| − | find the laws which govern them “simple,” that is, composed
| |
| − | of a few conceptions natural to our minds.</p>
| |
| − |
| |
| − | <p class='c005'>The researches of Galileo, followed up by Huygens and
| |
| − | others, led to those modern conceptions of <i>Force</i> and <i>Law</i>,
| |
| − | which have revolutionized the intellectual world. The great
| |
| − | attention given to mechanics in the seventeenth century
| |
| − | soon so emphasized these conceptions as to give rise to the
| |
| − | Mechanical Philosophy, or doctrine that all the phenomena
| |
| − | of the physical universe are to be explained upon mechanical
| |
| − | principles. Newton’s great discovery imparted a new
| |
| − | <span class='pageno' id='Page_161'>161</span>impetus to this tendency. The old notion that heat consists
| |
| − | in an agitation of corpuscles was now applied to the explanation
| |
| − | of the chief properties of gases. The first suggestion
| |
| − | in this direction was that the pressure of gases is
| |
| − | explained by the battering of the particles against the walls
| |
| − | of the containing vessel, which explained Boyle’s law of the
| |
| − | compressibility of air. Later, the expansion of gases, Avogadro’s
| |
| − | chemical law, the diffusion and viscosity of gases,
| |
| − | and the action of Crookes’s radiometer were shown to be
| |
| − | consequences of the same kinetical theory; but other phenomena,
| |
| − | such as the ratio of the specific heat at constant
| |
| − | volume to that at constant pressure, require additional
| |
| − | hypotheses, which we have little reason to suppose are
| |
| − | simple, so that we find ourselves quite afloat. In like
| |
| − | manner with regard to light. That it consists of vibrations
| |
| − | was almost proved by the phenomena of diffraction, while
| |
| − | those of polarization showed the excursions of the particles
| |
| − | to be perpendicular to the line of propagation; but the
| |
| − | phenomena of dispersion, etc., require additional hypotheses
| |
| − | which may be very complicated. Thus, the further progress
| |
| − | of molecular speculation appears quite uncertain. If
| |
| − | hypotheses are to be tried haphazard, or simply because
| |
| − | they will suit certain phenomena, it will occupy the mathematical
| |
| − | physicists of the world say half a century on the
| |
| − | average to bring each theory to the test, and since the number
| |
| − | of possible theories may go up into the trillions, only
| |
| − | one of which can be true, we have little prospect of making
| |
| − | further solid additions to the subject in our time. When
| |
| − | we come to atoms, the presumption in favor of a simple law
| |
| − | seems very slender. There is room for serious doubt
| |
| − | <span class='pageno' id='Page_162'>162</span>whether the fundamental laws of mechanics hold good for
| |
| − | single atoms, and it seems quite likely that they are capable
| |
| − | of motion in more than three dimensions.</p>
| |
| − |
| |
| − | <p class='c005'>To find out much more about molecules and atoms, we
| |
| − | must search out a natural history of laws of nature, which
| |
| − | may fulfil that function which the presumption in favor
| |
| − | of simple laws fulfilled in the early days of dynamics, by
| |
| − | showing us what kind of laws we have to expect and by
| |
| − | answering such questions as this: Can we with reasonable
| |
| − | prospect of not wasting time, try the supposition that atoms
| |
| − | attract one another inversely as the seventh power of their
| |
| − | distances, or can we not? To suppose universal laws of
| |
| − | nature capable of being apprehended by the mind and yet
| |
| − | having no reason for their special forms, but standing inexplicable
| |
| − | and irrational, is hardly a justifiable position.
| |
| − | Uniformities are precisely the sort of facts that need to be
| |
| − | accounted for. That a pitched coin should sometimes turn
| |
| − | up heads and sometimes tails calls for no particular explanation;
| |
| − | but if it shows heads every time, we wish to know
| |
| − | how this result has been brought about. Law is <i>par excellence</i>
| |
| − | the thing that wants a reason.</p>
| |
| − |
| |
| − | <p class='c005'>Now the only possible way of accounting for the laws of
| |
| − | nature and for uniformity in general is to suppose them
| |
| − | results of evolution. This supposes them not to be absolute,
| |
| − | not to be obeyed precisely. It makes an element of
| |
| − | indeterminacy, spontaneity, or absolute chance in nature.
| |
| − | Just as, when we attempt to verify any physical law, we
| |
| − | find our observations cannot be precisely satisfied by it,
| |
| − | and rightly attribute the discrepancy to errors of observation,
| |
| − | so we must suppose far more minute discrepancies to
| |
| − | <span class='pageno' id='Page_163'>163</span>exist owing to the imperfect cogency of the law itself, to a
| |
| − | certain swerving of the facts from any definite formula.</p>
| |
| − |
| |
| − | <p class='c005'>Mr. Herbert Spencer wishes to explain evolution upon
| |
| − | mechanical principles. This is illogical, for four reasons.
| |
| − | First, because the principle of evolution requires no extraneous
| |
| − | cause; since the tendency to growth can be supposed
| |
| − | itself to have grown from an infinitesimal germ accidentally
| |
| − | started. Second, because law ought more than
| |
| − | anything else to be supposed a result of evolution. Third,
| |
| − | because exact law obviously never can produce heterogeneity
| |
| − | out of homogeneity; and arbitrary heterogeneity is the
| |
| − | feature of the universe the most manifest and characteristic.
| |
| − | Fourth, because the law of the conservation of energy is
| |
| − | equivalent to the proposition that all operations governed
| |
| − | by mechanical laws are reversible; so that an immediate
| |
| − | corollary from it is that growth is not explicable by those
| |
| − | laws, even if they be not violated in the process of growth.
| |
| − | In short, Spencer is not a philosophical evolutionist, but
| |
| − | only a half-evolutionist,—or, if you will, only a semi-Spencerian.
| |
| − | Now philosophy requires thoroughgoing evolutionism
| |
| − | or none.</p>
| |
| − |
| |
| − | <p class='c005'>The theory of Darwin was that evolution had been
| |
| − | brought about by the action of two factors: first, heredity,
| |
| − | as a principle making offspring nearly resemble their
| |
| − | parents, while yet giving room for “sporting,” or accidental
| |
| − | variations,—for very slight variations often, for wider ones
| |
| − | rarely; and, second, the destruction of breeds or races that
| |
| − | are unable to keep the birth rate up to the death rate.
| |
| − | This Darwinian principle is plainly capable of great generalization.
| |
| − | Wherever there are large numbers of objects,
| |
| − | <span class='pageno' id='Page_164'>164</span>having a tendency to retain certain characters unaltered,
| |
| − | this tendency, however, not being absolute but giving room
| |
| − | for chance variations, then, if the amount of variation is
| |
| − | absolutely limited in certain directions by the destruction
| |
| − | of everything which reaches those limits, there will be a
| |
| − | gradual tendency to change in directions of departure
| |
| − | from them. Thus, if a million players sit down to bet at
| |
| − | an even game, since one after another will get ruined, the
| |
| − | average wealth of those who remain will perpetually increase.
| |
| − | Here is indubitably a genuine formula of possible
| |
| − | evolution, whether its operation accounts for much or little
| |
| − | in the development of animal and vegetable species.</p>
| |
| − |
| |
| − | <p class='c005'>The Lamarckian theory also supposes that the development
| |
| − | of species has taken place by a long series of insensible
| |
| − | changes, but it supposes that those changes have
| |
| − | taken place during the lives of the individuals, in consequence
| |
| − | of effort and exercise, and that reproduction plays
| |
| − | no part in the process except in preserving these modifications.
| |
| − | Thus, the Lamarckian theory only explains the
| |
| − | development of characters for which individuals strive, while
| |
| − | the Darwinian theory only explains the production of characters
| |
| − | really beneficial to the race, though these may be
| |
| − | fatal to individuals.<a id='r55' /><a href='#f55' class='c011'><sup>[55]</sup></a> But more broadly and philosophically
| |
| − | conceived, Darwinian evolution is evolution by the operation
| |
| − | of chance, and the destruction of bad results, while
| |
| − | Lamarckian evolution is evolution by the effect of habit
| |
| − | and effort.</p>
| |
| − |
| |
| − | <p class='c005'>A third theory of evolution is that of Mr. Clarence King.
| |
| − | <span class='pageno' id='Page_165'>165</span>The testimony of monuments and of rocks is that species
| |
| − | are unmodified or scarcely modified, under ordinary circumstances,
| |
| − | but are rapidly altered after cataclysms or
| |
| − | rapid geological changes. Under novel circumstances, we
| |
| − | often see animals and plants sporting excessively in reproduction,
| |
| − | and sometimes even undergoing transformations
| |
| − | during individual life, phenomena no doubt due partly to
| |
| − | the enfeeblement of vitality from the breaking up of habitual
| |
| − | modes of life, partly to changed food, partly to direct
| |
| − | specific influence of the element in which the organism is
| |
| − | immersed. If evolution has been brought about in this
| |
| − | way, not only have its single steps not been insensible, as
| |
| − | both Darwinians and Lamarckians suppose, but they are
| |
| − | furthermore neither haphazard on the one hand, nor yet
| |
| − | determined by an inward striving on the other, but on the
| |
| − | contrary are effects of the changed environment, and have
| |
| − | a positive general tendency to adapt the organism to that
| |
| − | environment, since variation will particularly affect organs
| |
| − | at once enfeebled and stimulated. This mode of evolution,
| |
| − | by external forces and the breaking up of habits, seems to
| |
| − | be called for by some of the broadest and most important
| |
| − | facts of biology and paleontology; while it certainly has
| |
| − | been the chief factor in the historical evolution of institutions
| |
| − | as in that of ideas; and cannot possibly be refused
| |
| − | a very prominent place in the process of evolution of the
| |
| − | universe in general.</p>
| |
| − |
| |
| − | <p class='c005'>Passing to psychology, we find the elementary phenomena
| |
| − | of mind fall into three categories. First, we have Feelings,
| |
| − | comprising all that is immediately present, such as pain,
| |
| − | blue, cheerfulness, the feeling that arises when we contemplate
| |
| − | <span class='pageno' id='Page_166'>166</span>a consistent theory, etc. A feeling is a state of mind
| |
| − | having its own living quality, independent of any other
| |
| − | state of mind. Or, a feeling is an element of consciousness
| |
| − | which might conceivably override every other state until it
| |
| − | monopolized the mind, although such a rudimentary state
| |
| − | cannot actually be realized, and would not properly be
| |
| − | consciousness. Still, it is conceivable, or supposable, that
| |
| − | the quality of blue should usurp the whole mind, to the
| |
| − | exclusion of the ideas of shape, extension, contrast, commencement
| |
| − | and cessation, and all other ideas, whatsoever.
| |
| − | A feeling is necessarily perfectly simple, <i>in itself</i>, for if it
| |
| − | had parts these would also be in the mind, whenever the
| |
| − | whole was present, and thus the whole could not monopolize
| |
| − | the mind.<a id='r56' /><a href='#f56' class='c011'><sup>[56]</sup></a></p>
| |
| − |
| |
| − | <p class='c005'>Besides Feelings, we have Sensations of reaction; as
| |
| − | when a person blindfold suddenly runs against a post, when
| |
| − | we make a muscular effort, or when any feeling gives way
| |
| − | to a new feeling. Suppose I had nothing in my mind but
| |
| − | a feeling of blue, which were suddenly to give place to a
| |
| − | feeling of red; then, at the instant of transition there would
| |
| − | be a shock, a sense of reaction, my blue life being transmuted
| |
| − | into red life. If I were further endowed with a
| |
| − | memory, that sense would continue for some time, and there
| |
| − | would also be a peculiar feeling or sentiment connected
| |
| − | with it. This last feeling might endure (conceivably I
| |
| − | mean) after the memory of the occurrence and the feelings
| |
| − | of blue and red had passed away. But the <i>sensation</i> of
| |
| − | reaction cannot exist except in the actual presence of the
| |
| − | <span class='pageno' id='Page_167'>167</span>two feelings blue and red to which it relates. Wherever
| |
| − | we have two feelings and pay attention to a relation between
| |
| − | them of whatever kind, there is the sensation of
| |
| − | which I am speaking. But the sense of action and reaction
| |
| − | has two types: it may either be a perception of relation
| |
| − | between two ideas, or it may be a sense of action and reaction
| |
| − | between feeling and something out of feeling. And
| |
| − | this sense of external reaction again has two forms; for it
| |
| − | is either a sense of something happening to us, by no act of
| |
| − | ours, we being passive in the matter, or it is a sense of resistance,
| |
| − | that is, of our expending feeling upon something
| |
| − | without. The sense of reaction is thus a sense of connection
| |
| − | or comparison between feelings, either, <i>A</i>, between one
| |
| − | feeling and another, or <i>B</i>, between feeling and its absence
| |
| − | or lower degree; and under <i>B</i> we have, First, the sense of
| |
| − | the access of feeling, and Second, the sense of remission of
| |
| − | feeling.</p>
| |
| − |
| |
| − | <p class='c005'>Very different both from feelings and from reaction-sensations
| |
| − | or disturbances of feeling are general conceptions.
| |
| − | When we think, we are conscious that a connection between
| |
| − | feelings is determined by a general rule, we are aware of
| |
| − | being governed by a habit. Intellectual power is nothing
| |
| − | but facility in taking habits and in following them in cases
| |
| − | essentially analogous to, but in non-essentials widely remote
| |
| − | from, the normal cases of connections of feelings under
| |
| − | which those habits were formed.</p>
| |
| − |
| |
| − | <p class='c005'>The one primary and fundamental law of mental action
| |
| − | consists in a tendency to generalization. Feeling tends to
| |
| − | spread; connections between feelings awaken feelings;
| |
| − | neighboring feelings become assimilated; ideas are apt to
| |
| − | <span class='pageno' id='Page_168'>168</span>reproduce themselves. These are so many formulations of
| |
| − | the one law of the growth of mind. When a disturbance
| |
| − | of feeling takes place, we have a consciousness of gain, the
| |
| − | gain of experience; and a new disturbance will be apt to
| |
| − | assimilate itself to the one that preceded it. Feelings, by
| |
| − | being excited, become more easily excited, especially in the
| |
| − | ways in which they have previously been excited. The consciousness
| |
| − | of such a habit constitutes a general conception.</p>
| |
| − |
| |
| − | <p class='c005'>The cloudiness of psychological notions may be corrected
| |
| − | by connecting them with physiological conceptions. Feeling
| |
| − | may be supposed to exist, wherever a nerve-cell is in an
| |
| − | excited condition. The disturbance of feeling, or sense of
| |
| − | reaction, accompanies the transmission of disturbance between
| |
| − | nerve-cells or from a nerve-cell to a muscle-cell or
| |
| − | the external stimulation of a nerve-cell. General conceptions
| |
| − | arise upon the formation of habits in the nerve-matter,
| |
| − | which are molecular changes consequent upon its activity
| |
| − | and probably connected with its nutrition.</p>
| |
| − |
| |
| − | <p class='c005'>The law of habit exhibits a striking contrast to all physical
| |
| − | laws in the character of its commands. A physical law
| |
| − | is absolute. What it requires is an exact relation. Thus,
| |
| − | a physical force introduces into a motion a component
| |
| − | motion to be combined with the rest by the parallelogram
| |
| − | of forces; but the component motion must actually take
| |
| − | place exactly as required by the law of force. On the
| |
| − | other hand, no exact conformity is required by the mental
| |
| − | law. Nay, exact conformity would be in downright conflict
| |
| − | with the law; since it would instantly crystallize thought
| |
| − | and prevent all further formation of habit. The law of
| |
| − | mind only makes a given feeling <i>more likely</i> to arise. It
| |
| − | <span class='pageno' id='Page_169'>169</span>thus resembles the “non-conservative” forces of physics,
| |
| − | such as viscosity and the like, which are due to statistical
| |
| − | uniformities in the chance encounters of trillions of molecules.</p>
| |
| − |
| |
| − | <p class='c005'>The old dualistic notion of mind and matter, so prominent
| |
| − | in Cartesianism, as two radically different kinds of substance,
| |
| − | will hardly find defenders to-day. Rejecting this,
| |
| − | we are driven to some form of hylopathy, otherwise called
| |
| − | monism. Then the question arises whether physical laws
| |
| − | on the one hand, and the psychical law on the other are to
| |
| − | be taken—</p>
| |
| − |
| |
| − | <p class='c005'>(<i>A</i>) as independent, a doctrine often called <i>monism</i>, but
| |
| − | which I would name <i>neutralism</i>; or,</p>
| |
| − |
| |
| − | <p class='c005'>(<i>B</i>) the psychical law as derived and special, the physical
| |
| − | law alone as primordial, which is <i>materialism</i>; or,</p>
| |
| − |
| |
| − | <p class='c005'>(<i>C</i>) the physical law as derived and special, the psychical
| |
| − | law alone as primordial, which is <i>idealism</i>.</p>
| |
| − |
| |
| − | <p class='c005'>The materialistic doctrine seems to me quite as repugnant
| |
| − | to scientific logic as to common sense; since it requires us
| |
| − | to suppose that a certain kind of mechanism will feel, which
| |
| − | would be a hypothesis absolutely irreducible to reason,—an
| |
| − | ultimate, inexplicable regularity; while the only possible
| |
| − | justification of any theory is that it should make things
| |
| − | clear and reasonable.</p>
| |
| − |
| |
| − | <p class='c005'>Neutralism is sufficiently condemned by the logical maxim
| |
| − | known as Ockham’s razor, i.e., that not more independent
| |
| − | elements are to be supposed than necessary. By placing
| |
| − | the inward and outward aspects of substance on a par, it
| |
| − | seems to render both primordial.</p>
| |
| − |
| |
| − | <p class='c005'>The one intelligible theory of the universe is that of objective
| |
| − | <span class='pageno' id='Page_170'>170</span>idealism, that matter is effete mind, inveterate habits
| |
| − | becoming physical laws. But before this can be accepted
| |
| − | it must show itself capable of explaining the tridimensionality
| |
| − | of space, the laws of motion, and the general characteristics
| |
| − | of the universe, with mathematical clearness and
| |
| − | precision; for no less should be demanded of every
| |
| − | Philosophy.</p>
| |
| − |
| |
| − | <div class='figcenter id003'>
| |
| − | <img src='images/fig6.png' alt='Fig. 6.' class='ig001' />
| |
| − | <div class='ic002'>
| |
| − | <p>Figure 6.</p>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c005'>Modern mathematics is replete with ideas which may be
| |
| − | applied to philosophy. I can only notice one or two. The
| |
| − | manner in which mathematicians generalize is very instructive.
| |
| − | Thus, painters are accustomed to think of a picture
| |
| − | as consisting geometrically of the intersections of its plane
| |
| − | by rays of light from the natural objects to the eye. But
| |
| − | geometers use a generalized perspective.<a id='r57' /><a href='#f57' class='c011'><sup>[57]</sup></a> For instance
| |
| − | in the figure let <i>O</i> be the eye, let <i>A</i> <i>B</i> <i>C</i> <i>D</i> <i>E</i> be the edgewise
| |
| − | <span class='pageno' id='Page_171'>171</span>view of any plane, and let <i>a</i> <i>f</i> <i>e</i> <i>D</i> <i>c</i> be the edgewise
| |
| − | view of another plane. The geometers draw rays
| |
| − | through <i>O</i> cutting both these planes, and treat the points
| |
| − | of intersection of each ray with one plane as representing
| |
| − | the point of intersection of the same ray with the other
| |
| − | plane. Thus, <i>e</i> represents <i>E</i>, in the painter’s way. <i>D</i>
| |
| − | represents itself. <i>C</i> is represented by <i>c</i>, which is further
| |
| − | from the eye; and <i>A</i> is represented by <i>a</i> which is on the
| |
| − | other side of the eye. Such generalization is not bound
| |
| − | down to sensuous images. Further, according to this mode
| |
| − | of representation every point on one plane represents a
| |
| − | point on the other, and every point on the latter is represented
| |
| − | by a point on the former. But how about the point
| |
| − | <i>f</i> which is in a direction from <i>O</i> parallel to the represented
| |
| − | plane, and how about the point <i>B</i> which is in a direction
| |
| − | parallel to the representing plane? Some will say that
| |
| − | these are exceptions; but modern mathematics does not
| |
| − | allow exceptions which can be annulled by generalization.<a id='r58' /><a href='#f58' class='c011'><sup>[58]</sup></a>
| |
| − | As a point moves from <i>C</i> to <i>D</i> and thence to <i>E</i> and off
| |
| − | toward infinity, the corresponding point on the other plane
| |
| − | moves from <i>c</i> to <i>D</i> and thence to <i>e</i> and toward <i>f</i>. But this
| |
| − | second point can pass through <i>f</i> to <i>a</i>; and when it is there
| |
| − | the first point has arrived at <i>A</i>. We therefore say that the
| |
| − | first point has passed <i>through infinity</i>, and that every line
| |
| − | joins in to itself somewhat like an oval. Geometers talk of
| |
| − | <span class='pageno' id='Page_172'>172</span>the parts of lines at an infinite distance as points. This is
| |
| − | a kind of generalization very efficient in mathematics.</p>
| |
| − |
| |
| − | <p class='c005'>Modern views of measurement have a philosophical
| |
| − | aspect. There is an indefinite number of systems of measuring
| |
| − | along a line; thus, a perspective representation of a
| |
| − | scale on one line may be taken to measure another, although
| |
| − | of course such measurements will not agree with what we
| |
| − | call the distances of points on the latter line. To establish
| |
| − | a system of measurement on a line we must assign a distinct
| |
| − | number to each point of it, and for this purpose we shall
| |
| − | plainly have to suppose the numbers carried out into an
| |
| − | infinite number of places of decimals. These numbers
| |
| − | must be ranged along the line in unbroken sequence.
| |
| − | Further, in order that such a scale of numbers should be
| |
| − | of any use, it must be capable of being shifted into new
| |
| − | positions, each number continuing to be attached to a single
| |
| − | distinct point. Now it is found that if this is true for
| |
| − | “imaginary” as well as for real points (an expression
| |
| − | which I cannot stop to elucidate), any such shifting will
| |
| − | necessarily leave two numbers attached to the same points
| |
| − | as before. So that when the scale is moved over the line
| |
| − | by any continuous series of shiftings of one kind, there are
| |
| − | two points which no numbers on the scale can ever reach,
| |
| − | except the numbers fixed there. This pair of points, thus
| |
| − | unattainable in measurement, is called the Absolute. These
| |
| − | two points may be distinct and real, or they may coincide,
| |
| − | or they may be both imaginary. As an example of a linear
| |
| − | quantity with a double absolute we may take probability,
| |
| − | which ranges from an unattainable absolute certainty
| |
| − | <i>against</i> a proposition to an equally unattainable absolute
| |
| − | <span class='pageno' id='Page_173'>173</span>certainty <i>for</i> it. A line, according to ordinary notions, we
| |
| − | have seen is a linear quantity where the two points at infinity
| |
| − | coincide. A velocity is another example. A train going with
| |
| − | infinite velocity from Chicago to New York would be at all
| |
| − | the points on the line at the very same instant, and if the
| |
| − | time of transit were reduced to less than nothing it would be
| |
| − | moving in the other direction. An angle is a familiar example
| |
| − | of a mode of magnitude with no real immeasurable
| |
| − | values. One of the questions philosophy has to consider
| |
| − | is whether the development of the universe is like the increase
| |
| − | of an angle, so that it proceeds forever without tending
| |
| − | toward anything unattained, which I take to be the
| |
| − | Epicurean view, or whether the universe sprang from a
| |
| − | chaos in the infinitely distant past to tend toward something
| |
| − | different in the infinitely distant future, or whether
| |
| − | the universe sprang from nothing in the past to go on indefinitely
| |
| − | toward a point in the infinitely distant future,
| |
| − | which, were it attained, would be the mere nothing from
| |
| − | which it set out.</p>
| |
| − |
| |
| − | <p class='c005'>The doctrine of the absolute applied to space comes to
| |
| − | this, that either—</p>
| |
| − |
| |
| − | <p class='c005'>First, space is, as Euclid teaches, both <i>unlimited</i> and
| |
| − | <i>immeasurable</i>, so that the infinitely distant parts of any
| |
| − | plane seen in perspective appear as a straight line, in which
| |
| − | case the sum of the three angles of a triangle amounts to
| |
| − | 180°; or,</p>
| |
| − |
| |
| − | <p class='c005'>Second, space is <i>immeasurable</i> but <i>limited</i>, so that the
| |
| − | infinitely distant parts of any plane seen in perspective
| |
| − | appear as a circle, beyond which all is blackness, and in
| |
| − | this case the sum of the three angles of a triangle is less
| |
| − | <span class='pageno' id='Page_174'>174</span>than 180° by an amount proportional to the area of the
| |
| − | triangle; or,</p>
| |
| − |
| |
| − | <p class='c005'>Third, space is <i>unlimited</i> but <i>finite</i>, (like the surface of
| |
| − | a sphere), so that it has no infinitely distant parts; but a
| |
| − | finite journey along any straight line would bring one back
| |
| − | to his original position, and looking off with an unobstructed
| |
| − | view one would see the back of his own head enormously
| |
| − | magnified, in which case the sum of the three angles of a
| |
| − | triangle exceeds 180° by an amount proportional to the
| |
| − | area.</p>
| |
| − |
| |
| − | <p class='c005'>Which of these three hypotheses is true we know not.
| |
| − | The largest triangles we can measure are such as have the
| |
| − | earth’s orbit for base, and the distance of a fixed star for
| |
| − | altitude. The angular magnitude resulting from subtracting
| |
| − | the sum of the two angles at the base of such a triangle
| |
| − | from 180° is called the star’s <i>parallax</i>. The parallaxes of
| |
| − | only about forty stars have been measured as yet. Two
| |
| − | of them come out negative, that of Arided (α Cycni), a
| |
| − | star of magnitude 1-1/2, which is —0.“082, according to C. A.
| |
| − | F. Peters, and that of a star of magnitude 7-3/4, known as
| |
| − | Piazzi III 422, which is —0.”045, according to R. S. Ball.
| |
| − | But these negative parallaxes are undoubtedly to be attributed
| |
| − | to errors of observation; for the probable error of
| |
| − | such a determination is about ± 0.“075, and it would be
| |
| − | strange indeed if we were to be able to see, as it were,
| |
| − | more than half way round space, without being able to see
| |
| − | stars with larger negative parallaxes. Indeed, the very
| |
| − | fact that of all the parallaxes measured only two come out
| |
| − | negative would be a strong argument that the smallest
| |
| − | parallaxes really amount to +0.”1, were it not for the reflection
| |
| − | <span class='pageno' id='Page_175'>175</span>that the publication of other negative parallaxes
| |
| − | may have been suppressed. I think we may feel confident
| |
| − | that the parallax of the furthest star lies somewhere between
| |
| − | -0.”05 and +0.”15, and within another century our grandchildren
| |
| − | will surely know whether the three angles of a
| |
| − | triangle are greater or less than 180°,—that they are
| |
| − | <i>exactly</i> that amount is what nobody ever can be justified in
| |
| − | concluding. It is true that according to the axioms of
| |
| − | geometry the sum of the three sides of a triangle are precisely
| |
| − | 180°; but these axioms are now exploded, and
| |
| − | geometers confess that they, as geometers, know not the
| |
| − | slightest reason for supposing them to be precisely true.
| |
| − | They are expressions of our inborn conception of space,
| |
| − | and as such are entitled to credit, so far as their truth could
| |
| − | have influenced the formation of the mind. But that affords
| |
| − | not the slightest reason for supposing them exact.</p>
| |
| − |
| |
| − | <p class='c005'>Now, metaphysics has always been the ape of mathematics.
| |
| − | Geometry suggested the idea of a demonstrative
| |
| − | system of absolutely certain philosophical principles; and
| |
| − | the ideas of the metaphysicians have at all times been in
| |
| − | large part drawn from mathematics. The metaphysical
| |
| − | axioms are imitations of the geometrical axioms; and now
| |
| − | that the latter have been thrown overboard, without doubt
| |
| − | the former will be sent after them. It is evident, for instance,
| |
| − | that we can have no reason to think that every
| |
| − | phenomenon in all its minutest details is precisely determined
| |
| − | by law. That there is an arbitrary element in the
| |
| − | universe we see,—namely, its variety. This variety must
| |
| − | be attributed to spontaneity in some form.</p>
| |
| − |
| |
| − | <p class='c005'>Had I more space, I now ought to show how important
| |
| − | <span class='pageno' id='Page_176'>176</span>for philosophy is the mathematical conception of continuity.
| |
| − | Most of what is true in Hegel is a darkling glimmer of a
| |
| − | conception which the mathematicians had long before made
| |
| − | pretty clear, and which recent researches have still further
| |
| − | illustrated.</p>
| |
| − |
| |
| − | <p class='c005'>Among the many principles of Logic which find their
| |
| − | application in Philosophy, I can here only mention one.
| |
| − | Three conceptions are perpetually turning up at every point
| |
| − | in every theory of logic, and in the most rounded systems
| |
| − | they occur in connection with one another. They are conceptions
| |
| − | so very broad and consequently indefinite that they
| |
| − | are hard to seize and may be easily overlooked. I call
| |
| − | them the conceptions of First, Second, Third. First is the
| |
| − | conception of being or existing independent of anything else.
| |
| − | Second is the conception of being relative to, the conception
| |
| − | of reaction with, something else. Third is the conception
| |
| − | of mediation, whereby a first and second are brought
| |
| − | into relation. To illustrate these ideas, I will show how
| |
| − | they enter into those we have been considering. The origin
| |
| − | of things, considered not as leading to anything, but in
| |
| − | itself, contains the idea of First, the end of things that of
| |
| − | Second, the process mediating between them that of Third.
| |
| − | A philosophy which emphasizes the idea of the One, is
| |
| − | generally a dualistic philosophy in which the conception
| |
| − | of Second receives exaggerated attention; for this One
| |
| − | (though of course involving the idea of First) is always
| |
| − | the other of a manifold which is not one. The idea of the
| |
| − | Many, because variety is arbitrariness and arbitrariness is
| |
| − | repudiation of any Secondness, has for its principal component
| |
| − | the conception of First. In psychology Feeling is
| |
| − | <span class='pageno' id='Page_177'>177</span>First, Sense of reaction Second, General conception Third,
| |
| − | or mediation. In biology, the idea of arbitrary sporting is
| |
| − | First, heredity is Second, the process whereby the accidental
| |
| − | characters become fixed is Third. Chance is First, Law
| |
| − | is Second, the tendency to take habits is Third. Mind is
| |
| − | First, Matter is Second, Evolution is Third.</p>
| |
| − |
| |
| − | <p class='c005'>Such are the materials out of which chiefly a philosophical
| |
| − | theory ought to be built, in order to represent the state of
| |
| − | knowledge to which the nineteenth century has brought us.
| |
| − | Without going into other important questions of philosophical
| |
| − | architectonic, we can readily foresee what sort of
| |
| − | a metaphysics would appropriately be constructed from
| |
| − | those conceptions. Like some of the most ancient and
| |
| − | some of the most recent speculations it would be a Cosmogonic
| |
| − | Philosophy. It would suppose that in the beginning,—infinitely
| |
| − | remote,—there was a chaos of unpersonalized
| |
| − | feeling, which being without connection or regularity would
| |
| − | properly be without existence. This feeling, sporting here
| |
| − | and there in pure arbitrariness, would have started the germ
| |
| − | of a generalizing tendency. Its other sportings would be
| |
| − | evanescent, but this would have a growing virtue. Thus,
| |
| − | the tendency to habit would be started; and from this with
| |
| − | the other principles of evolution all the regularities of the
| |
| − | universe would be evolved. At any time, however, an
| |
| − | element of pure chance survives and will remain until the
| |
| − | world becomes an absolutely perfect, rational, and symmetrical
| |
| − | system, in which mind is at last crystallized in the
| |
| − | infinitely distant future.</p>
| |
| − |
| |
| − | <p class='c005'>That idea has been worked out by me with elaboration.
| |
| − | It accounts for the main features of the universe as we
| |
| − | <span class='pageno' id='Page_178'>178</span>know it,—the characters of time, space, matter, force,
| |
| − | gravitation, electricity, etc. It predicts many more things
| |
| − | which new observations can alone bring to the test. May
| |
| − | some future student go over this ground again, and have the
| |
| − | leisure to give his results to the world.</p>
| |
| − |
| |
| − | <div>
| |
| − | <span class='pageno' id='Page_179'>179</span>
| |
| − | <h3 id='chap2-2' class='c001'>II. THE DOCTRINE OF NECESSITY EXAMINED<a id='r59' /><a href='#f59' class='c011'><sup>[59]</sup></a></h3>
| |
| − | </div>
| |
| − | <p class='c006'>In <i>The Monist</i> for January, 1891, I endeavored to show
| |
| − | what elementary ideas ought to enter into our view of the
| |
| − | universe. I may mention that on those considerations I
| |
| − | had already grounded a cosmical theory, and from it had
| |
| − | deduced a considerable number of consequences capable
| |
| − | of being compared with experience. This comparison is
| |
| − | now in progress, but under existing circumstances must
| |
| − | occupy many years.</p>
| |
| − |
| |
| − | <p class='c005'>I propose here to examine the common belief that every
| |
| − | single fact in the universe is precisely determined by law.
| |
| − | It must not be supposed that this is a doctrine accepted
| |
| − | everywhere and at all times by all rational men. Its first
| |
| − | advocate appears to have been Democritus, the atomist, who
| |
| − | was led to it, as we are informed, by reflecting upon the
| |
| − | “impenetrability, translation, and impact of matter
| |
| − | (ἀντιτυπία καὶ φορὰ καὶ πληγὴ τῆς ὕλης).” That is to
| |
| − | say, having restricted his attention to a field where no influence
| |
| − | other than mechanical constraint could possibly come
| |
| − | before his notice, he straightway jumped to the conclusion
| |
| − | that throughout the universe that was the sole principle of
| |
| − | action,—a style of reasoning so usual in our day with men
| |
| − | not unreflecting as to be more than excusable in the infancy
| |
| − | of thought. But Epicurus, in revising the atomic
| |
| − | doctrine and repairing its defences, found himself obliged
| |
| − | <span class='pageno' id='Page_180'>180</span>to suppose that atoms swerve from their courses by spontaneous
| |
| − | chance; and thereby he conferred upon the theory
| |
| − | life and entelechy. For we now see clearly that the peculiar
| |
| − | function of the molecular hypothesis in physics is
| |
| − | to open an entry for the calculus of probabilities. Already,
| |
| − | the prince of philosophers had repeatedly and emphatically
| |
| − | condemned the dictum of Democritus (especially in the
| |
| − | “Physics,” Book II, chapters iv, v, vi), holding that events
| |
| − | come to pass in three ways, namely, (1) by external compulsion,
| |
| − | or the action of efficient causes, (2) by virtue of
| |
| − | an inward nature, or the influence of final causes, and (3)
| |
| − | irregularly without definite cause, but just by absolute
| |
| − | chance; and this doctrine is of the inmost essence of Aristotelianism.
| |
| − | It affords, at any rate, a valuable enumeration
| |
| − | of the possible ways in which anything can be supposed
| |
| − | to have come about. The freedom of the will, too, was
| |
| − | admitted both by Aristotle and by Epicurus. But the Stoa,
| |
| − | which in every department seized upon the most tangible,
| |
| − | hard, and lifeless element, and blindly denied the existence
| |
| − | of every other, which, for example, impugned the validity
| |
| − | of the inductive method and wished to fill its place with the
| |
| − | <i>reductio ad absurdum</i>, very naturally became the one school
| |
| − | of ancient philosophy to stand by a strict necessitarianism,
| |
| − | thus returning to a single principle of Democritus that
| |
| − | Epicurus had been unable to swallow. Necessitarianism
| |
| − | and materialism with the Stoics went hand in hand, as by
| |
| − | affinity they should. At the revival of learning, Stoicism
| |
| − | met with considerable favor, partly because it departed
| |
| − | just enough from Aristotle to give it the spice of novelty,
| |
| − | and partly because its superficialities well adapted it for
| |
| − | <span class='pageno' id='Page_181'>181</span>acceptance by students of literature and art who wanted
| |
| − | their philosophy drawn mild. Afterwards, the great discoveries
| |
| − | in mechanics inspired the hope that mechanical
| |
| − | principles might suffice to explain the universe; and though
| |
| − | without logical justification, this hope has since been continually
| |
| − | stimulated by subsequent advances in physics.
| |
| − | Nevertheless, the doctrine was in too evident conflict with
| |
| − | the freedom of the will and with miracles to be generally
| |
| − | acceptable, at first. But meantime there arose that most
| |
| − | widely spread of philosophical blunders, the notion that
| |
| − | associationalism belongs intrinsically to the materialistic
| |
| − | family of doctrines; and thus was evolved the theory of
| |
| − | motives; and libertarianism became weakened. At present,
| |
| − | historical criticism has almost exploded the miracles, great
| |
| − | and small; so that the doctrine of necessity has never been
| |
| − | in so great vogue as now.</p>
| |
| − |
| |
| − | <p class='c005'>The proposition in question is that the state of things
| |
| − | existing at any time, together with certain immutable laws,
| |
| − | completely determine the state of things at every other time
| |
| − | (for a limitation to <i>future</i> time is indefensible). Thus,
| |
| − | given the state of the universe in the original nebula, and
| |
| − | given the laws of mechanics, a sufficiently powerful mind
| |
| − | could deduce from these data the precise form of every
| |
| − | curlicue of every letter I am now writing.</p>
| |
| − |
| |
| − | <p class='c005'>Whoever holds that every act of the will as well as every
| |
| − | idea of the mind is under the rigid governance of a necessity
| |
| − | co-ordinated with that of the physical world, will logically
| |
| − | be carried to the proposition that minds are part of
| |
| − | the physical world in such a sense that the laws of mechanics
| |
| − | determine everything that happens according to
| |
| − | <span class='pageno' id='Page_182'>182</span>immutable attractions and repulsions. In that case, that
| |
| − | instantaneous state of things from which every other state
| |
| − | of things is calculable consists in the positions and velocities
| |
| − | of all the particles at any instant. This, the usual and
| |
| − | most logical form of necessitarianism, is called the mechanical
| |
| − | philosophy.</p>
| |
| − |
| |
| − | <p class='c005'>When I have asked thinking men what reason they had
| |
| − | to believe that every fact in the universe is precisely determined
| |
| − | by law, the first answer has usually been that
| |
| − | the proposition is a “presupposition” or postulate of scientific
| |
| − | reasoning. Well, if that is the best that can be said
| |
| − | for it, the belief is doomed. Suppose it be “postulated”:
| |
| − | that does not make it true, nor so much as afford the slightest
| |
| − | rational motive for yielding it any credence. It is as
| |
| − | if a man should come to borrow money, and when asked
| |
| − | for his security, should reply he “postulated” the loan.
| |
| − | To “postulate” a proposition is no more than to hope it is
| |
| − | true. There are, indeed, practical emergencies in which
| |
| − | we act upon assumptions of certain propositions as true,
| |
| − | because if they are not so, it can make no difference how
| |
| − | we act. But all such propositions I take to be hypotheses
| |
| − | of individual facts. For it is manifest that no universal
| |
| − | principle can in its universality be comprised in a special
| |
| − | case or can be requisite for the validity of any ordinary
| |
| − | inference. To say, for instance, that the demonstration
| |
| − | by Archimedes of the property of the lever would fall to
| |
| − | the ground if men were endowed with free-will, is extravagant;
| |
| − | yet this is implied by those who make a proposition
| |
| − | incompatible with the freedom of the will the postulate of
| |
| − | all inference. Considering, too, that the conclusions of
| |
| − | <span class='pageno' id='Page_183'>183</span>science make no pretence to being more than probable, and
| |
| − | considering that a probable inference can at most only
| |
| − | suppose something to be most frequently, or otherwise
| |
| − | approximately, true, but never that anything is precisely
| |
| − | true without exception throughout the universe, we see how
| |
| − | far this proposition in truth is from being so postulated.</p>
| |
| − |
| |
| − | <p class='c005'>But the whole notion of a postulate being involved in
| |
| − | reasoning appertains to a by-gone and false conception of
| |
| − | logic. Non-deductive, or ampliative inference, is of three
| |
| − | kinds: induction, hypothesis, and analogy. If there be
| |
| − | any other modes, they must be extremely unusual and
| |
| − | highly complicated, and may be assumed with little doubt
| |
| − | to be of the same nature as those enumerated. For induction,
| |
| − | hypothesis, and analogy, as far as their ampliative
| |
| − | character goes, that is, so far as they conclude something
| |
| − | not implied in the premises, depend upon one principle and
| |
| − | involve the same procedure. All are essentially inferences
| |
| − | from sampling. Suppose a ship arrives at Liverpool laden
| |
| − | with wheat in bulk. Suppose that by some machinery the
| |
| − | whole cargo be stirred up with great thoroughness. Suppose
| |
| − | that twenty-seven thimblefuls be taken equally from
| |
| − | the forward, midships, and aft parts, from the starboard,
| |
| − | center, and larboard parts, and from the top, half depth,
| |
| − | and lower parts of her hold, and that these being mixed
| |
| − | and the grains counted, four-fifths of the latter are found
| |
| − | to be of quality <i>A</i>. Then we infer, experientially and provisionally,
| |
| − | that approximately four-fifths of all the grain in
| |
| − | the cargo is of the same quality. I say we infer this <i>experientially</i>
| |
| − | and <i>provisionally</i>. By saying that we infer it
| |
| − | <i>experientially</i>, I mean that our conclusion makes no pretension
| |
| − | <span class='pageno' id='Page_184'>184</span>to knowledge of wheat-in-itself, our ἀλήθεια,
| |
| − | as the derivation of that word implies, has nothing to do
| |
| − | with <i>latent</i> wheat. We are dealing only with the matter
| |
| − | of possible experience,—experience in the full acceptation
| |
| − | of the term as something not merely affecting the senses
| |
| − | but also as the subject of thought. If there be any wheat
| |
| − | hidden on the ship, so that it can neither turn up in the
| |
| − | sample nor be heard of subsequently from purchasers,—or
| |
| − | if it be half-hidden, so that it may, indeed, turn up, but
| |
| − | is less likely to do so than the rest,—or if it can affect our
| |
| − | senses and our pockets, but from some strange cause or
| |
| − | causelessness cannot be reasoned about,—all such wheat
| |
| − | is to be excluded (or have only its proportional weight) in
| |
| − | calculating that true proportion of quality <i>A</i>, to which our
| |
| − | inference seeks to approximate. By saying that we draw
| |
| − | the inference <i>provisionally</i>, I mean that we do not hold
| |
| − | that we have reached any assigned degree of approximation
| |
| − | as yet, but only hold that if our experience be indefinitely
| |
| − | extended, and if every fact of whatever nature, as fast as it
| |
| − | presents itself, be duly applied, according to the inductive
| |
| − | method, in correcting the inferred ratio, then our approximation
| |
| − | will become indefinitely close in the long run; that
| |
| − | is to say, close to the experience <i>to come</i> (not merely close
| |
| − | by the exhaustion of a finite collection) so that if experience
| |
| − | in general is to fluctuate irregularly to and fro, in a manner
| |
| − | to deprive the ratio sought of all definite value, we shall
| |
| − | be able to find out approximately within what limits it
| |
| − | fluctuates, and if, after having one definite value, it changes
| |
| − | and assumes another, we shall be able to find that out, and
| |
| − | in short, whatever may be the variations of this ratio in
| |
| − | <span class='pageno' id='Page_185'>185</span>experience, experience indefinitely extended will enable us
| |
| − | to detect them, so as to predict rightly, at last, what its
| |
| − | ultimate value may be, if it have any ultimate value, or
| |
| − | what the ultimate law of succession of values may be, if
| |
| − | there be any such ultimate law, or that it ultimately fluctuates
| |
| − | irregularly within certain limits, if it do so ultimately
| |
| − | fluctuate. Now our inference, claiming to be no more than
| |
| − | thus experiential and provisional, manifestly involves no
| |
| − | postulate whatever.</p>
| |
| − |
| |
| − | <p class='c005'>For what is a postulate? It is the formulation of a material
| |
| − | fact which we are not entitled to assume as a premise,
| |
| − | but the truth of which is requisite to the validity of an
| |
| − | inference. Any fact, then, which might be supposed postulated,
| |
| − | must either be such that it would ultimately present
| |
| − | itself in experience, or not. If it will present itself, we
| |
| − | need not postulate it now in our provisional inference, since
| |
| − | we shall ultimately be entitled to use it as a premise. But
| |
| − | if it never would present itself in experience, our conclusion
| |
| − | is valid but for the possibility of this fact being otherwise
| |
| − | than assumed, that is, it is valid as far as possible experience
| |
| − | goes, and that is all that we claim. Thus, every
| |
| − | postulate is cut off, either by the provisionality or by the
| |
| − | experientiality of our inference. For instance, it has been
| |
| − | said that induction postulates that, if an indefinite succession
| |
| − | of samples be drawn, examined, and thrown back each
| |
| − | before the next is drawn, then in the long run every grain
| |
| − | will be drawn as often as any other, that is to say, postulates
| |
| − | that the ratio of the numbers of times in which any two
| |
| − | are drawn will indefinitely approximate to unity. But no
| |
| − | such postulate is made; for if, on the one hand, we are to
| |
| − | <span class='pageno' id='Page_186'>186</span>have no other experience of the wheat than from such
| |
| − | drawings, it is the ratio that presents itself in those drawings
| |
| − | and not the ratio which belongs to the wheat in its latent
| |
| − | existence that we are endeavoring to determine; while if,
| |
| − | on the other hand, there is some other mode by which the
| |
| − | wheat is to come under our knowledge, equivalent to another
| |
| − | kind of sampling, so that after all our care in stirring
| |
| − | up the wheat, some experiential grains will present themselves
| |
| − | in the first sampling operation more often than others
| |
| − | in the long run, this very singular fact will be sure to get
| |
| − | discovered by the inductive method, which must avail itself
| |
| − | of every sort of experience; and our inference, which was
| |
| − | only provisional, corrects itself at last. Again, it has been
| |
| − | said, that induction postulates that under like circumstances
| |
| − | like events will happen, and that this postulate is at bottom
| |
| − | the same as the principle of universal causation. But this
| |
| − | is a blunder, or <i>bevue</i>, due to thinking exclusively of inductions
| |
| − | where the concluded ratio is either 1 or 0. If
| |
| − | any such proposition were postulated, it would be that
| |
| − | under like circumstances (the circumstances of drawing the
| |
| − | different samples) different events occur in the same proportions
| |
| − | in all the different sets,—a proposition which is
| |
| − | false and even absurd. But in truth no such thing is postulated,
| |
| − | the experiential character of the inference reducing
| |
| − | the condition of validity to this, that if a certain result does
| |
| − | not occur, the opposite result will be manifested, a condition
| |
| − | assured by the provisionality of the inference. But it may
| |
| − | be asked whether it is not conceivable that every instance
| |
| − | of a certain class destined to be ever employed as a datum
| |
| − | of induction should have one character, while every instance
| |
| − | <span class='pageno' id='Page_187'>187</span>destined not to be so employed should have the opposite
| |
| − | character. The answer is that in that case, the instances
| |
| − | excluded from being subjects of reasoning would not be
| |
| − | experienced in the full sense of the word, but would be
| |
| − | among these <i>latent</i> individuals of which our conclusion does
| |
| − | not pretend to speak.</p>
| |
| − |
| |
| − | <p class='c005'>To this account of the rationale of induction I know of
| |
| − | but one objection worth mention: it is that I thus fail to
| |
| − | deduce the full degree of force which this mode of inference
| |
| − | in fact possesses; that according to my view, no matter
| |
| − | how thorough and elaborate the stirring and mixing process
| |
| − | had been, the examination of a single handful of grain
| |
| − | would not give me any assurance, sufficient to risk money
| |
| − | upon that the next handful would not greatly modify the
| |
| − | concluded value of the ratio under inquiry, while, in fact,
| |
| − | the assurance would be very high that this ratio was not
| |
| − | greatly in error. If the true ratio of grains of quality <i>A</i>
| |
| − | were 0.80 and the handful contained a thousand grains,
| |
| − | nine such handfuls out of every ten would contain from
| |
| − | 780 to 820 grains of quality <i>A</i>. The answer to this is that
| |
| − | the calculation given is correct when we know that the units
| |
| − | of this handful and the quality inquired into have the normal
| |
| − | independence of one another, if for instance the stirring
| |
| − | has been complete and the character sampled for has been
| |
| − | settled upon in advance of the examination of the sample.
| |
| − | But in so far as these conditions are not known to be complied
| |
| − | with, the above figures cease to be applicable. Random
| |
| − | sampling and predesignation of the character sampled
| |
| − | for should always be striven after in inductive reasoning,
| |
| − | but when they cannot be attained, so long as it is conducted
| |
| − | <span class='pageno' id='Page_188'>188</span>honestly, the inference retains some value. When we cannot
| |
| − | ascertain how the sampling has been done or the sample-character
| |
| − | selected, induction still has the essential validity
| |
| − | which my present account of it shows it to have.</p>
| |
| − |
| |
| − | <p class='c005'>I do not think a man who combines a willingness to be
| |
| − | convinced with a power of appreciating an argument upon
| |
| − | a difficult subject can resist the reasons which have been
| |
| − | given to show that the principle of universal necessity cannot
| |
| − | be defended as being a postulate of reasoning. But then
| |
| − | the question immediately arises whether it is not proved to
| |
| − | be true, or at least rendered highly probable, by observation
| |
| − | of nature.</p>
| |
| − |
| |
| − | <p class='c005'>Still, this question ought not long to arrest a person
| |
| − | accustomed to reflect upon the force of scientific reasoning.
| |
| − | For the essence of the necessitarian position is that certain
| |
| − | continuous quantities have certain exact values. Now, how
| |
| − | can observation determine the value of such a quantity with
| |
| − | a probable error absolutely <i>nil</i>? To one who is behind the
| |
| − | scenes, and knows that the most refined comparisons of
| |
| − | masses, lengths, and angles, far surpassing in precision all
| |
| − | other measurements, yet fall behind the accuracy of bank-accounts,
| |
| − | and that the ordinary determinations of physical
| |
| − | constants, such as appear from month to month in the
| |
| − | journals, are about on a par with an upholsterer’s measurements
| |
| − | of carpets and curtains, the idea of mathematical
| |
| − | exactitude being demonstrated in the laboratory will appear
| |
| − | simply ridiculous. There is a recognized method of estimating
| |
| − | the probable magnitudes of errors in physics,—the
| |
| − | method of least squares. It is universally admitted that
| |
| − | this method makes the errors smaller than they really are;
| |
| − | <span class='pageno' id='Page_189'>189</span>yet even according to that theory an error indefinitely small
| |
| − | is indefinitely improbable; so that any statement to the
| |
| − | effect that a certain continuous quantity has a certain exact
| |
| − | value, if well-founded at all, must be founded on something
| |
| − | other than observation.</p>
| |
| − |
| |
| − | <p class='c005'>Still, I am obliged to admit that this rule is subject to a
| |
| − | certain qualification. Namely, it only applies to continuous<a id='r60' /><a href='#f60' class='c011'><sup>[60]</sup></a>
| |
| − | quantity. Now, certain kinds of continuous quantity are
| |
| − | discontinuous at one or at two limits, and for such limits
| |
| − | the rule must be modified. Thus, the length of a line cannot
| |
| − | be less than zero. Suppose, then, the question arises
| |
| − | how long a line a certain person had drawn from a marked
| |
| − | point on a piece of paper. If no line at all can be seen, the
| |
| − | observed length is zero; and the only conclusion this observation
| |
| − | warrants is that the length of the line is less than the
| |
| − | smallest length visible with the optical power employed.
| |
| − | But indirect observations,—for example, that the person
| |
| − | supposed to have drawn the line was never within fifty
| |
| − | feet of the paper,—may make it probable that no line
| |
| − | at all was made, so that the concluded length will be strictly
| |
| − | zero. In like manner, experience no doubt would warrant
| |
| − | the conclusion that there is absolutely <i>no</i> indigo in a given
| |
| − | ear of wheat, and absolutely <i>no</i> attar in a given lichen.
| |
| − | But such inferences can only be rendered valid by positive
| |
| − | experiential evidence, direct or remote, and cannot rest
| |
| − | upon a mere inability to detect the quantity in question.
| |
| − | We have reason to think there is no indigo in the wheat,
| |
| − | because we have remarked that wherever indigo is produced
| |
| − | <span class='pageno' id='Page_190'>190</span>it is produced in considerable quantities, to mention
| |
| − | only one argument. We have reason to think there is no
| |
| − | attar in the lichen, because essential oils seem to be in
| |
| − | general peculiar to single species. If the question had been
| |
| − | whether there was iron in the wheat or the lichen, though
| |
| − | chemical analysis should fail to detect its presence, we
| |
| − | should think some of it probably was there, since iron is
| |
| − | almost everywhere. Without any such information, one
| |
| − | way or the other, we could only abstain from any opinion as
| |
| − | to the presence of the substance in question. It cannot, I
| |
| − | conceive, be maintained that we are in any <i>better</i> position
| |
| − | than this in regard to the presence of the element of chance
| |
| − | or spontaneous departures from law in nature.</p>
| |
| − |
| |
| − | <p class='c005'>Those observations which are generally adduced in favor
| |
| − | of mechanical causation simply prove that there is an element
| |
| − | of regularity in nature, and have no bearing whatever
| |
| − | upon the question of whether such regularity is exact
| |
| − | and universal, or not. Nay, in regard to this <i>exactitude</i>, all
| |
| − | observation is directly <i>opposed</i> to it; and the most that can
| |
| − | be said is that a good deal of this observation can be explained
| |
| − | away. Try to verify any law of nature, and you
| |
| − | will find that the more precise your observations, the more
| |
| − | certain they will be to show irregular departures from the
| |
| − | law. We are accustomed to ascribe these, and I do not
| |
| − | say wrongly, to errors of observation; yet we cannot usually
| |
| − | account for such errors in any antecedently probable way.
| |
| − | Trace their causes back far enough, and you will be forced
| |
| − | to admit they are always due to arbitrary determination,
| |
| − | or chance.</p>
| |
| − |
| |
| − | <p class='c005'>But it may be asked whether if there were an element
| |
| − | <span class='pageno' id='Page_191'>191</span>of real chance in the universe it must not occasionally be
| |
| − | productive of signal effects such as could not pass unobserved.
| |
| − | In answer to this question, without stopping to
| |
| − | point out that there is an abundance of great events which
| |
| − | one might be tempted to suppose were of that nature, it will
| |
| − | be simplest to remark that physicists hold that the particles
| |
| − | of gases are moving about irregularly, substantially as if
| |
| − | by real chance, and that by the principles of probabilities
| |
| − | there must occasionally happen to be concentrations of heat
| |
| − | in the gases contrary to the second law of thermodynamics,
| |
| − | and these concentrations, occurring in explosive mixtures,
| |
| − | must sometimes have tremendous effects. Here, then, is
| |
| − | in substance the very situation supposed; yet no phenomena
| |
| − | ever have resulted which we are forced to attribute to such
| |
| − | chance concentration of heat, or which anybody, wise or
| |
| − | foolish, has ever dreamed of accounting for in that manner.</p>
| |
| − |
| |
| − | <p class='c005'>In view of all these considerations, I do not believe that
| |
| − | anybody, not in a state of case-hardened ignorance respecting
| |
| − | the logic of science, can maintain that the precise and
| |
| − | universal conformity of facts to law is clearly proved, or
| |
| − | even rendered particularly probable, by any observations
| |
| − | hitherto made. In this way, the determined advocate of
| |
| − | exact regularity will soon find himself driven to <i>a priori</i>
| |
| − | reasons to support his thesis. These received such a socdolager
| |
| − | from Stuart Mill in his Examination of Hamilton,
| |
| − | that holding to them now seems to me to denote a high
| |
| − | degree of imperviousness to reason; so that I shall pass
| |
| − | them by with little notice.</p>
| |
| − |
| |
| − | <p class='c005'>To say that we cannot help believing a given proposition
| |
| − | is no argument, but it is a conclusive fact if it be
| |
| − | <span class='pageno' id='Page_192'>192</span>true; and with the substitution of “I” for “we,” it is
| |
| − | true in the mouths of several classes of minds, the blindly
| |
| − | passionate, the unreflecting and ignorant, and the person
| |
| − | who has overwhelming evidence before his eyes. But
| |
| − | that which has been inconceivable to-day has often turned
| |
| − | out indisputable on the morrow. Inability to conceive is
| |
| − | only a stage through which every man must pass in regard
| |
| − | to a number of beliefs,—unless endowed with extraordinary
| |
| − | obstinacy and obtuseness. His understanding is enslaved
| |
| − | to some blind compulsion which a vigorous mind is pretty
| |
| − | sure soon to cast off.</p>
| |
| − |
| |
| − | <p class='c005'>Some seek to back up the <i>a priori</i> position with empirical
| |
| − | arguments. They say that the exact regularity of the world
| |
| − | is a natural belief, and that natural beliefs have generally
| |
| − | been confirmed by experience. There is some reason in
| |
| − | this. Natural beliefs, however, if they generally have a
| |
| − | foundation of truth, also require correction and purification
| |
| − | from natural illusions. The principles of mechanics are undoubtedly
| |
| − | natural beliefs; but, for all that, the early formulations
| |
| − | of them were exceedingly erroneous. The general
| |
| − | approximation to truth in natural beliefs is, in fact, a case
| |
| − | of the general adaptation of genetic products to recognizable
| |
| − | utilities or ends. Now, the adaptations of nature,
| |
| − | beautiful and often marvelous as they verily are, are never
| |
| − | found to be quite perfect; so that the argument is quite
| |
| − | <i>against</i> the absolute exactitude of any natural belief, including
| |
| − | that of the principle of causation.</p>
| |
| − |
| |
| − | <p class='c005'>Another argument, or convenient commonplace, is that
| |
| − | absolute chance is <i>inconceivable</i>. (This word has eight current
| |
| − | significations. The <i>Century Dictionary</i> enumerates
| |
| − | <span class='pageno' id='Page_193'>193</span>six.) Those who talk like this will hardly be persuaded
| |
| − | to say in what sense they mean that chance is inconceivable.
| |
| − | Should they do so, it would easily be shown either
| |
| − | that they have no sufficient reason for the statement or
| |
| − | that the inconceivability is of a kind which does not prove
| |
| − | that chance is non-existent.</p>
| |
| − |
| |
| − | <p class='c005'>Another <i>a priori</i> argument is that chance is unintelligible;
| |
| − | that is to say, while it may perhaps be conceivable, it does
| |
| − | not disclose to the eye of reason the how or why of things;
| |
| − | and since a hypothesis can only be justified so far as it
| |
| − | renders some phenomenon intelligible, we never can have
| |
| − | any right to suppose absolute chance to enter into the
| |
| − | production of anything in nature. This argument may be
| |
| − | considered in connection with two others. Namely, instead
| |
| − | of going so far as to say that the supposition of chance can
| |
| − | <i>never</i> properly be used to explain any observed fact, it
| |
| − | may be alleged merely that no facts are known which such
| |
| − | a supposition could in any way help in explaining. Or
| |
| − | again, the allegation being still further weakened, it may be
| |
| − | said that since departures from law are not unmistakably
| |
| − | observed, chance is not a <i>vera causa</i>, and ought not unnecessarily
| |
| − | to be introduced into a hypothesis.</p>
| |
| − |
| |
| − | <p class='c005'>These are no mean arguments, and require us to examine
| |
| − | the matter a little more closely. Come, my superior opponent,
| |
| − | let me learn from your wisdom. It seems to me
| |
| − | that every throw of sixes with a pair of dice is a manifest
| |
| − | instance of chance.</p>
| |
| − |
| |
| − | <p class='c005'>“While you would hold a throw of deuce-ace to be
| |
| − | brought about by necessity?” (The opponent’s supposed
| |
| − | remarks are placed in quotation marks.)</p>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_194'>194</span>Clearly one throw is as much chance as another.</p>
| |
| − |
| |
| − | <p class='c005'>“Do you think throws of dice are of a different nature
| |
| − | from other events?”</p>
| |
| − |
| |
| − | <p class='c005'>I see that I must say that <i>all</i> the diversity and specificalness
| |
| − | of events is attributable to chance.</p>
| |
| − |
| |
| − | <p class='c005'>“Would you, then, deny that there is any regularity in
| |
| − | the world?”</p>
| |
| − |
| |
| − | <p class='c005'>That is clearly undeniable. I must acknowledge there
| |
| − | is an approximate regularity, and that every event is influenced
| |
| − | by it. But the diversification, specificalness, and
| |
| − | irregularity of things I suppose is chance. A throw of
| |
| − | sixes appears to me a case in which this element is particularly
| |
| − | obtrusive.</p>
| |
| − |
| |
| − | <p class='c005'>“If you reflect more deeply, you will come to see that
| |
| − | <i>chance</i> is only a name for a cause that is unknown to us.”</p>
| |
| − |
| |
| − | <p class='c005'>Do you mean that we have no idea whatever what kind
| |
| − | of causes could bring about a throw of sixes?</p>
| |
| − |
| |
| − | <p class='c005'>“On the contrary, each die moves under the influence
| |
| − | of precise mechanical laws.”</p>
| |
| − |
| |
| − | <p class='c005'>But it appears to me that it is not these <i>laws</i> which made
| |
| − | the die turn up sixes; for these laws act just the same when
| |
| − | other throws come up. The chance lies in the diversity of
| |
| − | throws; and this diversity cannot be due to laws which are
| |
| − | immutable.</p>
| |
| − |
| |
| − | <p class='c005'>“The diversity is due to the diverse circumstances under
| |
| − | which the laws act. The dice lie differently in the box,
| |
| − | and the motion given to the box is different. These are the
| |
| − | unknown causes which produce the throws, and to which
| |
| − | we give the name of chance; not the mechanical law which
| |
| − | regulates the operation of these causes. You see you are
| |
| − | already beginning to think more clearly about this subject.”</p>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_195'>195</span>Does the operation of mechanical law not increase the
| |
| − | diversity?</p>
| |
| − |
| |
| − | <p class='c005'>“Properly not. You must know that the instantaneous
| |
| − | state of a system of particles is defined by six times as many
| |
| − | numbers as there are particles, three for the co-ordinates
| |
| − | of each particle’s position, and three more for the components
| |
| − | of its velocity. This number of numbers, which
| |
| − | expresses the amount of diversity in the system, remains
| |
| − | the same at all times. There may be, to be sure, some
| |
| − | kind of relation between the co-ordinates and component
| |
| − | velocities of the different particles, by means of which the
| |
| − | state of the system might be expressed by a smaller number
| |
| − | of numbers. But, if this is the case, a precisely corresponding
| |
| − | relationship must exist between the co-ordinates and
| |
| − | component velocities at any other time, though it may
| |
| − | doubtless be a relation less obvious to us. Thus, the intrinsic
| |
| − | complexity of the system is the same at all times.”</p>
| |
| − |
| |
| − | <p class='c005'>Very well, my obliging opponent, we have now reached an
| |
| − | issue. You think all the arbitrary specifications of the
| |
| − | universe were introduced in one dose, in the beginning, if
| |
| − | there was a beginning, and that the variety and complication
| |
| − | of nature has always been just as much as it is now.
| |
| − | But I, for my part, think that the diversification, the specification,
| |
| − | has been continually taking place. Should you
| |
| − | condescend to ask me why I so think, I should give my
| |
| − | reasons as follows:</p>
| |
| − |
| |
| − | <p class='c005'>(1) Question any science which deals with the course of
| |
| − | time. Consider the life of an individual animal or plant,
| |
| − | or of a mind. Glance at the history of states, of institutions,
| |
| − | of language, of ideas. Examine the successions of
| |
| − | <span class='pageno' id='Page_196'>196</span>forms shown by paleontology, the history of the globe as
| |
| − | set forth in geology, of what the astronomer is able to
| |
| − | make out concerning the changes of stellar systems.
| |
| − | Everywhere the main fact is growth and increasing complexity.
| |
| − | Death and corruption are mere accidents or secondary
| |
| − | phenomena. Among some of the lower organisms, it
| |
| − | is a moot point with biologists whether there be anything
| |
| − | which ought to be called death. Races, at any rate, do not
| |
| − | die out except under unfavorable circumstances. From
| |
| − | these broad and ubiquitous facts we may fairly infer, by
| |
| − | the most unexceptionable logic, that there is probably in
| |
| − | nature some agency by which the complexity and diversity
| |
| − | of things can be increased; and that consequently the
| |
| − | rule of mechanical necessity meets in some way with
| |
| − | interference.</p>
| |
| − |
| |
| − | <p class='c005'>(2) By thus admitting pure spontaneity or life as a character
| |
| − | of the universe, acting always and everywhere though
| |
| − | restrained within narrow bounds by law, producing infinitesimal
| |
| − | departures from law continually, and great ones
| |
| − | with infinite infrequency, I account for all the variety and
| |
| − | diversity of the universe, in the only sense in which the
| |
| − | really <i>sui generis</i> and new can be said to be accounted for.
| |
| − | The ordinary view has to admit the inexhaustible multitudinous
| |
| − | variety of the world, has to admit that its mechanical
| |
| − | law cannot account for this in the least, that
| |
| − | variety can spring only from spontaneity, and yet denies
| |
| − | without any evidence or reason the existence of this spontaneity,
| |
| − | or else shoves it back to the beginning of time and
| |
| − | supposes it dead ever since. The superior logic of my view
| |
| − | appears to me not easily controverted.</p>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_197'>197</span>(3) When I ask the necessitarian how he would explain
| |
| − | the diversity and irregularity of the universe, he replies to
| |
| − | me out of the treasury of his wisdom that irregularity is
| |
| − | something which from the nature of things we must not
| |
| − | seek to explain. Abashed at this, I seek to cover my confusion
| |
| − | by asking how he would explain the uniformity and
| |
| − | regularity of the universe, whereupon he tells me that the
| |
| − | laws of nature are immutable and ultimate facts, and no
| |
| − | account is to be given of them. But my hypothesis of
| |
| − | spontaneity does explain irregularity, in a certain sense;
| |
| − | that is, it explains the general fact of irregularity, though
| |
| − | not, of course, what each lawless event is to be. At the
| |
| − | same time, by thus loosening the bond of necessity, it gives
| |
| − | room for the influence of another kind of causation, such
| |
| − | as seems to be operative in the mind in the formation of
| |
| − | associations, and enables us to understand how the uniformity
| |
| − | of nature could have been brought about. That
| |
| − | single events should be hard and unintelligible, logic will
| |
| − | permit without difficulty: we do not expect to make the
| |
| − | shock of a personally experienced earthquake appear natural
| |
| − | and reasonable by any amount of cogitation. But logic
| |
| − | does expect things <i>general</i> to be understandable. To say
| |
| − | that there is a universal law, and that it is a hard, ultimate,
| |
| − | unintelligible fact, the why and wherefore of which can
| |
| − | never be inquired into, at this a sound logic will revolt;
| |
| − | and will pass over at once to a method of philosophizing
| |
| − | which does not thus barricade the road of discovery.</p>
| |
| − |
| |
| − | <p class='c005'>(4) Necessitarianism cannot logically stop short of making
| |
| − | the whole action of the mind a part of the physical
| |
| − | universe. Our notion that we decide what we are going to
| |
| − | <span class='pageno' id='Page_198'>198</span>do, if as the necessitarian says, it has been calculable since
| |
| − | the earliest times, is reduced to illusion. Indeed, consciousness
| |
| − | in general thus becomes a mere illusory aspect of a
| |
| − | material system. What we call red, green, and violet are
| |
| − | in reality only different rates of vibration. The sole reality
| |
| − | is the distribution of qualities of matter in space and time.
| |
| − | Brain-matter is protoplasm in a certain degree and kind of
| |
| − | complication,—a certain arrangement of mechanical particles.
| |
| − | Its feeling is but an inward aspect, a phantom.
| |
| − | For, from the positions and velocities of the particles at any
| |
| − | one instant, and the knowledge of the immutable forces,
| |
| − | the positions at all other times are calculable; so that the
| |
| − | universe of space, time, and matter is a rounded system
| |
| − | uninterfered with from elsewhere. But from the state of
| |
| − | feeling at any instant, there is no reason to suppose the
| |
| − | states of feeling at all other instants are thus exactly calculable;
| |
| − | so that feeling is, as I said, a mere fragmentary
| |
| − | and illusive aspect of the universe. This is the way, then,
| |
| − | that necessitarianism has to make up its accounts. It enters
| |
| − | consciousness under the head of sundries, as a forgotten
| |
| − | trifle; its scheme of the universe would be more satisfactory
| |
| − | if this little fact could be dropped out of sight. On the
| |
| − | other hand, by supposing the rigid exactitude of causation
| |
| − | to yield, I care not how little,—be it but by a strictly
| |
| − | infinitesimal amount,—we gain room to insert mind into
| |
| − | our scheme, and to put it into the place where it is needed,
| |
| − | into the position which, as the sole self-intelligible thing,
| |
| − | it is entitled to occupy, that of the fountain of existence;
| |
| − | and in so doing we resolve the problem of the connection of
| |
| − | soul and body.</p>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_199'>199</span>(5) But I must leave undeveloped the chief of my reasons,
| |
| − | and can only adumbrate it. The hypothesis of chance-spontaneity
| |
| − | is one whose inevitable consequences are capable
| |
| − | of being traced out with mathematical precision into considerable
| |
| − | detail. Much of this I have done and find the
| |
| − | consequences to agree with observed facts to an extent
| |
| − | which seems to me remarkable. But the matter and
| |
| − | methods of reasoning are novel, and I have no right to
| |
| − | promise that other mathematicians shall find my deductions
| |
| − | as satisfactory as I myself do, so that the strongest reason
| |
| − | for my belief must for the present remain a private reason
| |
| − | of my own, and cannot influence others. I mention it to
| |
| − | explain my own position; and partly to indicate to future
| |
| − | mathematical speculators a veritable goldmine, should time
| |
| − | and circumstances and the abridger of all joys prevent my
| |
| − | opening it to the world.</p>
| |
| − |
| |
| − | <p class='c005'>If now I, in my turn, inquire of the necessitarian why
| |
| − | he prefers to suppose that all specification goes back to the
| |
| − | beginning of things, he will answer me with one of those
| |
| − | last three arguments which I left unanswered.</p>
| |
| − |
| |
| − | <p class='c005'>First, he may say that chance is a thing absolutely unintelligible,
| |
| − | and, therefore, that we never can be entitled
| |
| − | to make such a supposition. But does not this objection
| |
| − | smack of naïve impudence? It is not mine, it is his own
| |
| − | conception of the universe which leads abruptly up to hard,
| |
| − | ultimate, inexplicable, immutable law, on the one hand, and
| |
| − | to inexplicable specification and diversification of circumstances
| |
| − | on the other. My view, on the contrary, hypothetises
| |
| − | nothing at all, unless it be hypothesis to say that all
| |
| − | specification came about in some sense, and is not to be
| |
| − | <span class='pageno' id='Page_200'>200</span>accepted as unaccountable. To undertake to account for
| |
| − | anything by saying boldly that it is due to chance would,
| |
| − | indeed, be futile. But this I do not do. I make use of
| |
| − | chance chiefly to make room for a principle of generalization,
| |
| − | or tendency to form habits, which I hold has produced
| |
| − | all regularities. The mechanical philosopher leaves the
| |
| − | whole specification of the world utterly unaccounted for,
| |
| − | which is pretty nearly as bad as to boldly attribute it to
| |
| − | chance. I attribute it altogether to chance, it is true, but
| |
| − | to chance in the form of a spontaneity which is to some
| |
| − | degree regular. It seems to me clear at any rate that one
| |
| − | of these two positions must be taken, or else specification
| |
| − | must be supposed due to a spontaneity which develops itself
| |
| − | in a certain and not in a chance way, by an objective logic
| |
| − | like that of Hegel. This last way I leave as an open possibility,
| |
| − | for the present; for it is as much opposed to the
| |
| − | necessitarian scheme of existence as my own theory is.</p>
| |
| − |
| |
| − | <p class='c005'>Secondly, the necessitarian may say there are, at any rate,
| |
| − | no observed phenomena which the hypothesis of chance
| |
| − | could aid in explaining. In reply, I point first to the phenomenon
| |
| − | of growth and developing complexity, which appears
| |
| − | to be universal, and which though it may possibly be
| |
| − | an affair of mechanism perhaps, certainly presents all the
| |
| − | appearance of increasing diversification. Then, there is
| |
| − | variety itself, beyond comparison the most obtrusive character
| |
| − | of the universe: no mechanism can account for this.
| |
| − | Then, there is the very fact the necessitarian most insists
| |
| − | upon, the regularity of the universe which for him serves
| |
| − | only to block the road of inquiry. Then, there are the
| |
| − | regular relationships between the laws of nature,—similarities
| |
| − | <span class='pageno' id='Page_201'>201</span>and comparative characters, which appeal to our
| |
| − | intelligence as its cousins, and call upon us for a reason.
| |
| − | Finally, there is consciousness, feeling, a patent fact enough,
| |
| − | but a very inconvenient one to the mechanical philosopher.</p>
| |
| − |
| |
| − | <p class='c005'>Thirdly, the necessitarian may say that chance is not a
| |
| − | <i>vera causa</i>, that we cannot know positively there is any
| |
| − | such element in the universe. But the doctrine of the <i>vera
| |
| − | causa</i> has nothing to do with elementary conceptions.
| |
| − | Pushed to that extreme, it at once cuts off belief in the
| |
| − | existence of a material universe; and without that necessitarianism
| |
| − | could hardly maintain its ground. Besides, variety
| |
| − | is a fact which must be admitted; and the theory of
| |
| − | chance merely consists in supposing this diversification does
| |
| − | not antedate all time. Moreover, the avoidance of hypotheses
| |
| − | involving causes nowhere positively known to act—is
| |
| − | only a recommendation of logic, not a positive command.
| |
| − | It cannot be formulated in any precise terms without
| |
| − | at once betraying its untenable character,—I mean as
| |
| − | rigid rule, for as a recommendation it is wholesome enough.</p>
| |
| − |
| |
| − | <p class='c005'>I believe I have thus subjected to fair examination all
| |
| − | the important reasons for adhering to the theory of universal
| |
| − | necessity, and have shown their nullity. I earnestly
| |
| − | beg that whoever may detect any flaw in my reasoning will
| |
| − | point it out to me, either privately or publicly; for if I am
| |
| − | wrong, it much concerns me to be set right speedily. If
| |
| − | my argument remains unrefuted, it will be time, I think, to
| |
| − | doubt the absolute truth of the principle of universal law;
| |
| − | and when once such a doubt has obtained a living root in
| |
| − | any man’s mind, my cause with him, I am persuaded, is
| |
| − | gained.</p>
| |
| − |
| |
| − | <div>
| |
| − | <span class='pageno' id='Page_202'>202</span>
| |
| − | <h3 id='chap2-3' class='c001'>III. THE LAW OF MIND<a id='r61' /><a href='#f61' class='c011'><sup>[61]</sup></a></h3>
| |
| − | </div>
| |
| − | <p class='c006'>In an article published in <i>The Monist</i> for January, 1891,
| |
| − | I endeavored to show what ideas ought to form the warp
| |
| − | of a system of philosophy, and particularly emphasized
| |
| − | that of absolute chance. In the number of April, 1892, I
| |
| − | argued further in favor of that way of thinking, which it
| |
| − | will be convenient to christen <i>tychism</i> (from τύχη, chance).
| |
| − | A serious student of philosophy will be in no haste to
| |
| − | accept or reject this doctrine; but he will see in it one of
| |
| − | the chief attitudes which speculative thought may take,
| |
| − | feeling that it is not for an individual, nor for an age, to
| |
| − | pronounce upon a fundamental question of philosophy.
| |
| − | That is a task for a whole era to work out. I have begun
| |
| − | by showing that <i>tychism</i> must give birth to an evolutionary
| |
| − | cosmology, in which all the regularities of nature and of
| |
| − | mind are regarded as products of growth, and to a Schelling-fashioned
| |
| − | idealism which holds matter to be mere specialized
| |
| − | and partially deadened mind. I may mention, for the benefit
| |
| − | of those who are curious in studying mental biographies,
| |
| − | that I was born and reared in the neighborhood of Concord,—I
| |
| − | mean in Cambridge,—at the time when Emerson,
| |
| − | Hedge, and their friends were disseminating the ideas that
| |
| − | they had caught from Schelling, and Schelling from Plotinus,
| |
| − | from Boehm, or from God knows what minds stricken with
| |
| − | the monstrous mysticism of the East. But the atmosphere
| |
| − | <span class='pageno' id='Page_203'>203</span>of Cambridge held many an antiseptic against Concord
| |
| − | transcendentalism; and I am not conscious of having contracted
| |
| − | any of that virus. Nevertheless, it is probable that
| |
| − | some cultured bacilli, some benignant form of the disease
| |
| − | was implanted in my soul, unawares, and that now, after
| |
| − | long incubation, it comes to the surface, modified by mathematical
| |
| − | conceptions and by training in physical investigations.</p>
| |
| − |
| |
| − | <p class='c005'>The next step in the study of cosmology must be to examine
| |
| − | the general law of mental action. In doing this, I
| |
| − | shall for the time drop my tychism out of view, in order to
| |
| − | allow a free and independent expansion to another conception
| |
| − | signalized in my first <i>Monist</i> paper as one of the
| |
| − | most indispensable to philosophy, though it was not there
| |
| − | dwelt upon; I mean the idea of continuity. The tendency
| |
| − | to regard continuity, in the sense in which I shall define it,
| |
| − | as an idea of prime importance in philosophy may conveniently
| |
| − | be termed <i>synechism</i>. The present paper is intended
| |
| − | chiefly to show what synechism is, and what it leads
| |
| − | to. I attempted, a good many years ago, to develop this
| |
| − | doctrine in the <i>Journal of Speculative Philosophy</i> (Vol. II.);
| |
| − | but I am able now to improve upon that exposition, in which
| |
| − | I was a little blinded by nominalistic prepossessions. I
| |
| − | refer to it, because students may possibly find that some
| |
| − | points not sufficiently explained in the present paper are
| |
| − | cleared up in those earlier ones.</p>
| |
| − | <h4 class='c012'>WHAT THE LAW IS</h4>
| |
| − | <p class='c006'>Logical analysis applied to mental phenomena shows that
| |
| − | there is but one law of mind, namely, that ideas tend to
| |
| − | <span class='pageno' id='Page_204'>204</span>spread continuously and to affect certain others which stand
| |
| − | to them in a peculiar relation of affectibility. In this
| |
| − | spreading they lose intensity, and especially the power of
| |
| − | affecting others, but gain generality and become welded with
| |
| − | other ideas.</p>
| |
| − |
| |
| − | <p class='c005'>I set down this formula at the beginning, for convenience;
| |
| − | and now proceed to comment upon it.</p>
| |
| − | <h4 class='c012'>INDIVIDUALITY OF IDEAS</h4>
| |
| − | <p class='c006'>We are accustomed to speak of ideas as reproduced, as
| |
| − | passed from mind to mind, as similar or dissimilar to one
| |
| − | another, and, in short, as if they were substantial things;
| |
| − | nor can any reasonable objection be raised to such expressions.
| |
| − | But taking the word “idea” in the sense of an
| |
| − | event in an individual consciousness, it is clear that an idea
| |
| − | once past is gone forever, and any supposed recurrence of
| |
| − | it is another idea. These two ideas are not present in the
| |
| − | same state of consciousness, and therefore cannot possibly
| |
| − | be compared. To say, therefore, that they are similar can
| |
| − | only mean that an occult power from the depths of the soul
| |
| − | forces us to connect them in our thoughts after they are
| |
| − | both no more. We may note, here, in passing, that of the
| |
| − | two generally recognized principles of association, contiguity
| |
| − | and similarity, the former is a connection due to a power
| |
| − | without, the latter a connection due to a power within.</p>
| |
| − |
| |
| − | <p class='c005'>But what can it mean to say that ideas wholly past are
| |
| − | thought of at all, any longer? They are utterly unknowable.
| |
| − | What distinct meaning can attach to saying that an
| |
| − | idea in the past in any way affects an idea in the future,
| |
| − | from which it is completely detached? A phrase between
| |
| − | <span class='pageno' id='Page_205'>205</span>the assertion and the denial of which there can in no case
| |
| − | be any sensible difference is mere gibberish.</p>
| |
| − |
| |
| − | <p class='c005'>I will not dwell further upon this point, because it is a
| |
| − | commonplace of philosophy.</p>
| |
| − | <h4 class='c012'>CONTINUITY OF IDEAS</h4>
| |
| − | <p class='c006'>We have here before us a question of difficulty, analogous
| |
| − | to the question of nominalism and realism. But when once
| |
| − | it has been clearly formulated, logic leaves room for one
| |
| − | answer only. How can a past idea be present? Can it
| |
| − | be present vicariously? To a certain extent, perhaps; but
| |
| − | not merely so; for then the question would arise how the
| |
| − | past idea can be related to its vicarious representation.
| |
| − | The relation, being between ideas, can only exist in some
| |
| − | consciousness: now that past idea was in no consciousness
| |
| − | but that past consciousness that alone contained it; and
| |
| − | that did not embrace the vicarious idea.</p>
| |
| − |
| |
| − | <p class='c005'>Some minds will here jump to the conclusion that a past
| |
| − | idea cannot in any sense be present. But that is hasty
| |
| − | and illogical. How extravagant, too, to pronounce our
| |
| − | whole knowledge of the past to be mere delusion! Yet it
| |
| − | would seem that the past is as completely beyond the
| |
| − | bounds of possible experience as a Kantian thing-in-itself.</p>
| |
| − |
| |
| − | <p class='c005'>How can a past idea be present? Not vicariously. Then,
| |
| − | only by direct perception. In other words, to be present,
| |
| − | it must be <i>ipso facto</i> present. That is, it cannot be wholly
| |
| − | past; it can only be going, infinitesimally past, less past
| |
| − | than any assignable past date. We are thus brought to
| |
| − | the conclusion that the present is connected with the past
| |
| − | by a series of real infinitesimal steps.</p>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_206'>206</span>It has already been suggested by psychologists that consciousness
| |
| − | necessarily embraces an interval of time. But
| |
| − | if a finite time be meant, the opinion is not tenable. If the
| |
| − | sensation that precedes the present by half a second were
| |
| − | still immediately before me, then, on the same principle
| |
| − | the sensation preceding that would be immediately present,
| |
| − | and so on <i>ad infinitum</i>. Now, since there is a time, say a
| |
| − | year, at the end of which an idea is no longer <i>ipso facto</i>
| |
| − | present, it follows that this is true of any finite interval,
| |
| − | however short.</p>
| |
| − |
| |
| − | <p class='c005'>But yet consciousness must essentially cover an interval
| |
| − | of time; for if it did not, we could gain no knowledge of
| |
| − | time, and not merely no veracious cognition of it, but no
| |
| − | conception whatever. We are, therefore, forced to say
| |
| − | that we are immediately conscious through an infinitesimal
| |
| − | interval of time.</p>
| |
| − |
| |
| − | <p class='c005'>This is all that is requisite. For, in this infinitesimal
| |
| − | interval, not only is consciousness continuous in a subjective
| |
| − | sense, that is, considered as a subject or substance
| |
| − | having the attribute of duration; but also, because it is
| |
| − | immediate consciousness, its object is <i>ipso facto</i> continuous.
| |
| − | In fact, this infinitesimally spread-out consciousness is a
| |
| − | direct feeling of its contents as spread out. This will be
| |
| − | further elucidated below. In an infinitesimal interval we
| |
| − | directly perceive the temporal sequence of its beginning,
| |
| − | middle, and end,—not, of course, in the way of recognition,
| |
| − | for recognition is only of the past, but in the way of
| |
| − | immediate feeling. Now upon this interval follows another,
| |
| − | whose beginning is the middle of the former, and whose
| |
| − | middle is the end of the former. Here, we have an immediate
| |
| − | <span class='pageno' id='Page_207'>207</span>perception of the temporal sequence of its beginning,
| |
| − | middle, and end, or say of the second, third, and
| |
| − | fourth instants. From these two immediate perceptions,
| |
| − | we gain a mediate, or inferential, perception of the relation
| |
| − | of all four instants. This mediate perception is objectively,
| |
| − | or as to the object represented, spread over the four instants;
| |
| − | but subjectively, or as itself the subject of duration,
| |
| − | it is completely embraced in the second moment. (The
| |
| − | reader will observe that I use the word <i>instant</i> to mean a
| |
| − | point of time, and <i>moment</i> to mean an infinitesimal duration.)
| |
| − | If it is objected that, upon the theory proposed,
| |
| − | we must have more than a mediate perception of the succession
| |
| − | of the four instants, I grant it; for the sum of the two
| |
| − | infinitesimal intervals is itself infinitesimal, so that it is
| |
| − | immediately perceived. It is immediately perceived in the
| |
| − | whole interval, but only mediately perceived in the last two-thirds
| |
| − | of the interval. Now, let there be an indefinite
| |
| − | succession of these inferential acts of comparative perception;
| |
| − | and it is plain that the last moment will contain objectively
| |
| − | the whole series. Let there be, not merely an
| |
| − | indefinite succession, but a continuous flow of inference
| |
| − | through a finite time; and the result will be a mediate objective
| |
| − | consciousness of the whole time in the last moment.
| |
| − | In this last moment, the whole series will be recognized,
| |
| − | or known as known before, except only the last moment,
| |
| − | which of course will be absolutely unrecognizable to itself.
| |
| − | Indeed, even this last moment will be recognized like the
| |
| − | rest, or, at least, be just beginning to be so. There is a
| |
| − | little <i>elenchus</i>, or appearance of contradiction, here, which
| |
| − | the ordinary logic of reflection quite suffices to resolve.</p>
| |
| − | <div>
| |
| − | <span class='pageno' id='Page_208'>208</span>
| |
| − | <h4 class='c012'>INFINITY AND CONTINUITY, IN GENERAL</h4>
| |
| − | </div>
| |
| − | <p class='c006'>Most of the mathematicians who during the last two
| |
| − | generations have treated the differential calculus have been
| |
| − | of the opinion that an infinitesimal quantity is an absurdity;
| |
| − | although, with their habitual caution, they have often added
| |
| − | “or, at any rate, the conception of an infinitesimal is so
| |
| − | difficult, that we practically cannot reason about it with
| |
| − | confidence and security.” Accordingly, the doctrine of
| |
| − | limits has been invented to evade the difficulty, or, as some
| |
| − | say, to explain the signification of the word “infinitesimal.”
| |
| − | This doctrine, in one form or another, is taught in all the
| |
| − | text-books, though in some of them only as an alternative
| |
| − | view of the matter; it answers well enough the purposes of
| |
| − | calculation, though even in that application it has its
| |
| − | difficulties.</p>
| |
| − |
| |
| − | <p class='c005'>The illumination of the subject by a strict notation for
| |
| − | the logic of relatives had shown me clearly and evidently
| |
| − | that the idea of an infinitesimal involves no contradiction,
| |
| − | before I became acquainted with the writings of Dr. Georg
| |
| − | Cantor (though many of these had already appeared in the
| |
| − | <i>Mathematische Annalen</i> and in <i>Borchardt’s Journal</i>, if not
| |
| − | yet in the <i>Acta Mathematica</i>, all mathematical journals of
| |
| − | the first distinction), in which the same view is defended
| |
| − | with extraordinary genius and penetrating logic.</p>
| |
| − |
| |
| − | <p class='c005'>The prevalent opinion is that finite numbers are the only
| |
| − | ones that we can reason about, at least, in any ordinary
| |
| − | mode of reasoning, or, as some authors express it, they are
| |
| − | the only numbers that can be reasoned about mathematically.
| |
| − | But this is an irrational prejudice. I long ago
| |
| − | <span class='pageno' id='Page_209'>209</span>showed that finite collections are distinguished from infinite
| |
| − | ones only by one circumstance and its consequences, namely,
| |
| − | that to them is applicable a peculiar and unusual mode of
| |
| − | reasoning called by its discoverer, De Morgan, the “syllogism
| |
| − | of transposed quantity.”</p>
| |
| − |
| |
| − | <p class='c005'>Balzac, in the introduction of his <i>Physiologie du mariage</i>,
| |
| − | remarks that every young Frenchman boasts of having seduced
| |
| − | some Frenchwoman. Now, as a woman can only be
| |
| − | seduced once, and there are no more Frenchwomen than
| |
| − | Frenchmen, it follows, if these boasts are true, that no
| |
| − | French women escape seduction. If their number be
| |
| − | finite, the reasoning holds. But since the population is continually
| |
| − | increasing, and the seduced are on the average
| |
| − | younger than the seducers, the conclusion need not be true.
| |
| − | In like manner, De Morgan, as an actuary, might have
| |
| − | argued that if an insurance company pays to its insured on
| |
| − | an average more than they have ever paid it, including
| |
| − | interest, it must lose money. But every modern actuary
| |
| − | would see a fallacy in that, since the business is continually
| |
| − | on the increase. But should war, or other cataclysm, cause
| |
| − | the class of insured to be a finite one, the conclusion would
| |
| − | turn out painfully correct, after all. The above two reasonings
| |
| − | are examples of the syllogism of transposed quantity.</p>
| |
| − |
| |
| − | <p class='c005'>The proposition that finite and infinite collections are
| |
| − | distinguished by the applicability to the former of the syllogism
| |
| − | of transposed quantity ought to be regarded as the
| |
| − | basal one of scientific arithmetic.</p>
| |
| − |
| |
| − | <p class='c005'>If a person does not know how to reason logically, and
| |
| − | I must say that a great many fairly good mathematicians,—yea,
| |
| − | distinguished ones,—fall under this category, but
| |
| − | <span class='pageno' id='Page_210'>210</span>simply uses a rule of thumb in blindly drawing inferences
| |
| − | like other inferences that have turned out well, he will, of
| |
| − | course, be continually falling into error about infinite numbers.
| |
| − | The truth is such people do not reason, at all. But
| |
| − | for the few who do reason, reasoning about infinite numbers
| |
| − | is easier than about finite numbers, because the complicated
| |
| − | syllogism of transposed quantity is not called for. For
| |
| − | example, that the whole is greater than its part is not an
| |
| − | axiom, as that eminently bad reasoner, Euclid, made it to
| |
| − | be. It is a theorem readily proved by means of a syllogism
| |
| − | of transposed quantity, but not otherwise. Of finite collections
| |
| − | it is true, of infinite collections false. Thus, a part
| |
| − | of the whole numbers are even numbers. Yet the even
| |
| − | numbers are no fewer than all the numbers; an evident
| |
| − | proposition since if every number in the whole series of
| |
| − | whole numbers be doubled, the result will be the series of
| |
| − | even numbers.</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'>1, 2, 3, 4, 5, 6, etc.</div>
| |
| − | <div class='line'>2, 4, 6, 8, 10, 12, etc.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>So for every number there is a distinct even number. In
| |
| − | fact, there are as many distinct doubles of numbers as there
| |
| − | are of distinct numbers. But the doubles of numbers are
| |
| − | all even numbers.</p>
| |
| − |
| |
| − | <p class='c005'>In truth, of infinite collections there are but two grades
| |
| − | of magnitude, the <i>endless</i> and the <i>innumerable</i>. Just as a
| |
| − | finite collection is distinguished from an infinite one by the
| |
| − | applicability to it of a special mode of reasoning, the syllogism
| |
| − | of transposed quantity, so, as I showed in the paper
| |
| − | last referred to, a numerable collection is distinguished from
| |
| − | an innumerable one by the applicability to it of a certain
| |
| − | <span class='pageno' id='Page_211'>211</span>mode of reasoning, the Fermatian inference, or, as it is
| |
| − | sometimes improperly termed, “mathematical induction.”</p>
| |
| − |
| |
| − | <p class='c005'>As an example of this reasoning, Euler’s demonstration
| |
| − | of the binomial theorem for integral powers may be given.
| |
| − | The theorem is that (<i>x</i> + <i>y</i>)<sup>n</sup>, where <i>n</i> is a whole number,
| |
| − | may be expanded into the sum of a series of terms of which
| |
| − | the first is <i>x</i><sup>n</sup><i>y</i><sup>o</sup> and each of the others is derived from the
| |
| − | next preceding by diminishing the exponent of <i>x</i> by 1 and
| |
| − | multiplying by that exponent and at the same time increasing
| |
| − | the exponent of <i>y</i> by 1 and dividing by that increased
| |
| − | exponent. Now, suppose this proposition to be true for a
| |
| − | certain exponent, <i>n</i> = <i>M</i>, then it must also be true for
| |
| − | <i>n</i> = <i>M</i> + 1. For let one of the terms in the expansion of
| |
| − | (<i>x</i> + <i>y</i>)<sup>M</sup> be written A<i>x<sup>p</sup></i><i>y<sup>q</sup></i>. Then, this term with the two
| |
| − | following will be</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'>A<i>x<sup>p</sup></i><i>y<sup>q</sup></i> + A <i>p</i>/(<i>q</i> + 1) <i>x</i><sup><i>p</i> - 1</sup> <i>y</i><sup><i>q</i> + 1</sup> + A <i>p</i>/(<i>q</i> + 1) (<i>p</i> - 1)/(<i>q</i> + 2) <i>x</i><sup><i>p</i> - 2</sup> <i>y</i><sup><i>q</i> + 2</sup></div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>Now, when (<i>x</i> + <i>y</i>)<sup>M</sup> is multiplied by <i>x</i> + <i>y</i> to give (<i>x</i> + <i>y</i>)<sup>M + 1</sup>,
| |
| − | we multiply first by <i>x</i> and then by <i>y</i> instead of by <i>x</i> and add
| |
| − | the two results. When we multiply by <i>x</i>, the second of the
| |
| − | above three terms will be the only one giving a term involving
| |
| − | <i>x<sup>p</sup></i><i>y</i><sup><i>q</i> + 1</sup> and the third will be the only one giving a term in
| |
| − | <i>x</i><sup><i>p</i> - 1</sup><i>y</i><sup><i>q</i> + 2</sup>; and when we multiply by y the first will be the only
| |
| − | term giving a term in <i>x<sup>p</sup></i><i>y</i><sup><i>q</i> + 1</sup>, and the second will be the only
| |
| − | term giving a term in <i>x</i><sup><i>p</i> - 1</sup><i>y</i><sup><i>q</i> + 2</sup>. Hence, adding like terms, we
| |
| − | find that the coefficient of <i>x<sup>p</sup></i><i>y</i><sup><i>q</i> + 1</sup> in the expansion of (<i>x</i> + <i>y</i>)<sup>M + 1</sup>
| |
| − | will be the sum of the coefficients of the first two of the above
| |
| − | three terms, and that the coefficient of <i>x</i><sup><i>p</i> - 1</sup><i>y</i><sup><i>q</i> + 2</sup> will be the
| |
| − | sum of the coefficients of the last two terms. Hence, two
| |
| − | successive terms in the expansion of (<i>x</i> + <i>y</i>)<sup>M + 1</sup> will be</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'><span class='pageno' id='Page_212'>212</span>A[1 + (<i>p</i>/(<i>q</i> + 1))]<i>x<sup>p</sup></i><i>y</i><sup><i>q</i>+1</sup> + A(<i>p</i>/(<i>q</i> + 1))[1+ ((<i>p</i> - 1)/(<i>q</i> + 2))]<i>x</i><sup><i>p</i>-1</sup><i>y</i><sup><i>q</i>+2</sup></div>
| |
| − | <div class='line'>= A((<i>p</i> + <i>q</i> + 1)/(<i>q</i> + 1))<i>x<sup>p</sup></i><i>y</i><sup><i>q</i>+1</sup> + A((<i>p</i> + <i>q</i> + 1)/(<i>q</i> + 1))(<i>p</i>/(<i>q</i> + 2))<i>x</i><sup><i>p</i>-1</sup><i>y</i>{<i>q</i>+2}</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>It is, thus, seen that the succession of terms follows the rule.
| |
| − | Thus if any integral power follows the rule, so also does
| |
| − | the next higher power. But the first power obviously
| |
| − | follows the rule. Hence, all powers do so.</p>
| |
| − |
| |
| − | <p class='c005'>Such reasoning holds good of any collection of objects
| |
| − | capable of being ranged in a series which though it may be
| |
| − | endless, can be numbered so that each member of it receives
| |
| − | a definite integral number. For instance, all the
| |
| − | whole numbers constitute such a numerable collection.
| |
| − | Again, all numbers resulting from operating according to
| |
| − | any definite rule with any finite number of whole numbers
| |
| − | form such a collection. For they may be arranged
| |
| − | in a series thus. Let F be the symbol of operation. First
| |
| − | operate on 1, giving F(1). Then, operate on a second 1,
| |
| − | giving F(1,1). Next, introduce 2, giving 3rd, F(2); 4th
| |
| − | F(2,1); 5th, F(1,2); 6th, F(2,2). Next use a third variable
| |
| − | giving 7th, F(1,1,1); 8th, F(2,1,1); 9th, F(1,2,1);
| |
| − | 10th, F(2,2,1); 11th, F(1,1,2); 12th, F(2,1,2); 13th,
| |
| − | F(1,2,2); 14th, F(2,2,2). Next introduce 3, and so on,
| |
| − | alternately introducing new variables and new figures; and
| |
| − | in this way it is plain that every arrangement of integral
| |
| − | values of the variables will receive a numbered place in
| |
| − | the series.<a id='r62' /><a href='#f62' class='c011'><sup>[62]</sup></a></p>
| |
| − |
| |
| − | <p class='c005'>The class of endless but numerable collections (so called
| |
| − | because they can be so ranged that to each one corresponds
| |
| − | <span class='pageno' id='Page_213'>213</span>a distinct whole number) is very large. But there are
| |
| − | collections which are certainly innumerable. Such is the
| |
| − | collection of all numbers to which endless series of decimals
| |
| − | are capable of approximating. It has been recognized since
| |
| − | the time of Euclid that certain numbers are surd or incommensurable,
| |
| − | and are not exactly expressible by any finite
| |
| − | series of decimals, nor by a circulating decimal. Such is
| |
| − | the ratio of the circumference of a circle to its diameter,
| |
| − | which we know is nearly 3.1415926. The calculation of
| |
| − | this number has been carried to over 700 figures without
| |
| − | the slightest appearance of regularity in their sequence.
| |
| − | The demonstrations that this and many other numbers are
| |
| − | incommensurable are perfect. That the entire collection of
| |
| − | incommensurable numbers is innumerable has been clearly
| |
| − | proved by Cantor. I omit the demonstration; but it is easy
| |
| − | to see that to discriminate one from some other would, in
| |
| − | general, require the use of an endless series of numbers.
| |
| − | Now if they cannot be exactly expressed and discriminated,
| |
| − | clearly they cannot be ranged in a linear series.</p>
| |
| − |
| |
| − | <p class='c005'>It is evident that there are as many points on a line or in
| |
| − | an interval of time as there are of real numbers in all.
| |
| − | These are, therefore, innumerable collections. Many mathematicians
| |
| − | have incautiously assumed that the points on a
| |
| − | surface or in a solid are more than those on a line. But
| |
| − | this has been refuted by Cantor. Indeed, it is obvious that
| |
| − | for every set of values of coördinates there is a single distinct
| |
| − | number. Suppose, for instance, the values of the coordinates
| |
| − | all lie between 0 and + 1. Then if we compose
| |
| − | a number by putting in the first decimal place the first figure
| |
| − | of the first coördinate, in the second the first figure of the
| |
| − | <span class='pageno' id='Page_214'>214</span>second coördinate, and so on, and when the first figures are
| |
| − | all dealt out go on to the second figures in like manner,
| |
| − | it is plain that the values of the coördinates can be read off
| |
| − | from the single resulting number, so that a triad or tetrad of
| |
| − | numbers, each having innumerable values, has no more
| |
| − | values than a single incommensurable number.</p>
| |
| − |
| |
| − | <p class='c005'>Were the number of dimensions infinite, this would fail;
| |
| − | and the collection of infinite sets of numbers having each
| |
| − | innumerable variations, might, therefore, be greater than
| |
| − | the simple innumerable collection, and might be called
| |
| − | <i>endlessly infinite</i>. The single individuals of such a collection
| |
| − | could not, however, be designated, even approximately,
| |
| − | so that this is indeed a magnitude concerning which it would
| |
| − | be possible to reason only in the most general way, if at all.</p>
| |
| − |
| |
| − | <p class='c005'>Although there are but two grades of magnitudes of infinite
| |
| − | collections, yet when certain conditions are imposed
| |
| − | upon the order in which individuals are taken, distinctions
| |
| − | of magnitude arise from that cause. Thus, if a simply
| |
| − | endless series be doubled by separating each unit into two
| |
| − | parts, the successive first parts and also the second parts
| |
| − | being taken in the same order as the units from which they
| |
| − | are derived, this double endless series will, so long as it is
| |
| − | taken in that order, appear as twice as large as the original
| |
| − | series. In like manner the product of two innumerable
| |
| − | collections, that is, the collection of possible pairs composed
| |
| − | of one individual of each, if the order of continuity is to be
| |
| − | maintained, is, by virtue of that order, infinitely greater
| |
| − | than either of the component collections.</p>
| |
| − |
| |
| − | <p class='c005'>We now come to the difficult question. What is continuity?
| |
| − | Kant confounds it with infinite divisibility, saying
| |
| − | <span class='pageno' id='Page_215'>215</span>that the essential character of a continuous series is that
| |
| − | between any two members of it a third can always be found.
| |
| − | This is an analysis beautifully clear and definite; but unfortunately,
| |
| − | it breaks down under the first test. For according
| |
| − | to this, the entire series of rational fractions arranged
| |
| − | in the order of their magnitude, would be an infinite
| |
| − | series, although the rational fractions are numerable, while
| |
| − | the points of a line are innumerable. Nay, worse yet, if
| |
| − | from that series of fractions any two with all that lie between
| |
| − | them be excised, and any number of such finite gaps
| |
| − | be made, Kant’s definition is still true of the series, though
| |
| − | it has lost all appearance of continuity.</p>
| |
| − |
| |
| − | <p class='c005'>Cantor defines a continuous series as one which is <i>concatenated</i>
| |
| − | and <i>perfect</i>. By a concatenated series, he means
| |
| − | such a one that if any two points are given in it, and any
| |
| − | finite distance, however small, it is possible to proceed from
| |
| − | the first point to the second through a succession of points
| |
| − | of the series each at a distance from the preceding one less
| |
| − | than the given distance. This is true of the series of rational
| |
| − | fractions ranged in the order of their magnitude.
| |
| − | By a perfect series, he means one which contains every
| |
| − | point such that there is no distance so small that this point
| |
| − | has not an infinity of points of the series within that distance
| |
| − | of it. This is true of the series of numbers between
| |
| − | 0 and 1 capable of being expressed by decimals in which
| |
| − | only the digits 0 and 1 occur.</p>
| |
| − |
| |
| − | <p class='c005'>It must be granted that Cantor’s definition includes every
| |
| − | series that is continuous; nor can it be objected that it
| |
| − | includes any important or indubitable case of a series not
| |
| − | continuous. Nevertheless, it has some serious defects. In
| |
| − | <span class='pageno' id='Page_216'>216</span>the first place, it turns upon metrical considerations; while
| |
| − | the distinction between a continuous and a discontinuous
| |
| − | series is manifestly non-metrical. In the next place, a perfect
| |
| − | series is defined as one containing “every point” of
| |
| − | a certain description. But no positive idea is conveyed of
| |
| − | what all the points are: that is definition by negation, and
| |
| − | cannot be admitted. If that sort of thing were allowed,
| |
| − | it would be very easy to say, at once, that the continuous
| |
| − | linear series of points is one which contains every point of
| |
| − | the line between its extremities. Finally, Cantor’s definition
| |
| − | does not convey a distinct notion of what the components
| |
| − | of the conception of continuity are. It ingeniously
| |
| − | wraps up its properties in two separate parcels, but does not
| |
| − | display them to our intelligence.</p>
| |
| − |
| |
| − | <p class='c005'>Kant’s definition expresses one simple property of a continuum;
| |
| − | but it allows of gaps in the series. To mend the
| |
| − | definition, it is only necessary to notice how these gaps can
| |
| − | occur. Let us suppose, then, a linear series of points extending
| |
| − | from a point, <i>A</i>, to a point, <i>B</i>, having a gap from
| |
| − | <i>B</i> to a third point, <i>C</i>, and thence extending to a final limit,
| |
| − | <i>D</i>; and let us suppose this series conforms to Kant’s definition.
| |
| − | Then, of the two points, <i>B</i> and <i>C</i>, one or both must
| |
| − | be excluded from the series; for otherwise, by the definition,
| |
| − | there would be points between them. That is, if the series
| |
| − | contains <i>C</i>, though it contains all the points up to <i>B</i>, it cannot
| |
| − | contain <i>B</i>. What is required, therefore, is to state in
| |
| − | non-metrical terms that if a series of points up to a limit
| |
| − | is included in a continuum the limit is included. It may
| |
| − | be remarked that this is the property of a continuum to
| |
| − | which Aristotle’s attention seems to have been directed
| |
| − | <span class='pageno' id='Page_217'>217</span>when he defines a continuum as something whose parts
| |
| − | have a common limit. The property may be exactly stated
| |
| − | as follows: If a linear series of points is continuous between
| |
| − | two points, <i>A</i> and <i>D</i>, and if an endless series of
| |
| − | points be taken, the first of them between <i>A</i> and <i>D</i> and
| |
| − | each of the others between the last preceding one and <i>D</i>,
| |
| − | then there is a point of the continuous series between all
| |
| − | that endless series of points and <i>D</i>, and such that every
| |
| − | other point of which this is true lies between this point
| |
| − | and <i>D</i>. For example, take any number between 0 and 1,
| |
| − | as 0.1; then, any number between 0.1 and 1, as 0.11; then
| |
| − | any number between 0.11 and 1, as 0.111; and so on, without
| |
| − | end. Then, because the series of real numbers between
| |
| − | 0 and 1 is continuous, there must be a <i>least</i> real
| |
| − | number, greater than every number of that endless series.
| |
| − | This property, which may be called the Aristotelicity of the
| |
| − | series, together with Kant’s property, or its Kanticity,
| |
| − | completes the definition of a continuous series.</p>
| |
| − |
| |
| − | <p class='c005'>The property of Aristotelicity may be roughly stated
| |
| − | thus: a continuum contains the end point belonging to every
| |
| − | endless series of points which it contains. An obvious
| |
| − | corollary is that every continuum contains its limits. But
| |
| − | in using this principle it is necessary to observe that a series
| |
| − | may be continuous except in this, that it omits one or both
| |
| − | of the limits.</p>
| |
| − |
| |
| − | <p class='c005'>Our ideas will find expression more conveniently if, instead
| |
| − | of points upon a line, we speak of real numbers.
| |
| − | Every real number is, in one sense, the limit of a series,
| |
| − | for it can be indefinitely approximated to. Whether every
| |
| − | real number is a limit of a <i>regular</i> series may perhaps be
| |
| − | <span class='pageno' id='Page_218'>218</span>open to doubt. But the series referred to in the definition
| |
| − | of Aristotelicity must be understood as including all series
| |
| − | whether regular or not. Consequently, it is implied that
| |
| − | between any two points an innumerable series of points
| |
| − | can be taken.</p>
| |
| − |
| |
| − | <p class='c005'>Every number whose expression in decimals requires but
| |
| − | a finite number of places of decimals is commensurable.
| |
| − | Therefore, incommensurable numbers suppose an infinitieth
| |
| − | place of decimals. The word infinitesimal is simply the
| |
| − | Latin form of infinitieth; that is, it is an ordinal formed
| |
| − | from <i>infinitum</i>, as centesimal from <i>centum</i>. Thus, continuity
| |
| − | supposes infinitesimal quantities. There is nothing
| |
| − | contradictory about the idea of such quantities. In adding
| |
| − | and multiplying them the continuity must not be broken up,
| |
| − | and consequently they are precisely like any other quantities,
| |
| − | except that neither the syllogism of transposed
| |
| − | quantity, nor the Fermatian inference applies to them.</p>
| |
| − |
| |
| − | <p class='c005'>If A is a finite quantity and <i>i</i> an infinitesimal, then in a
| |
| − | certain sense we may write A + <i>i</i> = A. That is to say,
| |
| − | this is so for all purposes of measurement. But this principle
| |
| − | must not be applied except to get rid of <i>all</i> the terms
| |
| − | in the highest order of infinitesimals present. As a mathematician,
| |
| − | I prefer the method of infinitesimals to that of
| |
| − | limits, as far easier and less infested with snares. Indeed,
| |
| − | the latter, as stated in some books, involves propositions
| |
| − | that are false; but this is not the case with the forms of
| |
| − | the method used by Cauchy, Duhamel, and others. As they
| |
| − | understand the doctrine of limits, it involves the notion of
| |
| − | continuity, and, therefore, contains in another shape the
| |
| − | very same ideas as the doctrine of infinitesimals.</p>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_219'>219</span>Let us now consider an aspect of the Aristotelical principle
| |
| − | which is particularly important in philosophy. Suppose
| |
| − | a surface to be part red and part blue; so that every
| |
| − | point on it is either red or blue, and, of course, no part
| |
| − | can be both red and blue. What, then, is the color of the
| |
| − | boundary line between the red and the blue? The answer
| |
| − | is that red or blue, to exist at all, must be spread over a
| |
| − | surface; and the color of the surface is the color of the
| |
| − | surface in the immediate neighborhood of the point. I
| |
| − | purposely use a vague form of expression. Now, as the
| |
| − | parts of the surface in the immediate neighborhood of any
| |
| − | ordinary point upon a curved boundary are half of them
| |
| − | red and half blue, it follows that the boundary is half red
| |
| − | and half blue. In like manner, we find it necessary to
| |
| − | hold that consciousness essentially occupies time; and what
| |
| − | is present to the mind at any ordinary instant, is what is
| |
| − | present during a moment in which that instant occurs.
| |
| − | Thus, the present is half past and half to come. Again,
| |
| − | the color of the parts of a surface at any finite distance
| |
| − | from a point, has nothing to do with its color just at that
| |
| − | point; and, in the parallel, the feeling at any finite interval
| |
| − | from the present has nothing to do with the present feeling,
| |
| − | except vicariously. Take another case: the velocity of a
| |
| − | particle at any instant of time is its mean velocity during
| |
| − | an infinitesimal instant in which that time is contained.
| |
| − | Just so my immediate feeling is my feeling through an infinitesimal
| |
| − | duration containing the present instant.</p>
| |
| − | <div>
| |
| − | <span class='pageno' id='Page_220'>220</span>
| |
| − | <h4 class='c012'>ANALYSIS OF TIME</h4>
| |
| − | </div>
| |
| − | <p class='c006'>One of the most marked features about the law of mind
| |
| − | is that it makes time to have a definite direction of flow
| |
| − | from past to future. The relation of past to future is, in
| |
| − | reference to the law of mind, different from the relation of
| |
| − | future to past. This makes one of the great contrasts between
| |
| − | the law of mind and the law of physical force, where
| |
| − | there is no more distinction between the two opposite directions
| |
| − | in time than between moving northward and moving
| |
| − | southward.</p>
| |
| − |
| |
| − | <p class='c005'>In order, therefore, to analyze the law of mind, we must
| |
| − | begin by asking what the flow of time consists in. Now,
| |
| − | we find that in reference to any individual state of feeling,
| |
| − | all others are of two classes, those which affect this one
| |
| − | (or have a tendency to affect it, and what this means we
| |
| − | shall inquire shortly), and those which do not. The present
| |
| − | is affectible by the past but not by the future.</p>
| |
| − |
| |
| − | <p class='c005'>Moreover, if state <i>A</i> is affected by state <i>B</i>, and state <i>B</i>
| |
| − | by state <i>C</i>, then <i>A</i> is affected by state <i>C</i>, though not so much
| |
| − | so. It follows, that if <i>A</i> is affectible by <i>B</i>, <i>B</i> is not affectible
| |
| − | by <i>A</i>.</p>
| |
| − |
| |
| − | <p class='c005'>If, of two states, each is absolutely unaffectible by the
| |
| − | other, they are to be regarded as parts of the same state.
| |
| − | They are contemporaneous.</p>
| |
| − |
| |
| − | <p class='c005'>To say that a state is <i>between</i> two states means that it
| |
| − | affects one and is affected by the other. Between any two
| |
| − | states in this sense lies an innumerable series of states affecting
| |
| − | one another; and if a state lies between a given state
| |
| − | and any other state which can be reached by inserting
| |
| − | <span class='pageno' id='Page_221'>221</span>states between this state and any third state, these inserted
| |
| − | states not immediately affecting or being affected by either,
| |
| − | then the second rate mentioned, immediately affects or is
| |
| − | affected by the first, in the sense that in the one the other is
| |
| − | <i>ipso facto</i> present in a reduced degree.</p>
| |
| − |
| |
| − | <p class='c005'>These propositions involve a definition of time and of its
| |
| − | flow. Over and above this definition they involve a doctrine,
| |
| − | namely, that every state of feeling is affectible by
| |
| − | every earlier state.</p>
| |
| − | <h4 class='c012'>THAT FEELINGS HAVE INTENSIVE CONTINUITY</h4>
| |
| − | <p class='c006'>Time with its continuity logically involves some other
| |
| − | kind of continuity than its own. Time, as the universal
| |
| − | form of change, cannot exist unless there is something to
| |
| − | undergo change, and to undergo a change continuous in
| |
| − | time, there must be a continuity of changeable qualities.
| |
| − | Of the continuity of intrinsic qualities of feeling we can now
| |
| − | form but a feeble conception. The development of the
| |
| − | human mind has practically extinguished all feelings, except
| |
| − | a few sporadic kinds, sound, colors, smells, warmth,
| |
| − | etc., which now appear to be disconnected and disparate.
| |
| − | In the case of colors, there is a tridimensional spread of
| |
| − | feelings. Originally, all feelings may have been connected
| |
| − | in the same way, and the presumption is that the number
| |
| − | of dimensions was endless. For development essentially
| |
| − | involves a limitation of possibilities. But given a number
| |
| − | of dimensions of feeling, all possible varieties are obtainable
| |
| − | by varying the intensities of the different elements. Accordingly,
| |
| − | time logically supposes a continuous range of intensity
| |
| − | in feeling. It follows, then, from the definition of
| |
| − | <span class='pageno' id='Page_222'>222</span>continuity, that when any particular kind of feeling is
| |
| − | present, an infinitesimal continuum of all feelings differing
| |
| − | infinitesimally from that is present.</p>
| |
| − | <h4 class='c012'>THAT FEELINGS HAVE SPATIAL EXTENSION</h4>
| |
| − | <p class='c006'>Consider a gob of protoplasm, say an amœba or a slime-mould.
| |
| − | It does not differ in any radical way from the
| |
| − | contents of a nerve-cell, though its functions may be less
| |
| − | specialized. There is no doubt that this slime-mould, or
| |
| − | this amœba, or at any rate some similar mass of protoplasm
| |
| − | feels. That is to say, it feels when it is in its excited condition.
| |
| − | But note how it behaves. When the whole is
| |
| − | quiescent and rigid, a place upon it is irritated. Just at
| |
| − | this point, an active motion is set up, and this gradually
| |
| − | spreads to other parts. In this action, no unity nor relation
| |
| − | to a nucleus, or other unitary organ can be discerned. It
| |
| − | is a mere amorphous continuum of protoplasm, with feeling
| |
| − | passing from one part to another. Nor is there anything
| |
| − | like a wave-motion. The activity does not advance to
| |
| − | new parts, just as fast as it leaves old parts. Rather, in
| |
| − | the beginning, it dies out at a slower rate than that at which
| |
| − | it spreads. And while the process is going on, by exciting
| |
| − | the mass at another point, a second quite independent state
| |
| − | of excitation will be set up. In some places, neither excitation
| |
| − | will exist, in others each separately, in still other
| |
| − | places, both effects will be added together. Whatever there
| |
| − | is in the whole phenomenon to make us think there is feeling
| |
| − | in such a mass of protoplasm,—<i>feeling</i>, but plainly no
| |
| − | <i>personality</i>,—goes logically to show that that feeling has
| |
| − | a subjective, or substantial, spatial extension, as the excited
| |
| − | <span class='pageno' id='Page_223'>223</span>state has. This is, no doubt, a difficult idea to seize, for
| |
| − | the reason that it is a subjective, not an objective, extension.
| |
| − | It is not that we have a feeling of bigness; though Professor
| |
| − | James, perhaps rightly, teaches that we have. It is
| |
| − | that the feeling, as a subject of inhesion, is big. Moreover,
| |
| − | our own feelings are focused in attention to such a degree
| |
| − | that we are not aware that ideas are not brought to an absolute
| |
| − | unity; just as nobody not instructed by special experiment
| |
| − | has any idea how very, very little of the field of
| |
| − | vision is distinct. Still, we all know how the attention
| |
| − | wanders about among our feelings; and this fact shows
| |
| − | that those feelings that are not co-ordinated in attention
| |
| − | have a reciprocal externality, although they are present at
| |
| − | the same time. But we must not tax introspection to make
| |
| − | a phenomenon manifest which essentially involves externality.</p>
| |
| − |
| |
| − | <p class='c005'>Since space is continuous, it follows that there must be
| |
| − | an immediate community of feeling between parts of mind
| |
| − | infinitesimally near together. Without this, I believe it
| |
| − | would have been impossible for minds external to one
| |
| − | another, ever to become co-ordinated, and equally impossible
| |
| − | for any coördination to be established in the action of
| |
| − | the nerve-matter of one brain.</p>
| |
| − | <h4 class='c012'>AFFECTIONS OF IDEAS</h4>
| |
| − | <p class='c006'>But we are met by the question what is meant by saying
| |
| − | that one idea affects another. The unravelment of this
| |
| − | problem requires us to trace out phenomena a little further.</p>
| |
| − |
| |
| − | <p class='c005'>Three elements go to make up an idea. The first is its
| |
| − | intrinsic quality as a feeling. The second is the energy
| |
| − | <span class='pageno' id='Page_224'>224</span>with which it affects other ideas, an energy which is infinite
| |
| − | in the here-and-nowness of immediate sensation, finite and
| |
| − | relative in the recency of the past. The third element is
| |
| − | the tendency of an idea to bring along other ideas with it.</p>
| |
| − |
| |
| − | <p class='c005'>As an idea spreads, its power of affecting other ideas gets
| |
| − | rapidly reduced; but its intrinsic quality remains nearly
| |
| − | unchanged. It is long years now since I last saw a cardinal
| |
| − | in his robes; and my memory of their color has become
| |
| − | much dimmed. The color itself, however, is not remembered
| |
| − | as dim. I have no inclination to call it a dull red.
| |
| − | Thus, the intrinsic quality remains little changed; yet
| |
| − | more accurate observation will show a slight reduction of
| |
| − | it. The third element, on the other hand, has increased.
| |
| − | As well as I can recollect, it seems to me the cardinals I
| |
| − | used to see wore robes more scarlet than vermillion is,
| |
| − | and highly luminous. Still, I know the color commonly
| |
| − | called cardinal is on the crimson side of vermillion and of
| |
| − | quite moderate luminosity, and the original idea calls up
| |
| − | so many other hues with it, and asserts itself so feebly, that
| |
| − | I am unable any longer to isolate it.</p>
| |
| − |
| |
| − | <p class='c005'>A finite interval of time generally contains an innumerable
| |
| − | series of feelings; and when these become welded together
| |
| − | in association, the result is a general idea. For we
| |
| − | have just seen how by continuous spreading an idea becomes
| |
| − | generalised.</p>
| |
| − |
| |
| − | <p class='c005'>The first character of a general idea so resulting is that
| |
| − | it is living feeling. A continuum of this feeling, infinitesimal
| |
| − | in duration, but still embracing innumerable parts,
| |
| − | and also, though infinitesimal, entirely unlimited, is immediately
| |
| − | present. And in its absence of boundedness a
| |
| − | <span class='pageno' id='Page_225'>225</span>vague possibility of more than is present is directly felt.</p>
| |
| − |
| |
| − | <p class='c005'>Second, in the presence of this continuity of feeling,
| |
| − | nominalistic maxims appear futile. There is no doubt
| |
| − | about one idea affecting another, when we can directly
| |
| − | perceive the one gradually modified and shaping itself into
| |
| − | the other. Nor can there any longer be any difficulty about
| |
| − | one idea resembling another, when we can pass along the
| |
| − | continuous field of quality from one to the other and back
| |
| − | again to the point which we had marked.</p>
| |
| − |
| |
| − | <div class='figcenter id003'>
| |
| − | <img src='images/fig7.png' alt='Fig. 7.' class='ig001' />
| |
| − | <div class='ic002'>
| |
| − | <p>Figure 7.</p>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c005'>Third, consider the insistency of an idea. The insistency
| |
| − | of a past idea with reference to the present is a quantity
| |
| − | which is less the further back that past idea is, and rises to
| |
| − | infinity as the past idea is brought up into coincidence with
| |
| − | the present. Here we must make one of those inductive
| |
| − | applications of the law of continuity which have produced
| |
| − | <span class='pageno' id='Page_226'>226</span>such great results in all the positive sciences. We must
| |
| − | extend the law of insistency into the future. Plainly, the
| |
| − | insistency of a future idea with reference to the present is a
| |
| − | quantity affected by the minus sign; for it is the present
| |
| − | that affects the future, if there be any effect, not the future
| |
| − | that affects the present. Accordingly, the curve of insistency
| |
| − | is a sort of equilateral hyperbola. (See the figure.)
| |
| − | Such a conception is none the less mathematical, that its
| |
| − | quantification cannot now be exactly specified.</p>
| |
| − |
| |
| − | <p class='c005'>Now consider the induction which we have here been led
| |
| − | into. This curve says that feeling which has not yet
| |
| − | emerged into immediate consciousness is already affectible
| |
| − | and already affected. In fact, this is habit, by virtue of
| |
| − | which an idea is brought up into present consciousness by
| |
| − | a bond that had already been established between it and
| |
| − | another idea while it was still <i>in futuro</i>.</p>
| |
| − |
| |
| − | <p class='c005'>We can now see what the affection of one idea by another
| |
| − | consists in. It is that the affected idea is attached
| |
| − | as a logical predicate to the affecting idea as subject. So
| |
| − | when a feeling emerges into immediate consciousness, it
| |
| − | always appears as a modification of a more or less general
| |
| − | object already in the mind. The word suggestion is well
| |
| − | adapted to expressing this relation. The future is suggested
| |
| − | by, or rather is influenced by the suggestions of, the past.</p>
| |
| − | <h4 class='c012'>IDEAS CANNOT BE CONNECTED EXCEPT BY CONTINUITY</h4>
| |
| − | <p class='c006'>That ideas can nowise be connected without continuity
| |
| − | is sufficiently evident to one who reflects upon the matter.
| |
| − | But still the opinion may be entertained that after continuity
| |
| − | has once made the connection of ideas possible,
| |
| − | <span class='pageno' id='Page_227'>227</span>then they may get to be connected in other modes than
| |
| − | through continuity. Certainly, I cannot see how anyone
| |
| − | can deny that the infinite diversity of the universe, which
| |
| − | we call chance, may bring ideas into proximity which are
| |
| − | not associated in one general idea. It may do this many
| |
| − | times. But then the law of continuous spreading will produce
| |
| − | a mental association; and this I suppose is an abridged
| |
| − | statement of the way the universe has been evolved. But
| |
| − | if I am asked whether a blind ἀνάγκη cannot bring ideas
| |
| − | together, first I point out that it would not remain blind.
| |
| − | There being a continuous connection between the ideas,
| |
| − | they would infallibly become associated in a living, feeling,
| |
| − | and perceiving general idea. Next, I cannot see what the
| |
| − | mustness or necessity of this ἁνάγκη would consist in.
| |
| − | In the absolute uniformity of the phenomenon, says the
| |
| − | nominalist. Absolute is well put in; for if it merely happened
| |
| − | so three times in succession, or three million times
| |
| − | in succession, in the absence of any reason, the coincidence
| |
| − | could only be attributed to chance. But absolute uniformity
| |
| − | must extend over the whole infinite future; and it
| |
| − | is idle to talk of that except as an idea. No; I think we
| |
| − | can only hold that wherever ideas come together they tend
| |
| − | to weld into general ideas; and wherever they are generally
| |
| − | connected, general ideas govern the connection; and these
| |
| − | general ideas are living feelings spread out.</p>
| |
| − | <h4 class='c012'>MENTAL LAW FOLLOWS THE FORMS OF LOGIC</h4>
| |
| − | <p class='c006'>The three main classes of logical inference are Deduction,
| |
| − | Induction, and Hypothesis. These correspond to three
| |
| − | chief modes of action of the human soul. In deduction the
| |
| − | <span class='pageno' id='Page_228'>228</span>mind is under the dominion of a habit or association by
| |
| − | virtue of which a general idea suggests in each case a corresponding
| |
| − | reaction. But a certain sensation is seen to involve
| |
| − | that idea. Consequently, that sensation is followed
| |
| − | by that reaction. That is the way the hind legs of a frog,
| |
| − | separated from the rest of the body, reason, when you
| |
| − | pinch them. It is the lowest form of psychical manifestation.</p>
| |
| − |
| |
| − | <p class='c005'>By induction, a habit becomes established. Certain sensations,
| |
| − | all involving one general idea, are followed each
| |
| − | by the same reaction; and an association becomes established,
| |
| − | whereby that general idea gets to be followed uniformly
| |
| − | by that reaction.</p>
| |
| − |
| |
| − | <p class='c005'>Habit is that specialization of the law of mind whereby
| |
| − | a general idea gains the power of exciting reactions. But
| |
| − | in order that the general idea should attain all its functionality,
| |
| − | it is necessary, also, that it should become suggestible
| |
| − | by sensations. That is accomplished by a psychical
| |
| − | process having the form of hypothetic inference. By hypothetic
| |
| − | inference, I mean, as I have explained in other writings,
| |
| − | an induction from qualities. For example, I know
| |
| − | that the kind of man known and classed as a “mugwump”
| |
| − | has certain characteristics. He has a high self-respect and
| |
| − | places great value upon social distinction. He laments the
| |
| − | great part that rowdyism and unrefined good-fellowship
| |
| − | play in the dealings of American politicians with their constituency.
| |
| − | He thinks that the reform which would follow
| |
| − | from the abandonment of the system by which the distribution
| |
| − | of offices is made to strengthen party organizations
| |
| − | and a return to the original and essential conception of
| |
| − | <span class='pageno' id='Page_229'>229</span>office-filling would be found an unmixed good. He holds
| |
| − | that monetary considerations should usually be the decisive
| |
| − | ones in questions of public policy. He respects the principle
| |
| − | of individualism and of <i>laissez-faire</i> as the greatest
| |
| − | agency of civilization. These views, among others, I know
| |
| − | to be obtrusive marks of a “mugwump.” Now, suppose
| |
| − | I casually meet a man in a railway-train, and falling into
| |
| − | conversation find that he holds opinions of this sort; I am
| |
| − | naturally led to suppose that he is a “mugwump.” That
| |
| − | is hypothetic inference. That is to say, a number of readily
| |
| − | verifiable marks of a mugwump being selected, I find this
| |
| − | man has these, and infer that he has all the other characters
| |
| − | which go to make a thinker of that stripe. Or let us suppose
| |
| − | that I meet a man of a semi-clerical appearance and
| |
| − | a sub-pharisaical sniff, who appears to look at things from
| |
| − | the point of view of a rather wooden dualism. He cites
| |
| − | several texts of scripture and always with particular attention
| |
| − | to their logical implications; and he exhibits a sternness,
| |
| − | almost amounting to vindictiveness, toward evil-doers,
| |
| − | in general. I readily conclude that he is a minister of a
| |
| − | certain denomination. Now the mind acts in a way similar
| |
| − | to this, every time we acquire a power of co-ordinating reactions
| |
| − | in a peculiar way, as in performing any act requiring
| |
| − | skill. Thus, most persons have a difficulty in moving
| |
| − | the two hands simultaneously and in opposite directions
| |
| − | through two parallel circles nearly in the medial plane of
| |
| − | the body. To learn to do this, it is necessary to attend,
| |
| − | first, to the different actions in different parts of the motion,
| |
| − | when suddenly a general conception of the action springs
| |
| − | up and it becomes perfectly easy. We think the motion
| |
| − | <span class='pageno' id='Page_230'>230</span>we are trying to do involves this action, and this, and this.
| |
| − | Then, the general idea comes which unites all those actions,
| |
| − | and thereupon the desire to perform the motion calls up
| |
| − | the general idea. The same mental process is many times
| |
| − | employed whenever we are learning to speak a language
| |
| − | or are acquiring any sort of skill.</p>
| |
| − |
| |
| − | <p class='c005'>Thus, by induction, a number of sensations followed by
| |
| − | one reaction become united under one general idea followed
| |
| − | by the same reaction; while by the hypothetic process, a
| |
| − | number of reactions called for by one occasion get united
| |
| − | in a general idea which is called out by the same occasion.
| |
| − | By deduction, the habit fulfils its function of calling out
| |
| − | certain reactions on certain occasions.</p>
| |
| − | <h4 class='c012'>UNCERTAINTY OF MENTAL ACTION</h4>
| |
| − | <p class='c006'>The inductive and hypothetic forms of inference are
| |
| − | essentially probable inferences, not necessary; while deduction
| |
| − | may be either necessary or probable.</p>
| |
| − |
| |
| − | <p class='c005'>But no mental action seems to be necessary or invariable
| |
| − | in its character. In whatever manner the mind has reacted
| |
| − | under a given sensation, in that manner it is the more likely
| |
| − | to react again; were this, however, an absolute necessity,
| |
| − | habits would become wooden and ineradicable, and no room
| |
| − | being left for the formation of new habits, intellectual life
| |
| − | would come to a speedy close. Thus, the uncertainty of
| |
| − | the mental law is no mere defect of it, but is on the contrary
| |
| − | of its essence. The truth is, the mind is not subject
| |
| − | to “law,” in the same rigid sense that matter is. It only
| |
| − | experiences gentle forces which merely render it more likely
| |
| − | to act in a given way than it otherwise would be. There
| |
| − | <span class='pageno' id='Page_231'>231</span>always remains a certain amount of arbitrary spontaneity
| |
| − | in its action, without which it would be dead.</p>
| |
| − |
| |
| − | <p class='c005'>Some psychologists think to reconcile the uncertainty of
| |
| − | reactions with the principle of necessary causation by means
| |
| − | of the law of fatigue. Truly for a <i>law</i>, this law of fatigue
| |
| − | is a little lawless. I think it is merely a case of the general
| |
| − | principle that an idea in spreading loses its insistency.
| |
| − | Put me tarragon into my salad, when I have not tasted it
| |
| − | for years, and I exclaim “What nectar is this!” But add
| |
| − | it to every dish I taste for week after week, and a habit of
| |
| − | expectation has been created; and in thus spreading into
| |
| − | habit, the sensation makes hardly any more impression upon
| |
| − | me; or, if it be noticed, it is on a new side from which it
| |
| − | appears as rather a bore. The doctrine that fatigue is one
| |
| − | of the primordial phenomena of mind I am much disposed
| |
| − | to doubt. It seems a somewhat little thing to be allowed
| |
| − | as an exception to the great principle of mental uniformization.
| |
| − | For this reason, I prefer to explain it in the manner
| |
| − | here indicated, as a special case of that great principle.
| |
| − | To consider it as something distinct in its nature, certainly
| |
| − | somewhat strengthens the necessitarian position; but even
| |
| − | if it be distinct, the hypothesis that all the variety and
| |
| − | apparent arbitrariness of mental action ought to be explained
| |
| − | away in favor of absolute determinism does not
| |
| − | seem to me to recommend itself to a sober and sound judgment,
| |
| − | which seeks the guidance of observed facts and not
| |
| − | that of prepossessions.</p>
| |
| − | <div>
| |
| − | <span class='pageno' id='Page_232'>232</span>
| |
| − | <h4 class='c012'>RESTATEMENT OF THE LAW</h4>
| |
| − | </div>
| |
| − | <p class='c006'>Let me now try to gather up all these odds and ends of
| |
| − | commentary and restate the law of mind, in a unitary way.</p>
| |
| − |
| |
| − | <p class='c005'>First, then, we find that when we regard ideas from a
| |
| − | nominalistic, individualistic, sensualistic way, the simplest
| |
| − | facts of mind become utterly meaningless. That one idea
| |
| − | should resemble another or influence another, or that one
| |
| − | state of mind should so much as be thought of in another is,
| |
| − | from that standpoint, sheer nonsense.</p>
| |
| − |
| |
| − | <p class='c005'>Second, by this and other means we are driven to perceive,
| |
| − | what is quite evident of itself, that instantaneous
| |
| − | feelings flow together into a continuum of feeling, which
| |
| − | has in a modified degree the peculiar vivacity of feeling and
| |
| − | has gained generality. And in reference to such general
| |
| − | ideas, or continua of feeling, the difficulties about resemblance
| |
| − | and suggestion and reference to the external, cease
| |
| − | to have any force.</p>
| |
| − |
| |
| − | <p class='c005'>Third, these general ideas are not mere words, nor do
| |
| − | they consist in this, that certain concrete facts will every
| |
| − | time happen under certain descriptions of conditions; but
| |
| − | they are just as much, or rather far more, living realities
| |
| − | than the feelings themselves out of which they are concreted.
| |
| − | And to say that mental phenomena are governed by law
| |
| − | does not mean merely that they are describable by a general
| |
| − | formula; but that there is a living idea, a conscious continuum
| |
| − | of feeling, which pervades them, and to which they
| |
| − | are docile.</p>
| |
| − |
| |
| − | <p class='c005'>Fourth, this supreme law, which is the celestial and living
| |
| − | harmony, does not so much as demand that the special
| |
| − | <span class='pageno' id='Page_233'>233</span>ideas shall surrender their peculiar arbitrariness and caprice
| |
| − | entirely; for that would be self-destructive. It only requires
| |
| − | that they shall influence and be influenced by one
| |
| − | another.</p>
| |
| − |
| |
| − | <p class='c005'>Fifth, in what measure this unification acts, seems to be
| |
| − | regulated only by special rules; or, at least, we cannot in
| |
| − | our present knowledge say how far it goes. But it may
| |
| − | be said that, judging by appearances, the amount of arbitrariness
| |
| − | in the phenomena of human minds is neither
| |
| − | altogether trifling nor very prominent.</p>
| |
| − | <h4 class='c012'>PERSONALITY</h4>
| |
| − | <p class='c006'>Having thus endeavored to state the law of mind, in general,
| |
| − | I descend to the consideration of a particular phenomenon
| |
| − | which is remarkably prominent in our own consciousnesses,
| |
| − | that of personality. A strong light is thrown
| |
| − | upon this subject by recent observations of double and
| |
| − | multiple personality. The theory which at one time seemed
| |
| − | plausible that two persons in one body corresponded to the
| |
| − | two halves of the brain will, I take it, now be universally
| |
| − | acknowledged to be insufficient. But that which these
| |
| − | cases make quite manifest is that personality is some kind
| |
| − | of co-ordination or connection of ideas. Not much to say,
| |
| − | this, perhaps. Yet when we consider that, according to the
| |
| − | principle which we are tracing out, a connection between
| |
| − | ideas is itself a general idea, and that a general idea is a
| |
| − | living feeling, it is plain that we have at least taken an appreciable
| |
| − | step toward the understanding of personality.
| |
| − | This personality, like any general idea, is not a thing to
| |
| − | be apprehended in an instant. It has to be lived in time;
| |
| − | <span class='pageno' id='Page_234'>234</span>nor can any finite time embrace it in all its fullness. Yet
| |
| − | in each infinitesimal interval it is present and living, though
| |
| − | specially colored by the immediate feelings of that moment.
| |
| − | Personality, so far as it is apprehended in a moment, is
| |
| − | immediate self-consciousness.</p>
| |
| − |
| |
| − | <p class='c005'>But the word co-ordination implies somewhat more than
| |
| − | this; it implies a teleological harmony in ideas, and in the
| |
| − | case of personality this teleology is more than a mere purposive
| |
| − | pursuit of a predeterminate end; it is a developmental
| |
| − | teleology. This is personal character. A general
| |
| − | idea, living and conscious now, it is already determinative
| |
| − | of acts in the future to an extent to which it is not now
| |
| − | conscious.</p>
| |
| − |
| |
| − | <p class='c005'>This reference to the future is an essential element of
| |
| − | personality. Were the ends of a person already explicit,
| |
| − | there would be no room for development, for growth, for
| |
| − | life; and consequently there would be no personality. The
| |
| − | mere carrying out of predetermined purposes is mechanical.
| |
| − | This remark has an application to the philosophy of religion.
| |
| − | It is that a genuine evolutionary philosophy, that is, one
| |
| − | that makes the principle of growth a primordial element
| |
| − | of the universe, is so far from being antagonistic to the idea
| |
| − | of a personal creator, that it is really inseparable from that
| |
| − | idea; while a necessitarian religion is in an altogether false
| |
| − | position and is destined to become disintegrated. But a
| |
| − | pseudo-evolutionism which enthrones mechanical law above
| |
| − | the principle of growth, is at once scientifically unsatisfactory,
| |
| − | as giving no possible hint of how the universe has
| |
| − | come about, and hostile to all hopes of personal relations
| |
| − | to God.</p>
| |
| − | <div>
| |
| − | <span class='pageno' id='Page_235'>235</span>
| |
| − | <h4 class='c012'>COMMUNICATION</h4>
| |
| − | </div>
| |
| − | <p class='c006'>Consistently with the doctrine laid down in the beginning
| |
| − | of this paper, I am bound to maintain that an idea can only
| |
| − | be affected by an idea in continuous connection with it.
| |
| − | By anything but an idea, it cannot be affected at all. This
| |
| − | obliges me to say, as I do say, on other grounds, that what
| |
| − | we call matter is not completely dead, but is merely mind
| |
| − | hide-bound with habits. It still retains the element of
| |
| − | diversification; and in that diversification there is life.
| |
| − | When an idea is conveyed from one mind to another, it is
| |
| − | by forms of combination of the diverse elements of nature,
| |
| − | say by some curious symmetry, or by some union of a tender
| |
| − | color with a refined odor. To such forms the law of mechanical
| |
| − | energy has no application. If they are eternal,
| |
| − | it is in the spirit they embody; and their origin cannot be
| |
| − | accounted for by any mechanical necessity. They are embodied
| |
| − | ideas; and so only can they convey ideas. Precisely
| |
| − | how primary sensations, as colors and tones, are excited,
| |
| − | we cannot tell, in the present state of psychology. But in
| |
| − | our ignorance, I think that we are at liberty to suppose
| |
| − | that they arise in essentially the same manner as the other
| |
| − | feelings, called secondary. As far as sight and hearing
| |
| − | are in question, we know that they are only excited by vibrations
| |
| − | of inconceivable complexity; and the chemical
| |
| − | senses are probably not more simple. Even the least psychical
| |
| − | of peripheral sensations, that of pressure, has in its
| |
| − | excitation conditions which, though apparently simple, are
| |
| − | seen to be complicated enough when we consider the molecules
| |
| − | and their attractions. The principle with which I
| |
| − | <span class='pageno' id='Page_236'>236</span>set out requires me to maintain that these feelings are
| |
| − | communicated to the nerves by continuity, so that there
| |
| − | must be something like them in the excitants themselves.
| |
| − | If this seems extravagant, it is to be remembered that it is
| |
| − | the sole possible way of reaching any explanation of sensation,
| |
| − | which otherwise must be pronounced a general fact,
| |
| − | absolutely inexplicable and ultimate. Now absolute inexplicability
| |
| − | is a hypothesis which sound logic refuses under
| |
| − | any circumstances to justify.</p>
| |
| − |
| |
| − | <p class='c005'>I may be asked whether my theory would be favorable
| |
| − | or otherwise to telepathy. I have no decided answer to
| |
| − | give to this. At first sight, it seems unfavorable. Yet
| |
| − | there may be other modes of continuous connection between
| |
| − | minds other than those of time and space.</p>
| |
| − |
| |
| − | <p class='c005'>The recognition by one person of another’s personality
| |
| − | takes place by means to some extent identical with the means
| |
| − | by which he is conscious of his own personality. The idea
| |
| − | of the second personality, which is as much as to say that
| |
| − | second personality itself, enters within the field of direct
| |
| − | consciousness of the first person, and is as immediately
| |
| − | perceived as his ego, though less strongly. At the same
| |
| − | time, the opposition between the two persons is perceived,
| |
| − | so that the externality of the second is recognized.</p>
| |
| − |
| |
| − | <p class='c005'>The psychological phenomena of intercommunication between
| |
| − | two minds have been unfortunately little studied. So
| |
| − | that it is impossible to say, for certain, whether they are
| |
| − | favorable to this theory or not. But the very extraordinary
| |
| − | insight which some persons are able to gain of others from
| |
| − | indications so slight that it is difficult to ascertain what
| |
| − | they are, is certainly rendered more comprehensible by the
| |
| − | view here taken.</p>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_237'>237</span>A difficulty which confronts the synechistic philosophy is
| |
| − | this. In considering personality, that philosophy is forced
| |
| − | to accept the doctrine of a personal God; but in considering
| |
| − | communication, it cannot but admit that if there is a personal
| |
| − | God, we must have a direct perception of that person
| |
| − | and indeed be in personal communication with him. Now,
| |
| − | if that be the case, the question arises how it is possible that
| |
| − | the existence of this being should ever have been doubted
| |
| − | by anybody. The only answer that I can at present make
| |
| − | is that facts that stand before our face and eyes and stare
| |
| − | us in the face are far from being, in all cases, the ones most
| |
| − | easily discerned. That has been remarked from time immemorial.</p>
| |
| − | <h4 class='c012'>CONCLUSION</h4>
| |
| − | <p class='c006'>I have thus developed as well as I could in a little space
| |
| − | the <i>synechistic</i> philosophy, as applied to mind. I think
| |
| − | that I have succeeded in making it clear that this doctrine
| |
| − | gives room for explanations of many facts which without it
| |
| − | are absolutely and hopelessly inexplicable; and further that
| |
| − | it carries along with it the following doctrines: 1st, a logical
| |
| − | realism of the most pronounced type; 2nd, objective
| |
| − | idealism; 3rd, tychism, with its consequent thoroughgoing
| |
| − | evolutionism. We also notice that the doctrine presents no
| |
| − | hindrances to spiritual influences, such as some philosophies
| |
| − | are felt to do.</p>
| |
| − |
| |
| − | <div>
| |
| − | <span class='pageno' id='Page_238'>238</span>
| |
| − | <h3 id='chap2-4' class='c001'>IV. MAN’S GLASSY ESSENCE<a id='r63' /><a href='#f63' class='c011'><sup>[63]</sup></a></h3>
| |
| − | </div>
| |
| − | <p class='c006'>In <i>The Monist</i> for January, 1891, I tried to show what
| |
| − | conceptions ought to form the brick and mortar of a philosophical
| |
| − | system. Chief among these was that of absolute
| |
| − | chance for which I argued again in last April’s number.<a id='r64' /><a href='#f64' class='c011'><sup>[64]</sup></a>
| |
| − | In July, I applied another fundamental idea, that of continuity,
| |
| − | to the law of mind. Next in order, I have to elucidate,
| |
| − | from the point of view chosen, the relation between
| |
| − | the psychical and physical aspects of a substance.</p>
| |
| − |
| |
| − | <p class='c005'>The first step towards this ought, I think, to be the framing
| |
| − | of a molecular theory of protoplasm. But before doing
| |
| − | that, it seems indispensable to glance at the constitution
| |
| − | of matter, in general. We shall, thus, unavoidably make a
| |
| − | long detour; but, after all, our pains will not be wasted,
| |
| − | for the problems of the papers that are to follow in the series
| |
| − | will call for the consideration of the same question.</p>
| |
| − |
| |
| − | <p class='c005'>All physicists are rightly agreed the evidence is overwhelming
| |
| − | which shows all sensible matter is composed of
| |
| − | molecules in swift motion and exerting enormous mutual
| |
| − | attractions, and perhaps repulsions, too. Even Sir William
| |
| − | Thomson, Lord Kelvin, who wishes to explode action at a
| |
| − | distance and return to the doctrine of a plenum, not only
| |
| − | speaks of molecules, but undertakes to assign definite magnitudes
| |
| − | <span class='pageno' id='Page_239'>239</span>to them. The brilliant Judge Stallo, a man who did
| |
| − | not always rightly estimate his own qualities in accepting
| |
| − | tasks for himself, declared war upon the atomic theory in
| |
| − | a book well worth careful perusal. To the old arguments
| |
| − | in favor of atoms which he found in Fechner’s monograph,
| |
| − | he was able to make replies of considerable force, though
| |
| − | they were not sufficient to destroy those arguments. But
| |
| − | against modern proofs he made no headway at all. These
| |
| − | set out from the mechanical theory of heat. Rumford’s
| |
| − | experiments showed that heat is not a substance. Joule
| |
| − | demonstrated that it was a form of energy. The heating
| |
| − | of gases under constant volume, and other facts instanced
| |
| − | by Rankine, proved that it could not be an energy of strain.
| |
| − | This drove physicists to the conclusion that it was a mode
| |
| − | of motion. Then it was remembered that John Bernoulli
| |
| − | had shown that the pressure of gases could be accounted
| |
| − | for by assuming their molecules to be moving uniformly in
| |
| − | rectilinear paths. The same hypothesis was now seen to
| |
| − | account for Avogadro’s law, that in equal volumes of different
| |
| − | kinds of gases exposed to the same pressure and
| |
| − | temperature are contained equal numbers of molecules.
| |
| − | Shortly after, it was found to account for the laws of diffusion
| |
| − | and viscosity of gases, and for the numerical relation
| |
| − | between these properties. Finally, Crookes’s radiometer
| |
| − | furnished the last link in the strongest chain of evidence
| |
| − | which supports any physical hypothesis.</p>
| |
| − |
| |
| − | <p class='c005'>Such being the constitution of gases, liquids must clearly
| |
| − | be bodies in which the molecules wander in curvilinear
| |
| − | paths, while in solids they move in orbits or quasi-orbits.
| |
| − | (See my definition <i>solid</i> II, 1, in the <i>Century Dictionary</i>.)</p>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_240'>240</span>We see that the resistance to compression and to inter-penetration
| |
| − | between sensible bodies is, by one of the prime
| |
| − | propositions of the molecular theory, due in large measure
| |
| − | to the kinetical energy of the particles, which must be
| |
| − | supposed to be quite remote from one another, on the average,
| |
| − | even in solids. This resistance is no doubt influenced
| |
| − | by finite attractions and repulsions between the molecules.
| |
| − | All the impenetrability of bodies which we can observe is,
| |
| − | therefore, a limited impenetrability due to kinetic and
| |
| − | positional energy. This being the case, we have no logical
| |
| − | right to suppose that absolute impenetrability, or the exclusive
| |
| − | occupancy of space, belongs to molecules or to
| |
| − | atoms. It is an unwarranted hypothesis, not a <i>vera causa</i>.<a id='r65' /><a href='#f65' class='c011'><sup>[65]</sup></a>
| |
| − | Unless we are to give up the theory of energy, finite positional
| |
| − | attractions and repulsions between molecules must
| |
| − | be admitted. Absolute impenetrability would amount to
| |
| − | an infinite repulsion at a certain distance. No analogy of
| |
| − | known phenomena exists to excuse such a wanton violation
| |
| − | of the principle of continuity as such a hypothesis is. In
| |
| − | short, we are logically bound to adopt the Boscovichian idea
| |
| − | that an atom is simply a distribution of component potential
| |
| − | energy throughout space (this distribution being absolutely
| |
| − | rigid), combined with inertia. The potential energy belongs
| |
| − | to two molecules, and is to be conceived as different
| |
| − | between molecules <i>A</i> and <i>B</i> from what it is between molecules
| |
| − | <i>A</i> and <i>C</i>. The distribution of energy is not necessarily
| |
| − | spherical. Nay, a molecule may conceivably have
| |
| − | more than one center; it may even have a central curve,
| |
| − | <span class='pageno' id='Page_241'>241</span>returning into itself. But I do not think there are any
| |
| − | observed facts pointing to such multiple or linear centers.
| |
| − | On the other hand, many facts relating to crystals, especially
| |
| − | those observed by Voigt,<a id='r66' /><a href='#f66' class='c011'><sup>[66]</sup></a> go to show that the distribution
| |
| − | of energy is harmonical but not concentric. We can
| |
| − | easily calculate the forces which such atoms must exert
| |
| − | upon one another by considering<a id='r67' /><a href='#f67' class='c011'><sup>[67]</sup></a> that they are equivalent
| |
| − | to aggregations of pairs of electrically positive and negative
| |
| − | points infinitely near to one another. About such an atom
| |
| − | there would be regions of positive and of negative potential,
| |
| − | and the number and distribution of such regions would
| |
| − | determine the valency of the atom, a number which it is
| |
| − | easy to see would in many cases be somewhat indeterminate.
| |
| − | I must not dwell further upon this hypothesis, at present.
| |
| − | In another paper, its consequences will be further considered.</p>
| |
| − |
| |
| − | <p class='c005'>I cannot assume that the students of philosophy who
| |
| − | read this magazine are thoroughly versed in modern molecular
| |
| − | physics, and, therefore, it is proper to mention that
| |
| − | the governing principle in this branch of science is Clausius’s
| |
| − | law of the virial. I will first state the law, and then explain
| |
| − | the peculiar terms of the statement. This statement is that
| |
| − | the total kinetic energy of the particles of a system in stationary
| |
| − | motion is equal to the total virial. By a <i>system</i>
| |
| − | is here meant a number of particles acting upon one another.<a id='r68' /><a href='#f68' class='c011'><sup>[68]</sup></a>
| |
| − | Stationary motion is a quasi-orbital motion among
| |
| − | <span class='pageno' id='Page_242'>242</span>a system of particles so that none of them are removed to
| |
| − | indefinitely great distances nor acquire indefinitely great
| |
| − | velocities. The kinetic energy of a particle is the work
| |
| − | which would be required to bring it to rest, independently
| |
| − | of any forces which may be acting upon it. The virial of
| |
| − | a pair of particles is half the work which the force which
| |
| − | actually operates between them would do if, being independent
| |
| − | of the distance, it were to bring them together.
| |
| − | The equation of the virial is</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'>1/2∑<i>mv</i><sup>2</sup> = 1/2∑∑<i>Rr</i>.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>Here <i>m</i> is the mass of a particle, <i>v</i> its velocity, <i>R</i> is the
| |
| − | attraction between two particles, and <i>r</i> is the distance between
| |
| − | them. The sign ∑ on the left hand side signifies
| |
| − | that the values of <i>mv</i><sup>2</sup> are to be summed for all the particles,
| |
| − | and ∑∑ on the right hand side signifies that the
| |
| − | values of <i>Rr</i> are to be summed for all the pairs of particles.
| |
| − | If there is an external pressure <i>P</i> (as from the atmosphere)
| |
| − | upon the system, and the volume of vacant space within
| |
| − | the boundary of that pressure is <i>V</i>, then the virial must be
| |
| − | understood as including 3/2<i>PV</i>, so that the equation is</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'>1/2∑<i>mv</i><sup>2</sup> = 3/2<i>PV</i> + 1/2∑∑<i>Rr</i>.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>There is strong (if not demonstrative) reason for thinking
| |
| − | that the temperature of any body above the absolute zero
| |
| − | (-273° C.), is proportional to the average kinetic energy
| |
| − | <span class='pageno' id='Page_243'>243</span>of its molecules, or say <i>a</i>θ, where <i>a</i> is a constant and θ is
| |
| − | the absolute temperature. Hence, we may write the equation</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>a</i>θ = (1/2)avg(<i>mv</i><sup>2</sup>) = (3/2)<i>P</i> avg(<i>V</i>) + (1/2)∑ avg(<i>Rr</i>)</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>where the heavy lines above the different expressions signify
| |
| − | that the average values for single molecules are to be taken.
| |
| − | In 1872, a student in the University of Leyden, Van der
| |
| − | Waals, propounded in his thesis for the doctorate a specialization
| |
| − | of the equation of the virial which has since attracted
| |
| − | great attention. Namely, he writes it</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>a</i>θ = (<i>P</i> + <i>c</i>/<i>V</i><sup>2</sup>)(<i>V</i> - <i>b</i>.)</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>The quantity <i>b</i> is the volume of a molecule, which he supposes
| |
| − | to be an impenetrable body, and all the virtue of the
| |
| − | equation lies in this term which makes the equation a cubic
| |
| − | in <i>V</i>, which is required to account for the shape of certain
| |
| − | isothermal curves.<a id='r69' /><a href='#f69' class='c011'><sup>[69]</sup></a> But if the idea of an impenetrable
| |
| − | atom is illogical, that of an impenetrable molecule is almost
| |
| − | absurd. For the kinetical theory of matter teaches us that
| |
| − | a molecule is like a solar system or star-cluster in miniature.
| |
| − | Unless we suppose that in all heating of gases and vapors
| |
| − | internal work is performed upon the molecules, implying
| |
| − | that their atoms are at considerable distances, the whole
| |
| − | kinetical theory of gases falls to the ground. As for the
| |
| − | term added to <i>P</i>, there is no more than a partial and roughly
| |
| − | approximative justification for it. Namely, let us imagine
| |
| − | <span class='pageno' id='Page_244'>244</span>two spheres described round a particle as their center,
| |
| − | the radius of the larger being so great as to include all the
| |
| − | particles whose action upon the center is sensible, while
| |
| − | the radius of the smaller is so large that a good many molecules
| |
| − | are included within it. The possibility of describing
| |
| − | such a sphere as the outer one implies that the attraction
| |
| − | of the particles varies at some distances inversely as some
| |
| − | higher power of the distance than the cube, or, to speak
| |
| − | more clearly, that the attraction multiplied by the cube
| |
| − | of the distance diminishes as the distance increases; for the
| |
| − | number of particles at a given distance from any one particle
| |
| − | is proportionate to the square of that distance and
| |
| − | each of these gives a term of the virial which is the product
| |
| − | of the attraction into the distance. Consequently, unless
| |
| − | the attraction multiplied by the cube of the distance diminished
| |
| − | so rapidly with the distance as soon to become insensible,
| |
| − | no such outer sphere as is supposed could be described.
| |
| − | However, ordinary experience shows that such a
| |
| − | sphere is possible; and consequently there must be distances
| |
| − | at which the attraction does thus rapidly diminish as the
| |
| − | distance increases. The two spheres, then, being so drawn,
| |
| − | consider the virial of the central particle due to the particles
| |
| − | between them. Let the density of the substance be increased,
| |
| − | say, <i>N</i> times. Then, for every turn, <i>Rr</i>, of the
| |
| − | virial before the condensation, there will be <i>N</i> terms of the
| |
| − | same magnitude after the condensation. Hence, the virial
| |
| − | of each particle will be proportional to the density, and the
| |
| − | equation of the virial becomes</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>a</i>θ = <i>P</i> avg(<i>V</i>) + <i>c</i>/avg(<i>V</i>).</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'><span class='pageno' id='Page_245'>245</span>This omits the virial within the inner sphere, the radius of
| |
| − | which is so taken that within that distance the number of
| |
| − | particles is not proportional to the number in a large sphere.
| |
| − | For Van der Waals this radius is the diameter of his hard
| |
| − | molecules, which assumption gives his equation. But it is
| |
| − | plain that the attraction between the molecules must to
| |
| − | a certain extent modify their distribution, unless some peculiar
| |
| − | conditions are fulfilled. The equation of Van der
| |
| − | Waals can be approximately true, therefore, only for a gas.
| |
| − | In a solid or liquid condition, in which the removal of a
| |
| − | small amount of pressure has little effect on the volume,
| |
| − | and where consequently the virial must be much greater
| |
| − | than <i>P</i> avg(<i>V</i>), the virial must increase with the volume. For
| |
| − | suppose we had a substance in a critical condition in which
| |
| − | an increase of the volume would diminish the virial more
| |
| − | than it would increase (3/2)<i>P</i> avg(<i>V</i>). If we were forcibly to diminish
| |
| − | the volume of such a substance, when the temperature became
| |
| − | equalized, the pressure which it could withstand would
| |
| − | be less than before, and it would be still further condensed,
| |
| − | and this would go on indefinitely until a condition were
| |
| − | reached in which an increase of volume would increase
| |
| − | (3/2)<i>P</i> avg(<i>V</i>) more than it would decrease the virial. In the case
| |
| − | of solids, at least, <i>P</i> may be zero; so that the state reached
| |
| − | would be one in which the virial increases with the volume,
| |
| − | or the attraction between the particles does not increase so
| |
| − | fast with a diminution of their distance as it would if the
| |
| − | attraction were inversely as the distance.</p>
| |
| − |
| |
| − | <p class='c005'>Almost contemporaneously with Van der Waals’s paper,
| |
| − | another remarkable thesis for the doctorate was presented
| |
| − | at Paris by Amagat. It related to the elasticity and expansion
| |
| − | <span class='pageno' id='Page_246'>246</span>of gases, and to this subject the superb experimenter,
| |
| − | its author, has devoted his whole subsequent life.
| |
| − | Especially interesting are his observations of the volumes of
| |
| − | ethylene and of carbonic acid at temperatures from 20° to
| |
| − | 100° and at pressures ranging from an ounce to 5000 pounds
| |
| − | to the square inch. As soon as Amagat had obtained these
| |
| − | results, he remarked that the “coefficient of expansion at
| |
| − | constant volume,” as it is absurdly called, that is, the rate
| |
| − | of variation of the pressure with the temperature, was very
| |
| − | nearly constant for each volume. This accords with the
| |
| − | equation of the virial, which gives</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>dp</i>/<i>d</i>θ = <i>a</i>/avg(<i>V</i>) - <i>d</i>∑ avg(<i>Rr</i>)/<i>d</i>θ.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>Now, the virial must be nearly independent of the temperature,
| |
| − | and, therefore, the last term almost disappears. The
| |
| − | virial would not be quite independent of the temperature,
| |
| − | because if the temperature (i.e., the square of the velocity
| |
| − | of the molecules) is lowered, and the pressure correspondingly
| |
| − | lowered, so as to make the volume the same, the attractions
| |
| − | of the molecules will have more time to produce
| |
| − | their effects, and consequently, the pairs of molecules the
| |
| − | closest together will be held together longer and closer;
| |
| − | so that the virial will generally be increased by a decrease
| |
| − | of temperature. Now, Amagat’s experiments do show an
| |
| − | excessively minute effect of this sort, at least, when the
| |
| − | volumes are not too small. However, the observations are
| |
| − | well enough satisfied by assuming the “coefficient of expansion
| |
| − | at constant volume” to consist wholly of the first
| |
| − | term, <i>a</i>/avg(<i>V</i>). Thus, Amagat’s experiments enable us to determine
| |
| − | <span class='pageno' id='Page_247'>247</span>the values of a and thence to calculate the virial;
| |
| − | and this we find varies for carbonic acid gas nearly inversely
| |
| − | to avg(<i>V</i>)<sup>0.9</sup>. There is, thus, a rough approximation to satisfying
| |
| − | Van der Waals’s equation. But the most interesting
| |
| − | result of Amagat’s experiments, for our purpose at any
| |
| − | rate, is that the quantity <i>a</i>, though nearly constant for any
| |
| − | one volume, differs considerably with the volume, nearly
| |
| − | doubling when the volume is reduced fivefold. This can
| |
| − | only indicate that the mean kinetic energy of a given mass
| |
| − | of the gas for a given temperature is greater the more the
| |
| − | gas is compressed. But the laws of mechanics appear to
| |
| − | enjoin that the mean kinetic energy of a moving particle
| |
| − | shall be constant at any given temperature. The only
| |
| − | escape from contradiction, then, is to suppose that the
| |
| − | mean mass of a moving particle diminishes upon the condensation
| |
| − | of the gas. In other words, many of the molecules
| |
| − | are dissociated, or broken up into atoms or sub-molecules.
| |
| − | The idea that dissociation should be favored
| |
| − | by diminishing the volume will be pronounced by physicists,
| |
| − | at first blush, as contrary to all our experience. But it
| |
| − | must be remembered that the circumstances we are speaking
| |
| − | of, that of a gas under fifty or more atmospheres pressure,
| |
| − | are also unusual. That the “coefficient of expansion under
| |
| − | constant volume” when multiplied by the volumes should
| |
| − | increase with a decrement of the volume is also quite contrary
| |
| − | to ordinary experience; yet it undoubtedly takes place
| |
| − | in all gases under great pressure. Again, the doctrine of
| |
| − | Arrhenius<a id='r70' /><a href='#f70' class='c011'><sup>[70]</sup></a> is now generally accepted, that the molecular
| |
| − | <span class='pageno' id='Page_248'>248</span>conductivity of an electrolyte is proportional to the dissociation
| |
| − | of ions. Now the molecular conductivity of a
| |
| − | fused electrolyte is usually superior to that of a solution.
| |
| − | Here is a case, then, in which diminution of volume is accompanied
| |
| − | by increased dissociation.</p>
| |
| − |
| |
| − | <p class='c005'>The truth is that several different kinds of dissociation
| |
| − | have to be distinguished. In the first place, there is the
| |
| − | dissociation of a chemical molecule to form chemical molecules
| |
| − | under the regular action of chemical laws. This may
| |
| − | be a double decomposition, as when iodhydric acid is dissociated,
| |
| − | according to the formula</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>HI</i> + <i>HI</i> = <i>HH</i> + <i>II</i>;</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>or, it may be a simple decomposition, as when pentachloride
| |
| − | of phosphorus is dissociated according to the formula</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'><i>PCl</i><sub>5</sub> = <i>PCl</i><sub>3</sub> + <i>ClCl</i>.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>All these dissociations require, according to the laws of
| |
| − | thermo-chemistry, an elevated temperature. In the second
| |
| − | place, there is the dissociation of a physically polymerous
| |
| − | molecule, that is, of several chemical molecules joined by
| |
| − | physical attractions. This I am inclined to suppose is a
| |
| − | common concomitant of the heating of solids and liquids;
| |
| − | for in these bodies there is no increase of compressibility
| |
| − | with the temperature at all comparable with the increase
| |
| − | of the expansibility. But, in the third place, there is the
| |
| − | dissociation with which we are now concerned, which must
| |
| − | be supposed to be a throwing off of unsaturated sub-molecules
| |
| − | or atoms from the molecule. The molecule may, as
| |
| − | I have said, be roughly likened to a solar system. As such,
| |
| − | <span class='pageno' id='Page_249'>249</span>molecules are able to produce perturbations of one another’s
| |
| − | internal motions; and in this way a planet, i.e., a sub-molecule,
| |
| − | will occasionally get thrown off and wander about by
| |
| − | itself, till it finds another unsaturated sub-molecule with
| |
| − | which it can unite. Such dissociation by perturbation will
| |
| − | naturally be favored by the proximity of the molecules to
| |
| − | one another.</p>
| |
| − |
| |
| − | <p class='c005'>Let us now pass to the consideration of that special substance,
| |
| − | or rather class of substances, whose properties form
| |
| − | the chief subject of botany and of zoölogy, as truly as those
| |
| − | of the silicates form the chief subject of mineralogy: I mean
| |
| − | the life-slimes, or protoplasm. Let us begin by cataloguing
| |
| − | the general characters of these slimes. They one and all
| |
| − | exist in two states of aggregation, a solid or nearly solid
| |
| − | state and a liquid or nearly liquid state; but they do not
| |
| − | pass from the former to the latter by ordinary fusion. They
| |
| − | are readily decomposed by heat, especially in the liquid
| |
| − | state; nor will they bear any considerable degree of cold.
| |
| − | All their vital actions take place at temperatures very little
| |
| − | below the point of decomposition. This extreme instability
| |
| − | is one of numerous facts which demonstrate the chemical
| |
| − | complexity of protoplasm. Every chemist will agree that
| |
| − | they are far more complicated than the albumens. Now,
| |
| − | albumen is estimated to contain in each molecule about a
| |
| − | thousand atoms; so that it is natural to suppose that the
| |
| − | protoplasms contain several thousands. We know that
| |
| − | while they are chiefly composed of oxygen, hydrogen, carbon,
| |
| − | and nitrogen, a large number of other elements enter
| |
| − | into living bodies in small proportions; and it is likely that
| |
| − | most of these enter into the composition of protoplasms.
| |
| − | <span class='pageno' id='Page_250'>250</span>Now, since the numbers of chemical varieties increase at
| |
| − | an enormous rate with the number of atoms per molecule,
| |
| − | so that there are certainly hundreds of thousands of substances
| |
| − | whose molecules contain twenty atoms or fewer,
| |
| − | we may well suppose that the number of protoplasmic
| |
| − | substances runs into the billions or trillions. Professor
| |
| − | Cayley has given a mathematical theory of “trees,” with
| |
| − | a view of throwing a light upon such questions; and in that
| |
| − | light the estimate of trillions (in the English sense) seems
| |
| − | immoderately moderate. It is true that an opinion has
| |
| − | been emitted, and defended among biologists, that there is
| |
| − | but one kind of protoplasm; but the observations of biologists,
| |
| − | themselves, have almost exploded that hypothesis,
| |
| − | which from a chemical standpoint appears utterly incredible.
| |
| − | The anticipation of the chemist would decidedly be that
| |
| − | enough different chemical substances having protoplasmic
| |
| − | characters might be formed to account, not only for the
| |
| − | differences between nerve-slime and muscle-slime, between
| |
| − | whale-slime and lion-slime, but also for those minuter pervasive
| |
| − | variations which characterize different breeds and
| |
| − | single individuals.</p>
| |
| − |
| |
| − | <p class='c005'>Protoplasm, when quiescent, is, broadly speaking, solid;
| |
| − | but when it is disturbed in an appropriate way, or sometimes
| |
| − | even spontaneously without external disturbance, it
| |
| − | becomes, broadly speaking, liquid. A moner in this state
| |
| − | is seen under the microscope to have streams within its
| |
| − | matter; a slime-mould slowly flows by force of gravity.
| |
| − | The liquefaction starts from the point of disturbance and
| |
| − | spreads through the mass. This spreading, however, is not
| |
| − | uniform in all directions; on the contrary, it takes at one
| |
| − | <span class='pageno' id='Page_251'>251</span>time one course, at another another, through the homogeneous
| |
| − | mass, in a manner that seems a little mysterious.
| |
| − | The cause of disturbance being removed, these motions
| |
| − | gradually (with higher kinds of protoplasm, quickly) cease,
| |
| − | and the slime returns to its solid condition.</p>
| |
| − |
| |
| − | <p class='c005'>The liquefaction of protoplasm is accompanied by a mechanical
| |
| − | phenomenon. Namely, some kinds exhibit a tendency
| |
| − | to draw themselves up into a globular form. This
| |
| − | happens particularly with the contents of muscle-cells. The
| |
| − | prevalent opinion, founded on some of the most exquisite
| |
| − | experimental investigations that the history of science can
| |
| − | show, is undoubtedly that the contraction of muscle-cells
| |
| − | is due to osmotic pressure; and it must be allowed that
| |
| − | that is a factor in producing the effect. But it does not
| |
| − | seem to me that it satisfactorily accounts even for the phenomena
| |
| − | of muscular contraction; and besides, even naked
| |
| − | slimes often draw up in the same way. In this case, we
| |
| − | seem to recognize an increase of the surface-tension. In
| |
| − | some cases, too, the reverse action takes place, extraordinary
| |
| − | pseudopodia being put forth, as if the surface-tension were
| |
| − | diminished in spots. Indeed, such a slime always has a sort
| |
| − | of skin, due no doubt to surface-tension, and this seems to
| |
| − | give way at the point where a pseudopodium is put forth.</p>
| |
| − |
| |
| − | <p class='c005'>Long-continued or frequently repeated liquefaction of
| |
| − | the protoplasm results in an obstinate retention of the solid
| |
| − | state, which we call fatigue. On the other hand, repose
| |
| − | in this state, if not too much prolonged, restores the liquefiability.
| |
| − | These are both important functions.</p>
| |
| − |
| |
| − | <p class='c005'>The life-slimes have, further, the peculiar property of
| |
| − | growing. Crystals also grow; their growth, however, consists
| |
| − | <span class='pageno' id='Page_252'>252</span>merely in attracting matter like their own from the
| |
| − | circumambient fluid. To suppose the growth of protoplasm
| |
| − | of the same nature, would be to suppose this substance to
| |
| − | be spontaneously generated in copious supplies wherever
| |
| − | food is in solution. Certainly, it must be granted that
| |
| − | protoplasm is but a chemical substance, and that there is
| |
| − | no reason why it should not be formed synthetically like
| |
| − | any other chemical substance. Indeed, Clifford has clearly
| |
| − | shown that we have overwhelming evidence that it is so
| |
| − | formed. But to say that such formation is as regular and
| |
| − | frequent as the assimilation of food is quite another matter.
| |
| − | It is more consonant with the facts of observation to suppose
| |
| − | that assimilated protoplasm is formed at the instant of
| |
| − | assimilation, under the influence of the protoplasm already
| |
| − | present. For each slime in its growth preserves its distinctive
| |
| − | characters with wonderful truth, nerve-slime growing
| |
| − | nerve-slime and muscle-slime muscle-slime, lion-slime growing
| |
| − | lion-slime, and all the varieties of breeds and even individual
| |
| − | characters being preserved in the growth. Now
| |
| − | it is too much to suppose there are billions of different kinds
| |
| − | of protoplasm floating about wherever there is food.</p>
| |
| − |
| |
| − | <p class='c005'>The frequent liquefaction of protoplasm increases its
| |
| − | power of assimilating food; so much so, indeed, that it is
| |
| − | questionable whether in the solid form it possesses this
| |
| − | power.</p>
| |
| − |
| |
| − | <p class='c005'>The life-slime wastes as well as grows; and this too takes
| |
| − | place chiefly if not exclusively in its liquid phases.</p>
| |
| − |
| |
| − | <p class='c005'>Closely connected with growth is reproduction; and
| |
| − | though in higher forms this is a specialized function, it is
| |
| − | universally true that wherever there is protoplasm, there is,
| |
| − | <span class='pageno' id='Page_253'>253</span>will be, or has been a power of reproducing that same kind
| |
| − | of protoplasm in a separated organism. Reproduction
| |
| − | seems to involve the union of two sexes; though it is not
| |
| − | demonstrable that this is always requisite.</p>
| |
| − |
| |
| − | <p class='c005'>Another physical property of protoplasm is that of taking
| |
| − | habits. The course which the spread of liquefaction has
| |
| − | taken in the past is rendered thereby more likely to be taken
| |
| − | in the future; although there is no absolute certainly that
| |
| − | the same path will be followed again.</p>
| |
| − |
| |
| − | <p class='c005'>Very extraordinary, certainly, are all these properties of
| |
| − | protoplasm; as extraordinary as indubitable. But the one
| |
| − | which has next to be mentioned, while equally undeniable,
| |
| − | is infinitely more wonderful. It is that protoplasm feels.
| |
| − | We have no direct evidence that this is true of protoplasm
| |
| − | universally, and certainly some kinds feel far more than
| |
| − | others. But there is a fair analogical inference that all
| |
| − | protoplasm feels. It not only feels but exercises all the
| |
| − | functions of mind.</p>
| |
| − |
| |
| − | <p class='c005'>Such are the properties of protoplasm. The problem is
| |
| − | to find a hypothesis of the molecular constitution of this
| |
| − | compound which will account for these properties, one
| |
| − | and all.</p>
| |
| − |
| |
| − | <p class='c005'>Some of them are obvious results of the excessively complicated
| |
| − | constitution of the protoplasm molecule. All very
| |
| − | complicated substances are unstable; and plainly a molecule
| |
| − | of several thousand atoms may be separated in many
| |
| − | ways into two parts in each of which the polar chemical
| |
| − | forces are very nearly saturated. In the solid protoplasm,
| |
| − | as in other solids, the molecules must be supposed to be
| |
| − | moving as it were in orbits, or, at least, so as not to wander
| |
| − | <span class='pageno' id='Page_254'>254</span>indefinitely. But this solid cannot be melted, for the same
| |
| − | reason that starch cannot be melted; because an amount of
| |
| − | heat insufficient to make the entire molecules wander is
| |
| − | sufficient to break them up completely and cause them to
| |
| − | form new and simpler molecules. But when one of the
| |
| − | molecules is disturbed, even if it be not quite thrown out
| |
| − | of its orbit at first, sub-molecules of perhaps several hundred
| |
| − | atoms each are thrown off from it. These will soon
| |
| − | acquire the same mean kinetic energy as the others, and,
| |
| − | therefore, velocities several times as great. They will
| |
| − | naturally begin to wander, and in wandering will perturb
| |
| − | a great many other molecules and cause them in their turn
| |
| − | to behave like the one originally deranged. So many molecules
| |
| − | will thus be broken up, that even those that are intact
| |
| − | will no longer be restrained within orbits, but will wander
| |
| − | about freely. This is the usual condition of a liquid,
| |
| − | as modern chemists understand it; for in all electrolytic
| |
| − | liquids there is considerable dissociation.</p>
| |
| − |
| |
| − | <p class='c005'>But this process necessarily chills the substance, not
| |
| − | merely on account of the heat of chemical combination,
| |
| − | but still more because the number of separate particles
| |
| − | being greatly increased, the mean kinetic energy must be
| |
| − | less. The substance being a bad conductor, this heat is
| |
| − | not at once restored. Now the particles moving more
| |
| − | slowly, the attractions between them have time to take
| |
| − | effect, and they approach the condition of equilibrium.
| |
| − | But their dynamic equilibrium is found in the restoration
| |
| − | of the solid condition, which, therefore, takes place, if the
| |
| − | disturbance is not kept up.</p>
| |
| − |
| |
| − | <p class='c005'>When a body is in the solid condition, most of its molecules
| |
| − | <span class='pageno' id='Page_255'>255</span>must be moving at the same rate, or, at least, at certain
| |
| − | regular sets of rates; otherwise the orbital motion would not
| |
| − | be preserved. The distances of neighboring molecules
| |
| − | must always be kept between a certain maximum and a
| |
| − | certain minimum value. But if, without absorption of
| |
| − | heat, the body be thrown into a liquid condition, the distances
| |
| − | of neighboring molecules will be far more unequally
| |
| − | distributed, and an effect upon the virial will result. The
| |
| − | chilling of protoplasm upon its liquefaction must also be
| |
| − | taken into account. The ordinary effect will no doubt be
| |
| − | to increase the cohesion and with that the surface-tension,
| |
| − | so that the mass will tend to draw itself up. But in special
| |
| − | cases, the virial will be increased so much that the surface-tension
| |
| − | will be diminished at points where the temperature
| |
| − | is first restored. In that case, the outer film will give way
| |
| − | and the tension at other places will aid in causing the general
| |
| − | fluid to be poured out at those points, forming
| |
| − | pseudopodia.</p>
| |
| − |
| |
| − | <p class='c005'>When the protoplasm is in a liquid state, and then only,
| |
| − | a solution of food is able to penetrate its mass by diffusion.
| |
| − | The protoplasm is then considerably dissociated; and so is
| |
| − | the food, like all dissolved matter. If then the separated
| |
| − | and unsaturated sub-molecules of the food happen to be
| |
| − | of the same chemical species as sub-molecules of the protoplasm,
| |
| − | they may unite with other sub-molecules of the
| |
| − | protoplasm to form new molecules, in such a fashion that
| |
| − | when the solid state is resumed, there may be more molecules
| |
| − | of protoplasm than there were at the beginning. It
| |
| − | is like the jackknife whose blade and handle, after having
| |
| − | been severally lost and replaced, were found and put together
| |
| − | to make a new knife.</p>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_256'>256</span>We have seen that protoplasm is chilled by liquefaction,
| |
| − | and that this brings it back to the solid state, when the heat
| |
| − | is recovered. This series of operations must be very rapid
| |
| − | in the case of nerve-slime and even of muscle-slime, and
| |
| − | may account for the unsteady or vibratory character of
| |
| − | their action. Of course, if assimilation takes place, the
| |
| − | heat of combination, which is probably trifling, is gained.
| |
| − | On the other hand, if work is done, whether by nerve or by
| |
| − | muscle, loss of energy must take place. In the case of
| |
| − | the muscle, the mode by which the instantaneous part of
| |
| − | the fatigue is brought about is easily traced out. If when
| |
| − | the muscle contracts it be under stress, it will contract less
| |
| − | than it otherwise would do, and there will be a loss of heat.
| |
| − | It is like an engine which should work by dissolving salt
| |
| − | in water and using the contraction during the solution to
| |
| − | lift a weight, the salt being recovered afterwards by distillation.
| |
| − | But the major part of fatigue has nothing to do
| |
| − | with the correlation of forces. A man must labor hard to
| |
| − | do in a quarter of an hour the work which draws from him
| |
| − | enough heat to cool his body by a single degree. Meantime,
| |
| − | he will be getting heated, he will be pouring out extra
| |
| − | products of combustion, perspiration, etc., and he will be
| |
| − | driving the blood at an accelerated rate through minute
| |
| − | tubes at great expense. Yet all this will have little to do
| |
| − | with his fatigue. He may sit quietly at his table writing,
| |
| − | doing practically no physical work at all, and yet in a few
| |
| − | hours be terribly fagged. This seems to be owing to the
| |
| − | deranged sub-molecules of the nerve-slime not having had
| |
| − | time to settle back into their proper combinations. When
| |
| − | such sub-molecules are thrown out, as they must be from
| |
| − | time to time, there is so much waste of material.</p>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_257'>257</span>In order that a sub-molecule of food may be thoroughly
| |
| − | and firmly assimilated into a broken molecule of protoplasm,
| |
| − | it is necessary not only that it should have precisely
| |
| − | the right chemical composition, but also that it should be
| |
| − | at precisely the right spot at the right time and should be
| |
| − | moving in precisely the right direction with precisely the
| |
| − | right velocity. If all these conditions are not fulfilled, it
| |
| − | will be more loosely retained than the other parts of the
| |
| − | molecule; and every time it comes round into the situation
| |
| − | in which it was drawn in, relatively to the other parts of
| |
| − | that molecule and to such others as were near enough to
| |
| − | be factors in the action, it will be in special danger of being
| |
| − | thrown out again. Thus, when a partial liquefaction of
| |
| − | the protoplasm takes place many times to about the same
| |
| − | extent, it will, each time, be pretty nearly the same molecules
| |
| − | that were last drawn in that are now thrown out.
| |
| − | They will be thrown out, too, in about the same way, as to
| |
| − | position, direction of motion, and velocity, in which they
| |
| − | were drawn in; and this will be in about the same course
| |
| − | that the ones last before them were thrown out. Not exactly,
| |
| − | however; for the very cause of their being thrown
| |
| − | off so easily is their not having fulfilled precisely the conditions
| |
| − | of stable retention. Thus, the law of habit is accounted
| |
| − | for, and with it its peculiar characteristic of not
| |
| − | acting with exactitude.</p>
| |
| − |
| |
| − | <p class='c005'>It seems to me that this explanation of habit, aside from
| |
| − | the question of its truth or falsity, has a certain value as an
| |
| − | addition to our little store of mechanical examples of actions
| |
| − | analogous to habit. All the others, so far as I know, are
| |
| − | either statical or else involve forces which, taking only the
| |
| − | <span class='pageno' id='Page_258'>258</span>sensible motions into account, violate the law of energy.
| |
| − | It is so with the stream that wears its own bed. Here, the
| |
| − | sand is carried to its most stable situation and left there.
| |
| − | The law of energy forbids this; for when anything reaches
| |
| − | a position of stable equilibrium, its momentum will be at
| |
| − | a maximum, so that it can according to this law only be
| |
| − | left at rest in an unstable situation. In all the statical
| |
| − | illustrations, too, things are brought into certain states and
| |
| − | left there. A garment receives folds and keeps them; that
| |
| − | is, its limit of elasticity is exceeded. This failure to spring
| |
| − | back is again an apparent violation of the law of energy;
| |
| − | for the substance will not only not spring back of itself
| |
| − | (which might be due to an unstable equilibrium being
| |
| − | reached) but will not even do so when an impulse that way
| |
| − | is applied to it. Accordingly, Professor James says, “the
| |
| − | phenomena of habit ... are due to the plasticity of the ...
| |
| − | materials.” Now, plasticity of materials means the
| |
| − | having of a low limit of elasticity. (See the <i>Century
| |
| − | Dictionary</i>, under <i>solid</i>.) But the hypothetical constitution
| |
| − | of protoplasm here proposed involves no forces but
| |
| − | attractions and repulsions strictly following the law of
| |
| − | energy. The action here, that is, the throwing of an atom
| |
| − | out of its orbit in a molecule, and the entering of a new
| |
| − | atom into nearly, but not quite the same orbit, is somewhat
| |
| − | similar to the molecular actions which may be supposed
| |
| − | to take place in a solid strained beyond its limit of elasticity.
| |
| − | Namely, in that case certain molecules must be thrown out
| |
| − | of their orbits, to settle down again shortly after into new
| |
| − | orbits. In short, the plastic solid resembles protoplasm in
| |
| − | being partially and temporarily liquefied by a slight mechanical
| |
| − | <span class='pageno' id='Page_259'>259</span>force. But the taking of a set by a solid body
| |
| − | has but a moderate resemblance to the taking of a habit,
| |
| − | inasmuch as the characteristic feature of the latter, its
| |
| − | inexactitude and want of complete determinacy, is not so
| |
| − | marked in the former, if it can be said to be present there,
| |
| − | at all.</p>
| |
| − |
| |
| − | <p class='c005'>The truth is that though the molecular explanation of
| |
| − | habit is pretty vague on the mathematical side, there can
| |
| − | be no doubt that systems of atoms having polar forces
| |
| − | would act substantially in that manner, and the explanation
| |
| − | is even too satisfactory to suit the convenience of an advocate
| |
| − | of tychism. For it may fairly be urged that since the
| |
| − | phenomena of habit may thus result from a purely mechanical
| |
| − | arrangement, it is unnecessary to suppose that
| |
| − | habit-taking is a primordial principle of the universe. But
| |
| − | one fact remains unexplained mechanically, which concerns
| |
| − | not only the facts of habit, but all cases of actions apparently
| |
| − | violating the law of energy; it is that all these phenomena
| |
| − | depend upon aggregations of trillions of molecules
| |
| − | in one and the same condition and neighborhood; and it is
| |
| − | by no means clear how they could have all been brought
| |
| − | and left in the same place and state by any conservative
| |
| − | forces. But let the mechanical explanation be as perfect
| |
| − | as it may, the state of things which it supposes presents
| |
| − | evidence of a primordial habit-taking tendency. For it
| |
| − | shows us like things acting in like ways because they are
| |
| − | alike. Now, those who insist on the doctrine of necessity
| |
| − | will for the most part insist that the physical world is entirely
| |
| − | individual. Yet law involves an element of generality.
| |
| − | Now to say that generality is primordial, but generalization
| |
| − | <span class='pageno' id='Page_260'>260</span>not, is like saying that diversity is primordial
| |
| − | but diversification not. It turns logic upside down. At
| |
| − | any rate, it is clear that nothing but a principle of habit,
| |
| − | itself due to the growth by habit of an infinitesimal chance
| |
| − | tendency toward habit-taking, is the only bridge that can
| |
| − | span the chasm between the chance-medley of chaos and
| |
| − | the cosmos of order and law.</p>
| |
| − |
| |
| − | <p class='c005'>I shall not attempt a molecular explanation of the phenomena
| |
| − | of reproduction, because that would require a subsidiary
| |
| − | hypothesis, and carry me away from my main
| |
| − | object. Such phenomena, universally diffused though they
| |
| − | be, appear to depend upon special conditions; and we do
| |
| − | not find that all protoplasm has reproductive powers.</p>
| |
| − |
| |
| − | <p class='c005'>But what is to be said of the property of feeling? If
| |
| − | consciousness belongs to all protoplasm, by what mechanical
| |
| − | constitution is this to be accounted for? The slime
| |
| − | is nothing but a chemical compound. There is no inherent
| |
| − | impossibility in its being formed synthetically in the laboratory,
| |
| − | out of its chemical elements; and if it were so made,
| |
| − | it would present all the characters of natural protoplasm.
| |
| − | No doubt, then, it would feel. To hesitate to admit this
| |
| − | would be puerile and ultra-puerile. By what element of
| |
| − | the molecular arrangement, then, would that feeling be
| |
| − | caused? This question cannot be evaded or pooh-poohed.
| |
| − | Protoplasm certainly does feel; and unless we are to accept
| |
| − | a weak dualism, the property must be shown to arise from
| |
| − | some peculiarity of the mechanical system. Yet the attempt
| |
| − | to deduce it from the three laws of mechanics, applied
| |
| − | to never so ingenious a mechanical contrivance, would
| |
| − | obviously be futile. It can never be explained, unless we
| |
| − | <span class='pageno' id='Page_261'>261</span>admit that physical events are but degraded or undeveloped
| |
| − | forms of psychical events. But once grant that the phenomena
| |
| − | of matter are but the result of the sensibly complete
| |
| − | sway of habits upon mind, and it only remains to
| |
| − | explain why in the protoplasm these habits are to some
| |
| − | slight extent broken up, so that according to the law of
| |
| − | mind, in that special clause of it sometimes called the principle
| |
| − | of accommodation,<a id='r71' /><a href='#f71' class='c011'><sup>[71]</sup></a> feeling becomes intensified. Now
| |
| − | the manner in which habits generally get broken up is this.
| |
| − | Reactions usually terminate in the removal of a stimulus;
| |
| − | for the excitation continues as long as the stimulus is present.
| |
| − | Accordingly, habits are general ways of behavior
| |
| − | which are associated with the removal of stimuli. But
| |
| − | when the expected removal of the stimulus fails to occur,
| |
| − | the excitation continues and increases, and non-habitual
| |
| − | reactions take place; and these tend to weaken the habit.
| |
| − | If, then, we suppose that matter never does obey its ideal
| |
| − | laws with absolute precision, but that there are almost insensible
| |
| − | fortuitous departures from regularity, these will
| |
| − | produce, in general, equally minute effects. But protoplasm
| |
| − | is in an excessively unstable condition; and it is the
| |
| − | characteristic of unstable equilibrium, that near that point
| |
| − | excessively minute causes may produce startlingly large
| |
| − | effects. Here, then, the usual departures from regularity
| |
| − | will be followed by others that are very great; and the large
| |
| − | fortuitous departures from law so produced, will tend still
| |
| − | further to break up the laws, supposing that these are of
| |
| − | <span class='pageno' id='Page_262'>262</span>the nature of habits. Now, this breaking up of habit and
| |
| − | renewed fortuitous spontaneity will, according to the law
| |
| − | of mind, be accompanied by an intensification of feeling.
| |
| − | The nerve-protoplasm is, without doubt, in the most unstable
| |
| − | condition of any kind of matter; and consequently,
| |
| − | there the resulting feeling is the most manifest.</p>
| |
| − |
| |
| − | <p class='c005'>Thus we see that the idealist has no need to dread a
| |
| − | mechanical theory of life. On the contrary, such a theory,
| |
| − | fully developed, is bound to call in a tychistic idealism as
| |
| − | its indispensable adjunct. Wherever chance-spontaneity
| |
| − | is found, there, in the same proportion, feeling exists. In
| |
| − | fact, chance is but the outward aspect of that which within
| |
| − | itself is feeling. I long ago showed that real existence, or
| |
| − | thing-ness, consists in regularities. So, that primeval chaos
| |
| − | in which there was no regularity was mere nothing, from
| |
| − | a physical aspect. Yet it was not a blank zero; for there
| |
| − | was an intensity of consciousness there in comparison with
| |
| − | which all that we ever feel is but as the struggling of a
| |
| − | molecule or two to throw off a little of the force of law to
| |
| − | an endless and innumerable diversity of chance utterly unlimited.</p>
| |
| − |
| |
| − | <p class='c005'>But after some atoms of the protoplasm have thus become
| |
| − | partially emancipated from law, what happens next to them?
| |
| − | To understand this, we have to remember that no mental
| |
| − | tendency is so easily strengthened by the action of habit
| |
| − | as is the tendency to take habits. Now, in the higher kinds
| |
| − | of protoplasm, especially, the atoms in question have not
| |
| − | only long belonged to one molecule or another of the particular
| |
| − | mass of slime of which they are parts; but before
| |
| − | that, they were constituents of food of a protoplasmic constitution.
| |
| − | <span class='pageno' id='Page_263'>263</span>During all this time, they have been liable to
| |
| − | lose habits and to recover them again; so that now, when
| |
| − | the stimulus is removed, and the foregone habits tend to
| |
| − | reassert themselves, they do so in the case of such atoms
| |
| − | with great promptness. Indeed, the return is so prompt
| |
| − | that there is nothing but the feeling to show conclusively
| |
| − | that the bonds of law have ever been relaxed.</p>
| |
| − |
| |
| − | <p class='c005'>In short, diversification is the vestige of chance-spontaneity;
| |
| − | and wherever diversity is increasing, there chance
| |
| − | must be operative. On the other hand, wherever uniformity
| |
| − | is increasing, habit must be operative. But wherever actions
| |
| − | take place under an established uniformity, there so
| |
| − | much feeling as there may be takes the mode of a sense of
| |
| − | reaction. That is the manner in which I am led to define
| |
| − | the relation between the fundamental elements of consciousness
| |
| − | and their physical equivalents.</p>
| |
| − |
| |
| − | <p class='c005'>It remains to consider the physical relations of general
| |
| − | ideas. It may be well here to reflect that if matter has no
| |
| − | existence except as a specialization of mind, it follows that
| |
| − | whatever affects matter according to regular laws is itself
| |
| − | matter. But all mind is directly or indirectly connected
| |
| − | with all matter, and acts in a more or less regular way;
| |
| − | so that all mind more or less partakes of the nature of
| |
| − | matter. Hence, it would be a mistake to conceive of the
| |
| − | psychical and the physical aspects of matter as two aspects
| |
| − | absolutely distinct. Viewing a thing from the outside, considering
| |
| − | its relations of action and reaction with other
| |
| − | things, it appears as matter. Viewing it from the inside,
| |
| − | looking at its immediate character as feeling, it appears as
| |
| − | consciousness. These two views are combined when we
| |
| − | <span class='pageno' id='Page_264'>264</span>remember that mechanical laws are nothing but acquired
| |
| − | habits, like all the regularities of mind, including the tendency
| |
| − | to take habits, itself; and that this action of habit
| |
| − | is nothing but generalization, and generalization is nothing
| |
| − | but the spreading of feelings. But the question is, how do
| |
| − | general ideas appear in the molecular theory of protoplasm?</p>
| |
| − |
| |
| − | <p class='c005'>The consciousness of a habit involves a general idea. In
| |
| − | each action of that habit certain atoms get thrown out of
| |
| − | their orbit, and replaced by others. Upon all the different
| |
| − | occasions it is different atoms that are thrown off, but they
| |
| − | are analogous from a physical point of view, and there is
| |
| − | an inward sense of their being analogous. Every time
| |
| − | one of the associated feelings recurs, there is a more or less
| |
| − | vague sense that there are others, that it has a general
| |
| − | character, and of about what this general character is. We
| |
| − | ought not, I think, to hold that in protoplasm habit never
| |
| − | acts in any other than the particular way suggested above.
| |
| − | On the contrary, if habit be a primary property of mind,
| |
| − | it must be equally so of matter, as a kind of mind. We
| |
| − | can hardly refuse to admit that wherever chance motions
| |
| − | have general characters, there is a tendency for this generality
| |
| − | to spread and to perfect itself. In that case, a general
| |
| − | idea is a certain modification of consciousness which accompanies
| |
| − | any regularity or general relation between chance
| |
| − | actions.</p>
| |
| − |
| |
| − | <p class='c005'>The consciousness of a general idea has a certain “unity
| |
| − | of the ego,” in it, which is identical when it passes from
| |
| − | one mind to another. It is, therefore, quite analogous to
| |
| − | a person; and, indeed, a person is only a particular kind
| |
| − | of general idea. Long age, in the <i>Journal of Speculative
| |
| − | <span class='pageno' id='Page_265'>265</span>Philosophy</i> (Vol. II, p. 156), I pointed out that a person
| |
| − | is nothing but a symbol involving a general idea; but my
| |
| − | views were, then, too nominalistic to enable me to see that
| |
| − | every general idea has the unified living feeling of a person.</p>
| |
| − |
| |
| − | <p class='c005'>All that is necessary, upon this theory, to the existence
| |
| − | of a person is that the feelings out of which he is constructed
| |
| − | should be in close enough connection to influence one another.
| |
| − | Here we can draw a consequence which it may be
| |
| − | possible to submit to experimental test. Namely, if this
| |
| − | be the case, there should be something like personal consciousness
| |
| − | in bodies of men who are in intimate and intensely
| |
| − | sympathetic communion. It is true that when the
| |
| − | generalization of feeling has been carried so far as to include
| |
| − | all within a person, a stopping-place, in a certain
| |
| − | sense, has been attained; and further generalization will
| |
| − | have a less lively character. But we must not think it will
| |
| − | cease. <i>Esprit de corps</i>, national sentiment, sympathy, are
| |
| − | no mere metaphors. None of us can fully realize what the
| |
| − | minds of corporations are, any more than one of my brain-cells
| |
| − | can know what the whole brain is thinking. But the
| |
| − | law of mind clearly points to the existence of such personalities,
| |
| − | and there are many ordinary observations which,
| |
| − | if they were critically examined and supplemented by special
| |
| − | experiments, might, as first appearances promise, give evidence
| |
| − | of the influence of such greater persons upon individuals.
| |
| − | It is often remarked that on one day half a dozen
| |
| − | people, strangers to one another, will take it into their heads
| |
| − | to do one and the same strange deed, whether it be a physical
| |
| − | experiment, a crime, or an act of virtue. When the
| |
| − | thirty thousand young people of the society for Christian
| |
| − | <span class='pageno' id='Page_266'>266</span>Endeavor were in New York, there seemed to me to be some
| |
| − | mysterious diffusion of sweetness and light. If such a fact
| |
| − | is capable of being made out anywhere, it should be in the
| |
| − | church. The Christians have always been ready to risk
| |
| − | their lives for the sake of having prayers in common, of
| |
| − | getting together and praying simultaneously with great
| |
| − | energy, and especially for their common body, for “the
| |
| − | whole state of Christ’s church militant here in earth,” as
| |
| − | one of the missals has it. This practice they have been
| |
| − | keeping up everywhere, weekly, for many centuries.
| |
| − | Surely, a personality ought to have developed in that church,
| |
| − | in that “bride of Christ,” as they call it, or else there is a
| |
| − | strange break in the action of mind, and I shall have to
| |
| − | acknowledge my views are much mistaken. Would not the
| |
| − | societies for psychical research be more likely to break
| |
| − | through the clouds, in seeking evidences of such corporate
| |
| − | personality, than in seeking evidences of telepathy, which,
| |
| − | upon the same theory, should be a far weaker phenomenon?</p>
| |
| − |
| |
| − | <div>
| |
| − | <span class='pageno' id='Page_267'>267</span>
| |
| − | <h3 id='chap2-5' class='c001'>V. EVOLUTIONARY LOVE<a id='r72' /><a href='#f72' class='c011'><sup>[72]</sup></a> <br /> AT FIRST BLUSH. COUNTER-GOSPELS</h3>
| |
| − | </div>
| |
| − | <p class='c006'>Philosophy, when just escaping from its golden pupa-skin,
| |
| − | mythology, proclaimed the great evolutionary agency of the
| |
| − | universe to be Love. Or, since this pirate-lingo, English,
| |
| − | is poor in such-like words, let us say Eros, the exuberance-love.
| |
| − | Afterwards, Empedocles set up passionate-love and
| |
| − | hate as the two co-ordinate powers of the universe. In some
| |
| − | passages, kindness is the word. But certainly, in any sense
| |
| − | in which it has an opposite, to be senior partner of that
| |
| − | opposite, is the highest position that love can attain. Nevertheless,
| |
| − | the ontological gospeller, in whose days those views
| |
| − | were familiar topics, made the One Supreme Being, by
| |
| − | whom all things have been made out of nothing, to be
| |
| − | cherishing-love. What, then, can he say to hate? Never
| |
| − | mind, at this time, what the scribe of the apocalypse, if he
| |
| − | were John, stung at length by persecution into a rage unable
| |
| − | to distinguish suggestions of evil from visions of heaven,
| |
| − | and so become the Slanderer of God to men, may have
| |
| − | dreamed. The question is rather what the sane John
| |
| − | thought, or ought to have thought, in order to carry out
| |
| − | his idea consistently. His statement that God is love seems
| |
| − | aimed at that saying of Ecclesiastes that we cannot tell
| |
| − | whether God bears us love or hatred. “Nay,” says John,
| |
| − | “we can tell, and very simply! We know and have
| |
| − | <span class='pageno' id='Page_268'>268</span>trusted the love which God hath in us. God is love.”
| |
| − | There is no logic in this, unless it means that God loves all
| |
| − | men. In the preceding paragraph, he had said, “God is
| |
| − | light and in him is no darkness at all.” We are to understand,
| |
| − | then, that as darkness is merely the defect of light,
| |
| − | so hatred and evil are mere imperfect stages of ἀγἀπη
| |
| − | and ἀγαθόν, love and loveliness. This concords with that
| |
| − | utterance reported in John’s Gospel: “God sent not the
| |
| − | Son into the world to judge the world; but that the world
| |
| − | should through him be saved. He that believeth on him is
| |
| − | not judged: he that believeth not hath been judged already....
| |
| − | And this is the judgment, that the light is
| |
| − | come into the world, and that men loved darkness rather
| |
| − | than the light.” That is to say, God visits no punishment
| |
| − | on them; they punish themselves, by their natural affinity
| |
| − | for the defective. Thus, the love that God is, is not a love
| |
| − | of which hatred is the contrary; otherwise Satan would be
| |
| − | a co-ordinate power; but it is a love which embraces hatred
| |
| − | as an imperfect stage of it, an Anteros—yea, even needs
| |
| − | hatred and hatefulness as its object. For self-love is no
| |
| − | love; so if God’s self is love, that which he loves must be
| |
| − | defect of love; just as a luminary can light up only that
| |
| − | which otherwise would be dark. Henry James, the Swedenborgian,
| |
| − | says: “It is no doubt very tolerable finite or
| |
| − | creaturely love to love one’s own in another, to love another
| |
| − | for his conformity to one’s self: but nothing can be in
| |
| − | more flagrant contrast with the creative Love, all whose
| |
| − | tenderness <i>ex vi termini</i> must be reserved only for what
| |
| − | intrinsically is most bitterly hostile and negative to itself.”
| |
| − | This is from <i>Substance and Shadow</i>: an <i>Essay on the
| |
| − | <span class='pageno' id='Page_269'>269</span>Physics of Creation</i>. It is a pity he had not filled his pages
| |
| − | with things like this, as he was able easily to do, instead of
| |
| − | scolding at his reader and at people generally, until the
| |
| − | physics of creation was well-nigh forgot. I must deduct,
| |
| − | however, from what I just wrote: obviously no genius could
| |
| − | make his every sentence as sublime as one which discloses
| |
| − | for the problem of evil its everlasting solution.</p>
| |
| − |
| |
| − | <p class='c005'>The movement of love is circular, at one and the same
| |
| − | impulse projecting creations into independency and drawing
| |
| − | them into harmony. This seems complicated when
| |
| − | stated so; but it is fully summed up in the simple formula
| |
| − | we call the Golden Rule. This does not, of course, say,
| |
| − | Do everything possible to gratify the egoistic impulses of
| |
| − | others, but it says, Sacrifice your own perfection to the
| |
| − | perfectionment of your neighbor. Nor must it for a moment
| |
| − | be confounded with the Benthamite, or Helvetian, or
| |
| − | Beccarian motto, Act for the greatest good of the greatest
| |
| − | number. Love is not directed to abstractions but to persons;
| |
| − | not to persons we do not know, nor to numbers of
| |
| − | people, but to our own dear ones, our family and neighbors.
| |
| − | “Our neighbor,” we remember, is one whom we live near,
| |
| − | not locally perhaps, but in life and feeling.</p>
| |
| − |
| |
| − | <p class='c005'>Everybody can see that the statement of St. John is the
| |
| − | formula of an evolutionary philosophy, which teaches that
| |
| − | growth comes only from love, from—I will not say self-<i>sacrifice</i>,
| |
| − | but from the ardent impulse to fulfil another’s
| |
| − | highest impulse. Suppose, for example, that I have an idea
| |
| − | that interests me. It is my creation. It is my creature;
| |
| − | for as shown in last July’s <i>Monist</i>, it is a little person. I
| |
| − | love it; and I will sink myself in perfecting it. It is not
| |
| − | <span class='pageno' id='Page_270'>270</span>by dealing out cold justice to the circle of my ideas that
| |
| − | I can make them grow, but by cherishing and tending them
| |
| − | as I would the flowers in my garden. The philosophy we
| |
| − | draw from John’s gospel is that this is the way mind develops;
| |
| − | and as for the cosmos, only so far as it yet is mind,
| |
| − | and so has life, is it capable of further evolution. Love,
| |
| − | recognizing germs of loveliness in the hateful, gradually
| |
| − | warms it into life, and makes it lovely. That is the sort
| |
| − | of evolution which every careful student of my essay <i>The
| |
| − | Law of Mind</i>, must see that <i>synechism</i> calls for.</p>
| |
| − |
| |
| − | <p class='c005'>The nineteenth century is now fast sinking into the grave,
| |
| − | and we all begin to review its doings and to think what
| |
| − | character it is destined to bear as compared with other
| |
| − | centuries in the minds of future historians. It will be
| |
| − | called, I guess, the Economical Century; for political
| |
| − | economy has more direct relations with all the branches of
| |
| − | its activity than has any other science. Well, political
| |
| − | economy has its formula of redemption, too. It is this:
| |
| − | Intelligence in the service of greed ensures the justest
| |
| − | prices, the fairest contracts, the most enlightened conduct
| |
| − | of all the dealings between men, and leads to the <i>summum
| |
| − | bonum</i>, food in plenty and perfect comfort. Food for
| |
| − | whom? Why, for the greedy master of intelligence. I do
| |
| − | not mean to say that this is one of the legitimate conclusions
| |
| − | of political economy, the scientific character of which
| |
| − | I fully acknowledge. But the study of doctrines, themselves
| |
| − | true, will often temporarily encourage generalizations
| |
| − | extremely false, as the study of physics has encouraged
| |
| − | necessitarianism. What I say, then, is that the great attention
| |
| − | paid to economical questions during our century
| |
| − | <span class='pageno' id='Page_271'>271</span>has induced an exaggeration of the beneficial effects of
| |
| − | greed and of the unfortunate results of sentiment, until
| |
| − | there has resulted a philosophy which comes unwittingly
| |
| − | to this, that greed is the great agent in the elevation of
| |
| − | the human race and in the evolution of the universe.</p>
| |
| − |
| |
| − | <p class='c005'>I open a handbook of political economy,—the most
| |
| − | typical and middling one I have at hand,—and there find
| |
| − | some remarks of which I will here make a brief analysis.
| |
| − | I omit qualifications, sops thrown to Cerberus, phrases to
| |
| − | placate Christian prejudice, trappings which serve to hide
| |
| − | from author and reader alike the ugly nakedness of the
| |
| − | greed-god. But I have surveyed my position. The author
| |
| − | enumerates “three motives to human action:</p>
| |
| − |
| |
| − | <p class='c005'>The love of self;</p>
| |
| − |
| |
| − | <p class='c005'>The love of a limited class having common interests and
| |
| − | feelings with one’s self;</p>
| |
| − |
| |
| − | <p class='c005'>The love of mankind at large.”</p>
| |
| − |
| |
| − | <p class='c005'>Remark, at the outset, what obsequious title is bestowed
| |
| − | on greed,—“the love of self.” Love! The second motive
| |
| − | <i>is</i> love. In place of “a limited class” put “certain
| |
| − | persons,” and you have a fair description. Taking “class”
| |
| − | in the old-fashioned sense, a weak kind of love is described.
| |
| − | In the sequel, there seems to be some haziness as to the
| |
| − | delimitation of this motive. By the love of mankind at
| |
| − | large, the author does not mean that deep, subconscious
| |
| − | passion that is properly so called; but merely public-spirit,
| |
| − | perhaps little more than a fidget about pushing ideas. The
| |
| − | author proceeds to a comparative estimate of the worth of
| |
| − | these motives. Greed, says he, but using, of course, another
| |
| − | word, “is not so great an evil as is commonly supposed...
| |
| − | <span class='pageno' id='Page_272'>272</span>Every man can promote his own interests a
| |
| − | great deal more effectively than he can promote any one
| |
| − | else’s, or than any one else can promote his.” Besides, as
| |
| − | he remarks on another page, the more miserly a man is,
| |
| − | the more good he does. The second motive “is the most
| |
| − | dangerous one to which society is exposed.” Love is all
| |
| − | very pretty: “no higher or purer source of human happiness
| |
| − | exists.” (Ahem!) But it is a “source of enduring
| |
| − | injury,” and, in short, should be overruled by something
| |
| − | wiser. What is this wiser motive? We shall see.</p>
| |
| − |
| |
| − | <p class='c005'>As for public spirit, it is rendered nugatory by the “difficulties
| |
| − | in the way of its effective operation.” For example,
| |
| − | it might suggest putting checks upon the fecundity
| |
| − | of the poor and the vicious; and “no measure of repression
| |
| − | would be too severe,” in the case of criminals. The hint
| |
| − | is broad. But unfortunately, you cannot induce legislatures
| |
| − | to take such measures, owing to the pestiferous “tender
| |
| − | sentiments of man towards man.” It thus appears,
| |
| − | that public-spirit, or Benthamism, is not strong enough to
| |
| − | be the effective tutor of love, (I am skipping to another
| |
| − | page), which must, therefore, be handed over to “the motives
| |
| − | which animate men in the pursuit of wealth,” in which
| |
| − | alone we can confide, and which “are in the highest degree
| |
| − | beneficent.”<a id='r73' /><a href='#f73' class='c011'><sup>[73]</sup></a> Yes, in the “highest degree” without exception
| |
| − | are they beneficent to the being upon whom all their
| |
| − | blessings are poured out, namely, the Self, whose “sole
| |
| − | object,” says the writer in accumulating wealth is his individual
| |
| − | <span class='pageno' id='Page_273'>273</span>“sustenance and enjoyment.” Plainly, the author
| |
| − | holds the notion that some other motive might be in a higher
| |
| − | degree beneficent even for the man’s self to be a paradox
| |
| − | wanting in good sense. He seeks to gloze and modify his
| |
| − | doctrine; but he lets the perspicacious reader see what his
| |
| − | animating principle is; and when, holding the opinions I
| |
| − | have repeated, he at the same time acknowledges that society
| |
| − | could not exist upon a basis of intelligent greed alone,
| |
| − | he simply pigeon-holes himself as one of the eclectics of
| |
| − | inharmonious opinions. He wants his mammon flavored
| |
| − | with a <i>soupçon</i> of god.</p>
| |
| − |
| |
| − | <p class='c005'>The economists accuse those to whom the enunciation
| |
| − | of their atrocious villainies communicates a thrill of horror
| |
| − | of being <i>sentimentalists</i>. It may be so: I willingly confess
| |
| − | to having some tincture of sentimentalism in me, God be
| |
| − | thanked! Ever since the French Revolution brought this
| |
| − | leaning of thought into ill-repute,—and not altogether
| |
| − | undeservedly, I must admit, true, beautiful, and good as
| |
| − | that great movement was—it has been the tradition to
| |
| − | picture sentimentalists as persons incapable of logical
| |
| − | thought and unwilling to look facts in the eyes. This tradition
| |
| − | may be classed with the French tradition that an
| |
| − | Englishman says <i>godam</i> at every second sentence, the
| |
| − | English tradition that an American talks about “Britishers,”
| |
| − | and the American tradition that a Frenchman
| |
| − | carries forms of etiquette to an inconvenient extreme, in
| |
| − | short with all those traditions which survive simply because
| |
| − | the men who use their eyes and ears are few and far between.
| |
| − | Doubtless some excuse there was for all those
| |
| − | opinions in days gone by; and sentimentalism, when it
| |
| − | <span class='pageno' id='Page_274'>274</span>was the fashionable amusement to spend one’s evenings
| |
| − | in a flood of tears over a woeful performance on a candle-litten
| |
| − | stage, sometimes made itself a little ridiculous. But
| |
| − | what after all is sentimentalism? It is an <i>ism</i>, a doctrine,
| |
| − | namely, the doctrine that great respect should be paid to
| |
| − | the natural judgments of the sensible heart. This is what
| |
| − | sentimentalism precisely is; and I entreat the reader to
| |
| − | consider whether to contemn it is not of all blasphemies the
| |
| − | most degrading. Yet the nineteenth century has steadily
| |
| − | contemned it, because it brought about the Reign of Terror.
| |
| − | That it did so is true. Still, the whole question is
| |
| − | one of <i>how much</i>. The Reign of Terror was very bad; but
| |
| − | now the Gradgrind banner has been this century long
| |
| − | flaunting in the face of heaven, with an insolence to provoke
| |
| − | the very skies to scowl and rumble. Soon a flash and
| |
| − | quick peal will shake economists quite out of their complacency,
| |
| − | too late. The twentieth century, in its latter
| |
| − | half, shall surely see the deluge-tempest burst upon the
| |
| − | social order,—to clear upon a world as deep in ruin as
| |
| − | that greed-philosophy has long plunged it into guilt. No
| |
| − | post-thermidorian high jinks then!</p>
| |
| − |
| |
| − | <p class='c005'>So a miser is a beneficent power in a community, is he?
| |
| − | With the same reason precisely, only in a much higher degree,
| |
| − | you might pronounce the Wall Street sharp to be a
| |
| − | good angel, who takes money from heedless persons not
| |
| − | likely to guard it properly, who wrecks feeble enterprises
| |
| − | better stopped, and who administers wholesome lessons to
| |
| − | unwary scientific men, by passing worthless checks upon
| |
| − | them,—as you did, the other day, to me, my millionaire
| |
| − | Master in glomery, when you thought you saw your way
| |
| − | <span class='pageno' id='Page_275'>275</span>to using my process without paying for it, and of so bequeathing
| |
| − | to your children something to boast of their
| |
| − | father about,—and who by a thousand wiles puts money
| |
| − | at the service of intelligent greed, in his own person. Bernard
| |
| − | Mandeville, in his <i>Fable of the Bees</i>, maintains
| |
| − | that private vices of all descriptions are public benefits,
| |
| − | and proves it, too, quite as cogently as the economist proves
| |
| − | his point concerning the miser. He even argues, with no
| |
| − | slight force, that but for vice civilization would never
| |
| − | have existed. In the same spirit, it has been strongly
| |
| − | maintained and is to-day widely believed that all acts of
| |
| − | charity and benevolence, private and public, go seriously
| |
| − | to degrade the human race.</p>
| |
| − |
| |
| − | <p class='c005'>The <i>Origin of Species</i> of Darwin merely extends
| |
| − | politico-economical views of progress to the entire realm of
| |
| − | animal and vegetable life. The vast majority of our contemporary
| |
| − | naturalists hold the opinion that the true cause
| |
| − | of those exquisite and marvellous adaptations of nature
| |
| − | for which, when I was a boy, men used to extol the divine
| |
| − | wisdom is that creatures are so crowded together that those
| |
| − | of them that happen to have the slightest advantage force
| |
| − | those less pushing into situations unfavorable to multiplication
| |
| − | or even kill them before they reach the age of reproduction.
| |
| − | Among animals, the mere mechanical individualism
| |
| − | is vastly reënforced as a power making for good
| |
| − | by the animal’s ruthless greed. As Darwin puts it on his
| |
| − | title-page, it is the struggle for existence; and he should
| |
| − | have added for his motto: Every individual for himself,
| |
| − | and the Devil take the hindmost! Jesus, in his sermon
| |
| − | on the Mount, expressed a different opinion.</p>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_276'>276</span>Here, then, is the issue. The gospel of Christ says that
| |
| − | progress comes from every individual merging his individuality
| |
| − | in sympathy with his neighbors. On the other side,
| |
| − | the conviction of the nineteenth century is that progress
| |
| − | takes place by virtue of every individual’s striving for himself
| |
| − | with all his might and trampling his neighbor under
| |
| − | foot whenever he gets a chance to do so. This may accurately
| |
| − | be called the Gospel of Greed.</p>
| |
| − |
| |
| − | <p class='c005'>Much is to be said on both sides. I have not concealed,
| |
| − | I could not conceal, my own passionate predilection. Such
| |
| − | a confession will probably shock my scientific brethren.
| |
| − | Yet the strong feeling is in itself, I think, an argument of
| |
| − | some weight in favor of the agapastic theory of evolution,—so
| |
| − | far as it may be presumed to bespeak the normal
| |
| − | judgment of the Sensible Heart. Certainly, if it were
| |
| − | possible to believe in agapasm without believing it warmly,
| |
| − | that fact would be an argument against the truth of the
| |
| − | doctrine. At any rate, since the warmth of feeling exists,
| |
| − | it should on every account be candidly confessed; especially
| |
| − | since it creates a liability to onesidedness on my part
| |
| − | against which it behooves my readers and me to be severally
| |
| − | on our guard.</p>
| |
| − | <h4 class='c012'>SECOND THOUGHTS. IRENICA.</h4>
| |
| − | <p class='c006'>Let us try to define the logical affinities of the different
| |
| − | theories of evolution. Natural selection, as conceived by
| |
| − | Darwin, is a mode of evolution in which the only positive
| |
| − | agent of change in the whole passage from moner to man
| |
| − | is fortuitous variation. To secure advance in a definite
| |
| − | direction chance has to be seconded by some action that
| |
| − | <span class='pageno' id='Page_277'>277</span>shall hinder the propagation of some varieties or stimulate
| |
| − | that of others. In natural selection, strictly so called, it
| |
| − | is the crowding out of the weak. In sexual selection, it is
| |
| − | the attraction of beauty, mainly.</p>
| |
| − |
| |
| − | <p class='c005'>The <i>Origin of Species</i> was published toward the end
| |
| − | of the year 1859. The preceding years since 1846 had been
| |
| − | one of the most productive seasons,—or if extended so
| |
| − | as to cover the great book we are considering, <i>the</i> most productive
| |
| − | period of equal length in the entire history of
| |
| − | science from its beginnings until now. The idea that chance
| |
| − | begets order, which is one of the corner-stones of modern
| |
| − | physics (although Dr. Carus considers it “the weakest
| |
| − | point in Mr. Peirce’s system,”) was at that time put into
| |
| − | its clearest light. Quetelet had opened the discussion by his
| |
| − | <i>Letters on the Application of Probabilities to the Moral
| |
| − | and Political Sciences</i>, a work which deeply impressed
| |
| − | the best minds of that day, and to which Sir John Herschel
| |
| − | had drawn general attention in Great Britain. In 1857, the
| |
| − | first volume of Buckle’s <i>History of Civilisation</i> had
| |
| − | created a tremendous sensation, owing to the use he made of
| |
| − | this same idea. Meantime, the “statistical method” had,
| |
| − | under that very name, been applied with brilliant success
| |
| − | to molecular physics. Dr. John Herapath, an English
| |
| − | chemist, had in 1847 outlined the kinetical theory of gases
| |
| − | in his <i>Mathematical Physics</i>; and the interest the theory
| |
| − | excited had been refreshed in 1856 by notable memoirs by
| |
| − | Clausius and Krönig. In the very summer preceding Darwin’s
| |
| − | publication, Maxwell had read before the British
| |
| − | Association the first and most important of his researches
| |
| − | on this subject. The consequence was that the idea that
| |
| − | <span class='pageno' id='Page_278'>278</span>fortuitous events may result in a physical law, and further
| |
| − | that this is the way in which those laws which appear to
| |
| − | conflict with the principle of the conservation of energy
| |
| − | are to be explained, had taken a strong hold upon the minds
| |
| − | of all who were abreast of the leaders of thought. By such
| |
| − | minds, it was inevitable that the <i>Origin of Species</i>, whose
| |
| − | teaching was simply the application of the same principle
| |
| − | to the explanation of another “non-conservative” action,
| |
| − | that of organic development, should be hailed and welcomed.
| |
| − | The sublime discovery of the conservation of energy
| |
| − | by Helmholtz in 1847, and that of the mechanical theory of
| |
| − | heat by Clausius and by Rankine, independently, in 1850,
| |
| − | had decidedly overawed all those who might have been
| |
| − | inclined to sneer at physical science. Thereafter a belated
| |
| − | poet still harping upon “science peddling with the names
| |
| − | of things” would fail of his effect. Mechanism was now
| |
| − | known to be all, or very nearly so. All this time, utilitarianism,—that
| |
| − | improved substitute for the Gospel,—was
| |
| − | in its fullest feather; and was a natural ally of an individualistic
| |
| − | theory. Dean Mansell’s injudicious advocacy
| |
| − | had led to mutiny among the bondsmen of Sir William
| |
| − | Hamilton, and the nominalism of Mill had profited accordingly;
| |
| − | and although the real science that Darwin was
| |
| − | leading men to was sure some day to give a death-blow to
| |
| − | the sham-science of Mill, yet there were several elements
| |
| − | of the Darwinian theory which were sure to charm the
| |
| − | followers of Mill. Another thing: anæsthetics had been in
| |
| − | use for thirteen years. Already, people’s acquaintance with
| |
| − | suffering had dropped off very much; and as a consequence,
| |
| − | that unlovely hardness by which our times are so contrasted
| |
| − | <span class='pageno' id='Page_279'>279</span>with those that immediately preceded them, had already
| |
| − | set in, and inclined people to relish a ruthless theory. The
| |
| − | reader would quite mistake the drift of what I am saying
| |
| − | if he were to understand me as wishing to suggest that
| |
| − | any of those things (except perhaps Malthus) influenced
| |
| − | Darwin himself. What I mean is that his hypothesis, while
| |
| − | without dispute one of the most ingenious and pretty ever
| |
| − | devised, and while argued with a wealth of knowledge, a
| |
| − | strength of logic, a charm of rhetoric, and above all with
| |
| − | a certain magnetic genuineness that was almost irresistible,
| |
| − | did not appear, at first, at all near to being proved;
| |
| − | and to a sober mind its case looks less hopeful now than
| |
| − | it did twenty years ago; but the extraordinarily favorable
| |
| − | reception it met with was plainly owing, in large measure,
| |
| − | to its ideas being those toward which the age was favorably
| |
| − | disposed, especially, because of the encouragement it gave
| |
| − | to the greed-philosophy.</p>
| |
| − |
| |
| − | <p class='c005'>Diametrically opposed to evolution by chance, are those
| |
| − | theories which attribute all progress to an inward necessary
| |
| − | principle, or other form of necessity. Many naturalists
| |
| − | have thought that if an egg is destined to go through a
| |
| − | certain series of embryological transformations, from which
| |
| − | it is perfectly certain not to deviate, and if in geological
| |
| − | time almost exactly the same forms appear successively,
| |
| − | one replacing another in the same order, the strong presumption
| |
| − | is that this latter succession was as predeterminate
| |
| − | and certain to take place as the former. So, Nägeli, for
| |
| − | instance, conceives that it somehow follows from the first
| |
| − | law of motion and the peculiar, but unknown, molecular
| |
| − | constitution of protoplasm, that forms must complicate
| |
| − | <span class='pageno' id='Page_280'>280</span>themselves more and more. Kolliker makes one form
| |
| − | generate another after a certain maturation has been accomplished.
| |
| − | Weismann, too, though he calls himself a
| |
| − | Darwinian, holds that nothing is due to chance, but that
| |
| − | all forms are simple mechanical resultants of the heredity
| |
| − | from two parents.<a id='r74' /><a href='#f74' class='c011'><sup>[74]</sup></a> It is very noticeable that all these different
| |
| − | sectaries seek to import into their science a mechanical
| |
| − | necessity to which the facts that come under their observation
| |
| − | do not point. Those geologists who think that the
| |
| − | variation of species is due to cataclysmic alterations of
| |
| − | climate or of the chemical constitution of the air and water
| |
| − | are also making mechanical necessity chief factor of
| |
| − | evolution.</p>
| |
| − |
| |
| − | <p class='c005'>Evolution by sporting and evolution by mechanical necessity
| |
| − | are conceptions warring against one another. A third
| |
| − | method, which supersedes their strife, lies enwrapped in
| |
| − | the theory of Lamarck. According to his view, all that
| |
| − | distinguishes the highest organic forms from the most
| |
| − | rudimentary has been brought about by little hypertrophies
| |
| − | or atrophies which have affected individuals early in their
| |
| − | lives, and have been transmitted to their offspring. Such
| |
| − | a transmission of acquired characters is of the general
| |
| − | nature of habit-taking, and this is the representative and
| |
| − | derivative within the physiological domain of the law of
| |
| − | mind. Its action is essentially dissimilar to that of a physical
| |
| − | force; and that is the secret of the repugnance of such
| |
| − | necessitarians as Weismann to admitting its existence. The
| |
| − | Lamarckians further suppose that although some of the
| |
| − | <span class='pageno' id='Page_281'>281</span>modifications of form so transmitted were originally due to
| |
| − | mechanical causes, yet the chief factors of their first production
| |
| − | were the straining of endeavor and the overgrowth
| |
| − | superinduced by exercise, together with the opposite actions.
| |
| − | Now, endeavor, since it is directed toward an end, is essentially
| |
| − | psychical, even though it be sometimes unconscious;
| |
| − | and the growth due to exercise, as I argued in my
| |
| − | last paper, follows a law of a character quite contrary to
| |
| − | that of mechanics.</p>
| |
| − |
| |
| − | <p class='c005'>Lamarckian evolution is thus evolution by the force of
| |
| − | habit.—That sentence slipped off my pen while one of
| |
| − | those neighbors whose function in the social cosmos seems
| |
| − | to be that of an Interrupter, was asking me a question. Of
| |
| − | course, it is nonsense. Habit is mere inertia, a resting on
| |
| − | one’s oars, not a propulsion. Now it is energetic projaculation
| |
| − | (lucky there is such a word, or this untried
| |
| − | hand might have been put to inventing one) by which in
| |
| − | the typical instances of Lamarckian evolution the new
| |
| − | elements of form are first created. Habit, however, forces
| |
| − | them to take practical shapes, compatible with the structures
| |
| − | they affect, and in the form of heredity and otherwise,
| |
| − | gradually replaces the spontaneous energy that sustains
| |
| − | them. Thus, habit plays a double part; it serves to
| |
| − | establish the new features, and also to bring them into
| |
| − | harmony with the general morphology and function of the
| |
| − | animals and plants to which they belong. But if the reader
| |
| − | will now kindly give himself the trouble of turning back a
| |
| − | page or two, he will see that this account of Lamarckian
| |
| − | evolution coincides with the general description of the
| |
| − | action of love, to which, I suppose, he yielded his assent.</p>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_282'>282</span>Remembering that all matter is really mind, remembering,
| |
| − | too, the continuity of mind, let us ask what aspect
| |
| − | Lamarckian evolution takes on within the domain of consciousness.
| |
| − | Direct endeavor can achieve almost nothing.
| |
| − | It is as easy by taking thought to add a cubit to one’s
| |
| − | stature, as it is to produce an idea acceptable to any of
| |
| − | the Muses by merely straining for it, before it is ready to
| |
| − | come. We haunt in vain the sacred well and throne of
| |
| − | Mnemosyne; the deeper workings of the spirit take place
| |
| − | in their own slow way, without our connivance. Let but
| |
| − | their bugle sound, and we may then make our effort, sure
| |
| − | of an oblation for the altar of whatsoever divinity its savor
| |
| − | gratifies. Besides this inward process, there is the operation
| |
| − | of the environment, which goes to break up habits destined
| |
| − | to be broken up and so to render the mind lively. Everybody
| |
| − | knows that the long continuance of a routine of habit
| |
| − | makes us lethargic, while a succession of surprises wonderfully
| |
| − | brightens the ideas. Where there is a motion, where
| |
| − | history is a-making, there is the focus of mental activity,
| |
| − | and it has been said that the arts and sciences reside within
| |
| − | the temple of Janus, waking when that is open, but slumbering
| |
| − | when it is closed. Few psychologists have perceived
| |
| − | how fundamental a fact this is. A portion of mind
| |
| − | abundantly commissured to other portions works almost
| |
| − | mechanically. It sinks to a condition of a railway junction.
| |
| − | But a portion of mind almost isolated, a spiritual peninsula,
| |
| − | or <i>cul-de-sac</i>, is like a railway terminus. Now mental
| |
| − | commissures are habits. Where they abound, originality is
| |
| − | not needed and is not found; but where they are
| |
| − | in defect, spontaneity is set free. Thus, the first
| |
| − | <span class='pageno' id='Page_283'>283</span>step in the Lamarckian evolution of mind is the putting of
| |
| − | sundry thoughts into situations in which they are free to
| |
| − | play. As to growth by exercise, I have already shown, in
| |
| − | discussing <i>Man’s Glassy Essence</i>, in last October’s
| |
| − | <i>Monist</i>, what its <i>modus operandi</i> must be conceived to be,
| |
| − | at least, until a second equally definite hypothesis shall
| |
| − | have been offered. Namely, it consists of the flying
| |
| − | asunder of molecules, and the reparation of the parts by
| |
| − | new matter. It is, thus, a sort of reproduction. It takes
| |
| − | place only during exercise, because the activity of protoplasm
| |
| − | consists in the molecular disturbance which is its
| |
| − | necessary condition. Growth by exercise takes place also
| |
| − | in the mind. Indeed, that is what it is to <i>learn</i>. But the
| |
| − | most perfect illustration is the development of a philosophical
| |
| − | idea by being put into practice. The conception which
| |
| − | appeared, at first, as unitary, splits up into special cases;
| |
| − | and into each of these new thought must enter to make a
| |
| − | practicable idea. This new thought, however, follows
| |
| − | pretty closely the model of the parent conception; and thus
| |
| − | a homogeneous development takes place. The parallel
| |
| − | between this and the course of molecular occurrences is
| |
| − | apparent. Patient attention will be able to trace all these
| |
| − | elements in the transaction called learning.</p>
| |
| − |
| |
| − | <p class='c005'>Three modes of evolution have thus been brought before
| |
| − | us; evolution by fortuitous variation, evolution by
| |
| − | mechanical necessity, and evolution by creative love. We
| |
| − | may term them <i>tychastic</i> evolution, or <i>tychasm</i>, <i>anancastic</i>
| |
| − | evolution, or <i>anancasm</i>, and <i>agapastic</i> evolution, or <i>agapasm</i>.
| |
| − | The doctrines which represent these as severally of
| |
| − | principal importance, we may term <i>tychasticism</i>, <i>anancasticism</i>,
| |
| − | <span class='pageno' id='Page_284'>284</span>and <i>agapasticism</i>. On the other hand the mere
| |
| − | propositions that absolute chance, mechanical necessity,
| |
| − | and the law of love, are severally operative in the cosmos,
| |
| − | may receive the names of <i>tychism</i>, <i>anancism</i>, and <i>agapism</i>.</p>
| |
| − |
| |
| − | <p class='c005'>All three modes of evolution are composed of the same
| |
| − | general elements. Agapasm exhibits them the most clearly.
| |
| − | The good result is here brought to pass, first, by the bestowal
| |
| − | of spontaneous energy by the parent upon the offspring,
| |
| − | and, second, by the disposition of the latter to catch
| |
| − | the general idea of those about it and thus to subserve
| |
| − | the general purpose. In order to express the relation
| |
| − | that tychasm and anancasm bear to agapasm, let me borrow
| |
| − | a word from geometry. An ellipse crossed by a
| |
| − | straight line is a sort of cubic curve; for a cubic is a curve
| |
| − | which is cut thrice by a straight line; now a straight line
| |
| − | might cut the ellipse twice and its associated straight line
| |
| − | a third time. Still the ellipse with the straight line across
| |
| − | it would not have the characteristics of a cubic. It would
| |
| − | have, for instance, no contrary flexure, which no true cubic
| |
| − | wants; and it would have two nodes, which no true cubic
| |
| − | has. The geometers say that it is a <i>degenerate</i> cubic. Just
| |
| − | so, tychasm and anancasm are degenerate forms of
| |
| − | agapasm.</p>
| |
| − |
| |
| − | <p class='c005'>Men who seek to reconcile the Darwinian idea with
| |
| − | Christianity will remark that tychastic evolution, like the
| |
| − | agapastic, depends upon a reproductive creation, the forms
| |
| − | preserved being those that use the spontaneity conferred
| |
| − | upon them in such wise as to be drawn into harmony with
| |
| − | their original, quite after the Christian scheme. Very
| |
| − | good! This only shows that just as love cannot have a
| |
| − | <span class='pageno' id='Page_285'>285</span>contrary, but must embrace what is most opposed to it, as a
| |
| − | degenerate case of it, so tychasm is a kind of agapasm.
| |
| − | Only, in the tychastic evolution progress is solely owing to
| |
| − | the distribution of the napkin-hidden talent of the rejected
| |
| − | servant among those not rejected, just as ruined
| |
| − | gamesters leave their money on the table to make those
| |
| − | not yet ruined so much the richer. It makes the felicity
| |
| − | of the lambs just the damnation of the goats, transposed
| |
| − | to the other side of the equation. In genuine agapasm,
| |
| − | on the other hand, advance takes place by virtue of a positive
| |
| − | sympathy among the created springing from continuity
| |
| − | of mind. This is the idea which tychasticism knows not
| |
| − | how to manage.</p>
| |
| − |
| |
| − | <p class='c005'>The anancasticist might here interpose, claiming that
| |
| − | the mode of evolution for which he contends agrees with
| |
| − | agapasm at the point at which tychasm departs from it.
| |
| − | For it makes development go through certain phases, having
| |
| − | its inevitable ebbs and flows, yet tending on the whole to a
| |
| − | foreordained perfection. Bare existence by this its destiny
| |
| − | betrays an intrinsic affinity for the good. Herein, it must
| |
| − | be admitted, anancasm shows itself to be in a broad acception
| |
| − | a species of agapasm. Some forms of it might easily
| |
| − | be mistaken for the genuine agapasm. The Hegelian philosophy
| |
| − | is such an anancasticism. With its revelatory religion,
| |
| − | with its synechism (however imperfectly set forth),
| |
| − | with its “reflection,” the whole idea of the theory is superb,
| |
| − | almost sublime. Yet, after all, living freedom is practically
| |
| − | omitted from its method. The whole movement is that
| |
| − | of a vast engine, impelled by a <i>vis a tergo</i>, with a blind and
| |
| − | mysterious fate of arriving at a lofty goal. I mean that
| |
| − | <span class='pageno' id='Page_286'>286</span>such an engine it <i>would</i> be, if it really worked; but in point
| |
| − | of fact, it is a Keely motor. Grant that it really acts as
| |
| − | it professes to act, and there is nothing to do but accept the
| |
| − | philosophy. But never was there seen such an example of
| |
| − | a long chain of reasoning,—shall I say with a flaw in
| |
| − | every link?—no, with every link a handful of sand,
| |
| − | squeezed into shape in a dream. Or say, it is a pasteboard
| |
| − | model of a philosophy that in reality does not exist. If we
| |
| − | use the one precious thing it contains, the idea of it, introducing
| |
| − | the tychism which the arbitrariness of its every
| |
| − | step suggests, and make that the support of a vital freedom
| |
| − | which is the breath of the spirit of love, we may be
| |
| − | able to produce that genuine agapasticism, at which Hegel
| |
| − | was aiming.</p>
| |
| − | <h4 class='c012'>A THIRD ASPECT. DISCRIMINATION</h4>
| |
| − | <p class='c006'>In the very nature of things, the line of demarcation between
| |
| − | the three modes of evolution is not perfectly sharp.
| |
| − | That does not prevent its being quite real; perhaps it is
| |
| − | rather a mark of its reality. There is in the nature of things
| |
| − | no sharp line of demarcation between the three fundamental
| |
| − | colors, red, green, and violet. But for all that they
| |
| − | are really different. The main question is whether three
| |
| − | radically different evolutionary elements have been operative;
| |
| − | and the second question is what are the most striking
| |
| − | characteristics of whatever elements have been operative.</p>
| |
| − |
| |
| − | <p class='c005'>I propose to devote a few pages to a very slight examination
| |
| − | of these questions in their relation to the historical
| |
| − | development of human thought. I first formulate for the
| |
| − | reader’s convenience the briefest possible definitions of the
| |
| − | <span class='pageno' id='Page_287'>287</span>three conceivable modes of development of thought, distinguishing
| |
| − | also two varieties of anancasm and three of
| |
| − | agapasm. The tychastic development of thought, then,
| |
| − | will consist in slight departures from habitual ideas in different
| |
| − | directions indifferently, quite purposeless and quite
| |
| − | unconstrained whether by outward circumstances or by
| |
| − | force of logic, these new departures being followed by unforeseen
| |
| − | results which tend to fix some of them as habits
| |
| − | more than others. The anancastic development of thought
| |
| − | will consist of new ideas adopted without foreseeing whither
| |
| − | they tend, but having a character determined by causes
| |
| − | either external to the mind, such as changed circumstances
| |
| − | of life, or internal to the mind as logical developments of
| |
| − | ideas already accepted, such as generalizations. The agapastic
| |
| − | development of thought is the adoption of certain
| |
| − | mental tendencies, not altogether heedlessly, as in tychasm,
| |
| − | nor quite blindly by the mere force of circumstances or of
| |
| − | logic, as in anancasm, but by an immediate attraction for
| |
| − | the idea itself, whose nature is divined before the mind
| |
| − | possesses it, by the power of sympathy, that is, by virtue
| |
| − | of the continuity of mind; and this mental tendency may
| |
| − | be of three varieties, as follows: First, it may affect a
| |
| − | whole people or community in its collective personality,
| |
| − | and be thence communicated to such individuals as are in
| |
| − | powerfully sympathetic connection with the collective
| |
| − | people, although they may be intellectually incapable of
| |
| − | attaining the idea by their private understandings or even
| |
| − | perhaps of consciously apprehending it. Second, it may
| |
| − | affect a private person directly, yet so that he is only enabled
| |
| − | to apprehend the idea, or to appreciate its attractiveness,
| |
| − | <span class='pageno' id='Page_288'>288</span>by virtue of his sympathy with his neighbors, under the influence
| |
| − | of a striking experience or development of thought.
| |
| − | The conversion of St. Paul may be taken as an example of
| |
| − | what is meant. Third, it may affect an individual, independently
| |
| − | of his human affections, by virtue of an attraction
| |
| − | it exercises upon his mind, even before he has comprehended
| |
| − | it. This is the phenomenon which has been well called the
| |
| − | <i>divination</i> of genius; for it is due to the continuity between
| |
| − | the man’s mind and the Most High.</p>
| |
| − |
| |
| − | <p class='c005'>Let us next consider by means of what tests we can discriminate
| |
| − | between these different categories of evolution.
| |
| − | No absolute criterion is possible in the nature of things,
| |
| − | since in the nature of things there is no sharp line of demarcation
| |
| − | between the different classes. Nevertheless,
| |
| − | quantitative symptoms may be found by which a sagacious
| |
| − | and sympathetic judge of human nature may be able to
| |
| − | estimate the approximate proportions in which the different
| |
| − | kinds of influence are commingled.</p>
| |
| − |
| |
| − | <p class='c005'>So far as the historical evolution of human thought has
| |
| − | been tychastic, it should have proceeded by insensible or
| |
| − | minute steps; for such is the nature of chances when so
| |
| − | multiplied as to show phenomena of regularity. For example,
| |
| − | assume that of the native-born white adult males
| |
| − | of the United States in 1880, one-fourth part were below
| |
| − | 5 feet 4 inches in stature and one-fourth part above 5 feet
| |
| − | 8 inches. Then by the principles of probability, among the
| |
| − | whole population, we should expect</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line in8'>216 under 4 feet 6 inches,</div>
| |
| − | <div class='line in9'>48 “ 4 ” 5 “</div>
| |
| − | <div class='line in10'>9 ” 4 “ 4 ”</div>
| |
| − | <div class='line'>less than 2 “ 4 ” 3 “</div>
| |
| − | </div>
| |
| − | <div class='group'>
| |
| − | <div class='line in8'>216 above 6 feet 6 inches,</div>
| |
| − | <div class='line in9'>48 “ 6 ” 7 “</div>
| |
| − | <div class='line in10'>9 ” 6 “ 8 ”</div>
| |
| − | <div class='line'>less than 2 “ 6 ” 9 “</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'><span class='pageno' id='Page_289'>289</span>I set down these figures to show how insignificantly few
| |
| − | are the cases in which anything very far out of the common
| |
| − | run presents itself by chance. Though the stature of only
| |
| − | every second man is included within the four inches between
| |
| − | 5 feet 4 inches and 5 feet 8 inches, yet if this interval
| |
| − | be extended by thrice four inches above and below, it will
| |
| − | embrace all our 8 millions odd of native-born adult white
| |
| − | males (of 1880), except only 9 taller and 9 shorter.</p>
| |
| − |
| |
| − | <p class='c005'>The test of minute variation, if <i>not</i> satisfied, absolutely
| |
| − | negatives tychasm. If it is satisfied, we shall find that it
| |
| − | negatives anancasm but not agapasm. We want a positive
| |
| − | test, satisfied by tychasm, only. Now wherever we find
| |
| − | men’s thought taking by imperceptible degrees a turn contrary
| |
| − | to the purposes which animate them, in spite of their
| |
| − | highest impulses, there, we may safely conclude, there has
| |
| − | been a tychastic action.</p>
| |
| − |
| |
| − | <p class='c005'>Students of the history of mind there be of an erudition
| |
| − | to fill an imperfect scholar like me with envy edulcorated
| |
| − | by joyous admiration, who maintain that ideas when just
| |
| − | started are and can be little more than freaks, since they
| |
| − | cannot yet have been critically examined, and further that
| |
| − | everywhere and at all times progress has been so gradual
| |
| − | that it is difficult to make out distinctly what original step
| |
| − | any given man has taken. It would follow that tychasm
| |
| − | has been the sole method of intellectual development. I
| |
| − | have to confess I cannot read history so; I cannot help
| |
| − | thinking that while tychasm has sometimes been operative,
| |
| − | at others great steps covering nearly the same ground and
| |
| − | made by different men independently, have been mistaken
| |
| − | for a succession of small steps, and further that students
| |
| − | <span class='pageno' id='Page_290'>290</span>have been reluctant to admit a real entitative “spirit” of
| |
| − | an age or of a people, under the mistaken and unscrutinized
| |
| − | impression that they should thus be opening the door to wild
| |
| − | and unnatural hypotheses. I find, on the contrary, that,
| |
| − | however it may be with the education of individual minds,
| |
| − | the historical development of thought has seldom been
| |
| − | of a tychastic nature, and exclusively in backward and
| |
| − | barbarizing movements. I desire to speak with the extreme
| |
| − | modesty which befits a student of logic who is required to
| |
| − | survey so very wide a field of human thought that he can
| |
| − | cover it only by a reconnaissance, to which only the greatest
| |
| − | skill and most adroit methods can impart any value at all;
| |
| − | but, after all, I can only express my own opinions and not
| |
| − | those of anybody else; and in my humble judgment, the
| |
| − | largest example of tychasm is afforded by the history of
| |
| − | Christianity, from about its establishment by Constantine,
| |
| − | to, say, the time of the Irish monasteries, an era or eon of
| |
| − | about 500 years. Undoubtedly the external circumstance
| |
| − | which more than all others at first inclined men to accept
| |
| − | Christianity in its loveliness and tenderness, was the fearful
| |
| − | extent to which society was broken up into units by the unmitigated
| |
| − | greed and hard-heartedness into which the
| |
| − | Romans had seduced the world. And yet it was that very
| |
| − | same fact, more than any other external circumstance, that
| |
| − | fostered that bitterness against the wicked world of which
| |
| − | the primitive gospel of Mark contains not a single trace.
| |
| − | At least, I do not detect it in the remark about the blasphemy
| |
| − | against the Holy Ghost, where nothing is said about
| |
| − | vengeance, nor even in that speech where the closing lines of
| |
| − | Isaiah are quoted, about the worm and the fire that feed
| |
| − | <span class='pageno' id='Page_291'>291</span>upon the “carcasses of the men that have transgressed
| |
| − | against me.” But little by little the bitterness increases
| |
| − | until in the last book of the New Testament, its poor distracted
| |
| − | author represents that all the time Christ was talking
| |
| − | about having come to save the world, the secret design
| |
| − | was to catch the entire human race, with the exception of a
| |
| − | paltry 144,000, and souse them all in a brimstone lake,
| |
| − | and as the smoke of their torment went up forever and ever,
| |
| − | to turn and remark, “There is no curse any more.” Would
| |
| − | it be an insensible smirk or a fiendish grin that should
| |
| − | accompany such an utterance? I wish I could believe St.
| |
| − | John did not write it; but it is his gospel which tells about
| |
| − | the “resurrection unto condemnation,”—that is of men’s
| |
| − | being resuscitated just for the sake of torturing them;—and,
| |
| − | at any rate, the Revelation is a very ancient composition.
| |
| − | One can understand that the early Christians were
| |
| − | like men trying with all their might to climb a steep declivity
| |
| − | of smooth wet clay; the deepest and truest element of
| |
| − | their life, animating both heart and head, was universal
| |
| − | love; but they were continually, and against their wills,
| |
| − | slipping into a party spirit, every slip serving as a precedent,
| |
| − | in a fashion but too familiar to every man. This party feeling
| |
| − | insensibily grew until by about <span class='fss'>A.D.</span> 330 the luster of
| |
| − | the pristine integrity that in St. Mark reflects the white
| |
| − | spirit of light was so far tarnished that Eusebius, (the Jared
| |
| − | Sparks of that day), in the preface to his History, could announce
| |
| − | his intention of exaggerating everything that tended
| |
| − | to the glory of the church and of suppressing whatever
| |
| − | might disgrace it. His Latin contemporary Lactantius is
| |
| − | worse, still; and so the darkling went on increasing until
| |
| − | <span class='pageno' id='Page_292'>292</span>before the end of the century the great library of Alexandria
| |
| − | was destroyed by Theophilus,<a id='r75' /><a href='#f75' class='c011'><sup>[75]</sup></a> until Gregory the Great,
| |
| − | two centuries later, burnt the great library of Rome, proclaiming
| |
| − | that “Ignorance is the mother of devotion,”
| |
| − | (which is true, just as oppression and injustice is the
| |
| − | mother of spirituality), until a sober description of the
| |
| − | state of the church would be a thing our not too nice newspapers
| |
| − | would treat as “unfit for publication.” All this
| |
| − | movement is shown by the application of the test given
| |
| − | above to have been tychastic. Another very much like
| |
| − | it on a small scale, only a hundred times swifter, for the
| |
| − | study of which there are documents by the library-full,
| |
| − | is to be found in the history of the French Revolution.</p>
| |
| − |
| |
| − | <p class='c005'>Anancastic evolution advances by successive strides
| |
| − | with pauses between. The reason is that in this process
| |
| − | a habit of thought having been overthrown is supplanted by
| |
| − | the next strongest. Now this next strongest is sure to be
| |
| − | widely disparate from the first, and as often as not is its
| |
| − | direct contrary. It reminds one of our old rule of making
| |
| − | the second candidate vice-president. This character, therefore,
| |
| − | clearly distinguishes anancasm from tychasm. The
| |
| − | character which distinguishes it from agapasm is its purposelessness.
| |
| − | But external and internal anancasm have to
| |
| − | be examined separately. Development under the pressure
| |
| − | of external circumstances, or cataclysmine evolution,
| |
| − | is in most cases unmistakable enough. It has numberless
| |
| − | degrees of intensity, from the brute force, the plain war,
| |
| − | which has more than once turned the current of the world’s
| |
| − | thought, down to the hard fact of evidence, or what has been
| |
| − | <span class='pageno' id='Page_293'>293</span>taken for it, which has been known to convince men by
| |
| − | hordes. The only hesitation than can subsist in the presence
| |
| − | of such a history is a quantitative one. Never are external
| |
| − | influences the only ones which affect the mind, and therefore
| |
| − | it must be a matter of judgment for which it would scarcely
| |
| − | be worth while to attempt to set rules, whether a given
| |
| − | movement is to be regarded as principally governed from
| |
| − | without or not. In the rise of medieval thought, I mean
| |
| − | scholasticism and the synchronistic art developments, undoubtedly
| |
| − | the crusades and the discovery of the writings of
| |
| − | Aristotle were powerful influences. The development of
| |
| − | scholasticism from Roscellin to Albertus Magnus closely
| |
| − | follows the successive steps in the knowledge of Aristotle.
| |
| − | Prantl thinks that that is the whole story, and few men
| |
| − | have thumbed more books than Carl Prantl. He has done
| |
| − | good solid work, notwithstanding his slap-dash judgments.
| |
| − | But we shall never make so much as a good beginning
| |
| − | of comprehending scholasticism until the whole has been
| |
| − | systematically explored and digested by a company of students
| |
| − | regularly organized and held under rule for that purpose.
| |
| − | But as for the period we are now specially considering,
| |
| − | that which synchronised the Romanesque architecture,
| |
| − | the literature is easily mastered. It does not quite justify
| |
| − | Prantl’s dicta as to the slavish dependence of these authors
| |
| − | upon their authorities. Moreover, they kept a definite
| |
| − | purpose steadily before their minds, throughout all their
| |
| − | studies. I am, therefore, unable to offer this period of
| |
| − | scholasticism as an example of pure external anancasm,
| |
| − | which seems to be the fluorine of the intellectual elements.
| |
| − | Perhaps the recent Japanese reception of western ideas is
| |
| − | <span class='pageno' id='Page_294'>294</span>the purest instance of it in history. Yet in combination
| |
| − | with other elements, nothing is commoner. If the development
| |
| − | of ideas under the influence of the study of external
| |
| − | facts be considered as external anancasm,—it is on the
| |
| − | border between the external and the internal forms,—it
| |
| − | is, of course, the principal thing in modern learning. But
| |
| − | Whewell, whose masterly comprehension of the history of
| |
| − | science critics have been too ignorant properly to appreciate,
| |
| − | clearly shows that it is far from being the overwhelmingly
| |
| − | preponderant influence, even there.</p>
| |
| − |
| |
| − | <p class='c005'>Internal anancasm, or logical groping, which advances
| |
| − | upon a predestined line without being able to foresee whither
| |
| − | it is to be carried nor to steer its course, this is the rule of
| |
| − | development of philosophy. Hegel first made the world
| |
| − | understand this; and he seeks to make logic not merely
| |
| − | the subjective guide and monitor of thought, which was all
| |
| − | it had been ambitioning before, but to be the very main-spring
| |
| − | of thinking, and not merely of individual thinking but
| |
| − | of discussion, of the history of the development of thought,
| |
| − | of all history, of all development. This involves a positive,
| |
| − | clearly demonstrable error. Let the logic in question be
| |
| − | of whatever kind it may, a logic of necessary inference or
| |
| − | a logic of probable inference (the theory might perhaps
| |
| − | be shaped to fit either), in any case it supposes that logic is
| |
| − | sufficient of itself to determine what conclusion follows
| |
| − | from given premises; for unless it will do so much, it will
| |
| − | not suffice to explain why an individual train of reasoning
| |
| − | should take just the course it does take, to say nothing
| |
| − | of other kinds of development. It thus supposes that from
| |
| − | given premises, only one conclusion can logically be drawn,
| |
| − | <span class='pageno' id='Page_295'>295</span>and that there is no scope at all for free choice. That from
| |
| − | given premises only one conclusion can logically be drawn,
| |
| − | is one of the false notions which have come from logicians’
| |
| − | confining their attention to that Nantucket of thought, the
| |
| − | logic of non-relative terms. In the logic of relatives, it
| |
| − | does not hold good.</p>
| |
| − |
| |
| − | <p class='c005'>One remark occurs to me. If the evolution of history is
| |
| − | in considerable part of the nature of internal anancasm, it
| |
| − | resembles the development of individual men; and just as
| |
| − | 33 years is a rough but natural unit of time for individuals,
| |
| − | being the average age at which man has issue, so there
| |
| − | should be an approximate period at the end of which one
| |
| − | great historical movement ought to be likely to be supplanted
| |
| − | by another. Let us see if we can make out anything
| |
| − | of the kind. Take the governmental development of
| |
| − | Rome as being sufficiently long and set down the principal
| |
| − | dates.</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'><span class='fss'>B.C.</span> 753, Foundation of Rome.</div>
| |
| − | <div class='line'><span class='fss'>B.C.</span> 510, Expulsion of the Tarquins.</div>
| |
| − | <div class='line'><span class='fss'>B.C.</span> 27, Octavius assumes title Augustus.</div>
| |
| − | <div class='line'><span class='fss'>A.D.</span> 476, End of Western Empire.</div>
| |
| − | <div class='line'><span class='fss'>A.D.</span> 962, Holy Roman Empire.</div>
| |
| − | <div class='line'><span class='fss'>A.D.</span> 1453, Fall of Constantinople.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>The last event was one of the most significant in history,
| |
| − | especially for Italy. The intervals are 243, 483, 502, 486,
| |
| − | 491 years. All are rather curiously near equal, except the
| |
| − | first which is half the others. Successive reigns of kings
| |
| − | would not commonly be so near equal. Let us set down
| |
| − | a few dates in the history of thought.</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'><span class='pageno' id='Page_296'>296</span><span class='fss'>B.C.</span> 585, Eclipse of Thales. Beginning of Greek philosophy.</div>
| |
| − | <div class='line'><span class='fss'>A.D.</span> 30, The crucifixion.</div>
| |
| − | <div class='line'><span class='fss'>A.D.</span> 529, Closing of Athenian schools. End of Greek philosophy.</div>
| |
| − | <div class='line'><span class='fss'>A.D.</span> 1125, (Approximate) Rise of the Universities of Bologna and Paris.</div>
| |
| − | <div class='line'><span class='fss'>A.D.</span> 1543, Publication of the “De Revolutionibus” of Copernicus. Beginning of Modern Science.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>The intervals are 615, 499, 596, 418, years. In the history
| |
| − | of metaphysics, we may take the following:</p>
| |
| − |
| |
| − | <div class='lg-container-b c013'>
| |
| − | <div class='linegroup'>
| |
| − | <div class='group'>
| |
| − | <div class='line'><span class='fss'>B.C.</span> 322, Death of Aristotle.</div>
| |
| − | <div class='line'><span class='fss'>A.D.</span> 1274, Death of Aquinas.</div>
| |
| − | <div class='line'><span class='fss'>A.D.</span> 1804, Death of Kant.</div>
| |
| − | </div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <p class='c014'>The intervals are 1595 and 530 years. The former is about
| |
| − | thrice the latter.</p>
| |
| − |
| |
| − | <p class='c005'>From these figures, no conclusion can fairly be drawn.
| |
| − | At the same time, they suggest that perhaps there may be
| |
| − | a rough natural era of about 500 years. Should there be
| |
| − | any independent evidence of this, the intervals noticed may
| |
| − | gain some significance.</p>
| |
| − |
| |
| − | <p class='c005'>The agapastic development of thought should, if it exists,
| |
| − | be distinguished by its purposive character, this purpose
| |
| − | being the development of an idea. We should have a direct
| |
| − | agapic or sympathetic comprehension and recognition of it,
| |
| − | by virtue of the continuity of thought. I here take it for
| |
| − | granted that such continuity of thought has been sufficiently
| |
| − | proved by the arguments used in my paper on the “Law
| |
| − | of Mind” in <i>The Monist</i> of last July. Even if those arguments
| |
| − | are not quite convincing in themselves, yet if they
| |
| − | <span class='pageno' id='Page_297'>297</span>are reënforced by an apparent agapasm in the history of
| |
| − | thought, the two propositions will lend one another mutual
| |
| − | aid. The reader will, I trust, be too well grounded in logic
| |
| − | to mistake such mutual support for a vicious circle in reasoning.
| |
| − | If it could be shown directly that there is such an
| |
| − | entity as the “spirit of an age” or of a people, and that
| |
| − | mere individual intelligence will not account for all the
| |
| − | phenomena, this would be proof enough at once of agapasticism
| |
| − | and of synechism. I must acknowledge that I am
| |
| − | unable to produce a cogent demonstration of this; but I
| |
| − | am, I believe, able to adduce such arguments as will serve
| |
| − | to confirm those which have been drawn from other facts.
| |
| − | I believe that all the greatest achievements of mind have
| |
| − | been beyond the powers of unaided individuals; and I find,
| |
| − | apart from the support this opinion receives from synechistic
| |
| − | considerations, and from the purposive character of many
| |
| − | great movements, direct reason for so thinking in the sublimity
| |
| − | of the ideas and in their occurring simultaneously
| |
| − | and independently to a number of individuals of no extraordinary
| |
| − | general powers. The pointed Gothic architecture
| |
| − | in several of its developments appears to me to be of
| |
| − | such a character. All attempts to imitate it by modern
| |
| − | architects of the greatest learning and genius appear flat
| |
| − | and tame, and are felt by their authors to be so. Yet at the
| |
| − | time the style was living, there was quite an abundance of
| |
| − | men capable of producing works of this kind of gigantic
| |
| − | sublimity and power. In more than one case, extant documents
| |
| − | show that the cathedral chapters, in the selection of
| |
| − | architects, treated high artistic genius as a secondary consideration,
| |
| − | as if there were no lack of persons able to supply
| |
| − | <span class='pageno' id='Page_298'>298</span>that; and the results justify their confidence. Were individuals
| |
| − | in general, then, in those ages possessed of such lofty
| |
| − | natures and high intellect? Such an opinion would break
| |
| − | down under the first examination.</p>
| |
| − |
| |
| − | <p class='c005'>How many times have men now in middle life seen great
| |
| − | discoveries made independently and almost simultaneously!
| |
| − | The first instance I remember was the prediction of a planet
| |
| − | exterior to Uranus by Leverrier and Adams. One hardly
| |
| − | knows to whom the principle of the conservation of energy
| |
| − | ought to be attributed, although it may reasonably be considered
| |
| − | as the greatest discovery science has ever made.
| |
| − | The mechanical theory of heat was set forth by Rankine
| |
| − | and by Clausius during the same month of February, 1850;
| |
| − | and there are eminent men who attribute this great step
| |
| − | to Thomson.<a id='r76' /><a href='#f76' class='c011'><sup>[76]</sup></a> The kinetical theory of gases, after being
| |
| − | started by John Bernoulli and long buried in oblivion, was
| |
| − | reinvented and applied to the explanation not merely of the
| |
| − | laws of Boyle, Charles, and Avogadro, but also of diffusion
| |
| − | and viscosity, by at least three modern physicists separately.
| |
| − | It is well known that the doctrine of natural selection was
| |
| − | presented by Wallace and by Darwin at the same meeting
| |
| − | of the British Association; and Darwin in his “Historical
| |
| − | Sketch” prefixed to the later editions of his book shows
| |
| − | that both were anticipated by obscure forerunners. The
| |
| − | method of spectrum analysis was claimed for Swan as well
| |
| − | as for Kirchhoff, and there were others who perhaps had
| |
| − | still better claims. The authorship of the Periodical Law
| |
| − | of the Chemical Elements is disputed between a Russian,
| |
| − | <span class='pageno' id='Page_299'>299</span>a German, and an Englishman; although there is no room
| |
| − | for doubt that the principal merit belongs to the first. These
| |
| − | are nearly all the greatest discoveries of our times. It is
| |
| − | the same with the inventions. It may not be surprising
| |
| − | that the telegraph should have been independently made by
| |
| − | several inventors, because it was an easy corollary from
| |
| − | scientific facts well made out before. But it was not so
| |
| − | with the telephone and other inventions. Ether, the first
| |
| − | anæsthetic, was introduced independently by three different
| |
| − | New England physicians. Now ether had been a common
| |
| − | article for a century. It had been in one of the pharmacopœias
| |
| − | three centuries before. It is quite incredible that
| |
| − | its anæsthetic property should not have been known; it
| |
| − | was known. It had probably passed from mouth to ear
| |
| − | as a secret from the days of Basil Valentine; but for long
| |
| − | it had been a secret of the Punchinello kind. In New
| |
| − | England, for many years, boys had used it for amusement.
| |
| − | Why then had it not been put to its serious use? No reason
| |
| − | can be given, except that the motive to do so was not strong
| |
| − | enough. The motives to doing so could only have been
| |
| − | desire for gain and philanthropy. About 1846, the date of
| |
| − | the introduction, philanthropy was undoubtedly in an unusually
| |
| − | active condition. That sensibility, or sentimentalism,
| |
| − | which had been introduced in the previous century,
| |
| − | had undergone a ripening process, in consequence of which,
| |
| − | though now less intense than it had previously been, it was
| |
| − | more likely to influence unreflecting people than it had ever
| |
| − | been. All three of the ether-claimants had probably been
| |
| − | influenced by the desire for gain; but nevertheless they were
| |
| − | certainly not insensible to the agapic influences.</p>
| |
| − |
| |
| − | <p class='c005'><span class='pageno' id='Page_300'>300</span>I doubt if any of the great discoveries ought, properly,
| |
| − | to be considered as altogether individual achievements; and
| |
| − | I think many will share this doubt. Yet, if not, what an
| |
| − | argument for the continuity of mind, and for agapasticism
| |
| − | is here! I do not wish to be very strenuous. If thinkers
| |
| − | will only be persuaded to lay aside their prejudices and
| |
| − | apply themselves to studying the evidences of this doctrine,
| |
| − | I shall be fully content to await the final decision.</p>
| |
| − |
| |
| − | <div class='chapter'>
| |
| − | <span class='pageno' id='Page_301'>301</span>
| |
| − | <h2 id='essay' class='c009'><i>Supplementary Essay</i> <br /> THE PRAGMATISM OF PEIRCE <br /> BY <br /> <span class='sc'>John Dewey</span></h2>
| |
| − | </div>
| |
| − | <p class='c006'>The term pragmatism was introduced into literature in the
| |
| − | opening sentences of Professor James’s California Union address
| |
| − | in 1898. The sentences run as follows: “The principle of
| |
| − | pragmatism, as we may call it, may be expressed in a variety
| |
| − | of ways, all of them very simple. In the <i>Popular Science
| |
| − | Monthly</i> for January, 1878, Mr. Charles S. Peirce introduces it
| |
| − | as follows:” etc. The readers who have turned to the volume
| |
| − | referred to have not, however, found the word there. From
| |
| − | other sources we know that the name as well as the idea was
| |
| − | furnished by Mr. Peirce. The latter has told us that both the
| |
| − | word and the idea were suggested to him by a reading of Kant,
| |
| − | the idea by the <i>Critique of Pure Reason</i>, the term by the
| |
| − | “Critique of Practical Reason.”<a id='r77' /><a href='#f77' class='c011'><sup>[77]</sup></a> The article in the <i>Monist</i>
| |
| − | gives such a good statement of both the idea and the reason for
| |
| − | selecting the term that it may be quoted <i>in extenso</i>. Peirce sets
| |
| − | out by saying that with men who work in laboratories, the habit
| |
| − | of mind is molded by experimental work much more than they
| |
| − | are themselves aware. “Whatever statement you may make to
| |
| − | him, he [the experimentalist] will either understand as meaning
| |
| − | that if a given prescription for an experiment ever can be and
| |
| − | ever is carried out in act, an experience of a given description
| |
| − | will result, or else he will see no sense at all in what you say.”
| |
| − | Having himself the experimental mind and being interested in
| |
| − | methods of thinking, “he framed the theory that a <i>conception</i>,
| |
| − | that is, the rational purport of a word or other expression, lies
| |
| − | <span class='pageno' id='Page_302'>302</span>exclusively in its bearing upon the conduct of life; so that,
| |
| − | since obviously nothing that might not result from experiment
| |
| − | can have any direct bearing upon conduct, if one can define accurately
| |
| − | all the conceivable experimental phenomena which the
| |
| − | affirmation or denial of a concept could imply, one will have
| |
| − | therein a complete definition of the concept, and <i>there is absolutely
| |
| − | nothing more in it</i>. For this doctrine, he invented the
| |
| − | name <i>pragmatism</i>.”</p>
| |
| − |
| |
| − | <p class='c005'>After saying that some of his friends wished him to call the
| |
| − | doctrine practicism or practicalism, he says that he had learned
| |
| − | philosophy from Kant, and that to one “who still thought in
| |
| − | Kantian terms most readily, <i>praktisch</i> and <i>pragmatisch</i> were as
| |
| − | far apart as the two poles, the former belonging to a region of
| |
| − | thought where no mind of the experimentalist type can ever
| |
| − | make sure of solid ground under his feet, the latter expressing
| |
| − | relation to some definite human purpose. Now quite the most
| |
| − | striking feature of the new theory was its recognition of an inseparable
| |
| − | connection between rational cognition and human
| |
| − | purpose.”<a id='r78' /><a href='#f78' class='c011'><sup>[78]</sup></a></p>
| |
| − |
| |
| − | <p class='c005'>From this brief statement, it will be noted that Peirce confined
| |
| − | the significance of the term to the determination of the
| |
| − | meaning of terms, or better, propositions; the theory was not, of
| |
| − | itself, a theory of the test, or the truth, of propositions. Hence
| |
| − | the title of his original article: <i>How to Make Ideas Clear</i>. In
| |
| − | his later writing, after the term had been used as a theory of
| |
| − | truth,—he proposed the more limited “pragmaticism” to
| |
| − | designate his original specific meaning.<a id='r79' /><a href='#f79' class='c011'><sup>[79]</sup></a> But even with respect
| |
| − | to the meaning of propositions, there is a marked difference
| |
| − | between his pragmaticism and the pragmatism of, say, James.
| |
| − | Some of the critics (especially continental) of the latter would
| |
| − | have saved themselves some futile beating of the air, if they
| |
| − | had reacted to James’s statements instead of to their own associations
| |
| − | <span class='pageno' id='Page_303'>303</span>with the word “pragmatic.” Thus James says in his
| |
| − | California address: “The effective meaning of any philosophic
| |
| − | proposition can always be brought down to some particular consequence,
| |
| − | in our future practical experience, whether active or
| |
| − | passive; the point lying rather in the fact that the experience
| |
| − | must be <i>particular</i>, than in the fact that it must be <i>active</i>.”
| |
| − | (Italics mine.)</p>
| |
| − |
| |
| − | <p class='c005'>Now the curious fact is that Peirce puts more emphasis upon
| |
| − | practise (or conduct) and less upon the particular; in fact, he
| |
| − | transfers the emphasis to the general. The following passage is
| |
| − | worth quotation because of the definiteness with which it identifies
| |
| − | meaning with both the future and with the general. “The
| |
| − | rational meaning of every proposition lies in the future. How
| |
| − | so? The meaning of a proposition is itself a proposition. Indeed,
| |
| − | it is no other than the very proposition of which it is the
| |
| − | meaning: it is a translation of it. But of the myriads of forms
| |
| − | into which a proposition may be translated, which is that one
| |
| − | which is to be called its very meaning? It is, according to the
| |
| − | pragmaticist, that form in which the proposition becomes applicable
| |
| − | to human conduct, not in these or those special circumstances
| |
| − | nor when one entertains this or that special design,
| |
| − | but that form which is most applicable to self-control under
| |
| − | every situation and to every purpose.” Hence, “it must be
| |
| − | simply the general description of all the experimental phenomena
| |
| − | which the assertion of the proposition virtually predicts.” Or,
| |
| − | paraphrasing, pragmatism identifies meaning with formation
| |
| − | of a habit, or way of acting having the greatest generality possible,
| |
| − | or the widest range of application to particulars. Since
| |
| − | habits or ways of acting are just as real as particulars, it is committed
| |
| − | to a belief in the reality of “universals.” Hence it is
| |
| − | not a doctrine of phenomenalism, for while the richness of phenomena
| |
| − | lies in their sensuous quality, pragmatism does not intend
| |
| − | to define these (leaving them, as it were, to speak for
| |
| − | themselves), but “eliminates their sential element, and endeavors
| |
| − | to define the rational purport, and this it finds in the
| |
| − | purposive bearing of the word or proposition in question.”
| |
| − | Moreover, not only are generals real, but they are physically
| |
| − | <span class='pageno' id='Page_304'>304</span>efficient. The meanings “the air is stuffy” and “stuffy air is
| |
| − | unwholesome” may determine, for example, the opening of the
| |
| − | window. Accordingly on the ethical side, “the pragmaticist does
| |
| − | not make the <i>summum bonum</i> to consist in action, but makes
| |
| − | it to consist in that process of evolution whereby the existent
| |
| − | comes more and more to embody those generals...; in other
| |
| − | words, becomes, through action an embodiment of rational purports
| |
| − | or habits generalized as widely as possible.”<a id='r80' /><a href='#f80' class='c011'><sup>[80]</sup></a></p>
| |
| − |
| |
| − | <p class='c005'>The passages quoted should be compared with what Peirce
| |
| − | has to say in the Baldwin Dictionary article. There he says
| |
| − | that James’s doctrine seems to commit us to the belief “that
| |
| − | the end of man is action—a stoical maxim which does not commend
| |
| − | itself as forcibly to the present writer at the age of sixty
| |
| − | as it did at thirty. If it be admitted, on the contrary, that
| |
| − | action wants an end, and that the end must be something of a
| |
| − | general description, then the spirit of the maxim itself ...
| |
| − | would direct us toward something different from practical facts,
| |
| − | namely, to general ideas.... The only ultimate good which
| |
| − | the practical facts to which the maxim directs attention can
| |
| − | subserve is to further the development of concrete reasonableness....
| |
| − | Almost everybody will now agree that the ultimate good
| |
| − | lies in the evolutionary process in some way. If so, it is not
| |
| − | in individual reactions in their segregation, but in something
| |
| − | general or continuous. Synechism is founded on the notion that
| |
| − | the coalescence, the becoming continuous, the becoming governed
| |
| − | by laws, the becoming instinct with general ideas, are
| |
| − | but phases of one and the same process of the growth of reasonableness.
| |
| − | This is first shown to be true with mathematical
| |
| − | exactitude in the field of logic, and is thence inferred to hold
| |
| − | good metaphysically. It is not opposed to pragmaticism ...
| |
| − | but includes that procedure as a step.”</p>
| |
| − |
| |
| − | <p class='c005'>Here again we have the doctrine of pragmaticism as a doctrine
| |
| − | that meaning or rational purport resides in the setting up
| |
| − | of habits or generalized methods, a doctrine passing over into
| |
| − | <span class='pageno' id='Page_305'>305</span>the metaphysics of synechism. It will be well now to recur
| |
| − | explicitly to Peirce’s earlier doctrine which he seems to qualify—although,
| |
| − | as he notes, he upheld the doctrine of the reality
| |
| − | of generals even at the earlier period. Peirce sets out, in his
| |
| − | article on the “Fixation of Belief,” with the empirical difference
| |
| − | of doubt and belief expressed in the facts that belief determines
| |
| − | a habit while doubt does not, and that belief is calm
| |
| − | and satisfactory while doubt is an uneasy and dissatisfied state
| |
| − | from which we struggle to emerge; to attain, that is, a state of
| |
| − | belief, a struggle which may be called inquiry. The sole object
| |
| − | of inquiry is the fixation of belief. The scientific method of fixation
| |
| − | has, however, certain rivals: one is that of “tenacity”—constant
| |
| − | reiteration, dwelling upon everything conducive to the
| |
| − | belief, avoidance of everything which might unsettle it—the
| |
| − | will to believe. The method breaks down in practice because
| |
| − | of man’s social nature; we have to take account of contrary
| |
| − | beliefs in others, so that the real problem is to fix the belief of
| |
| − | the community; for otherwise our own belief is precariously
| |
| − | exposed to attack and doubt. Hence the resort to the method
| |
| − | of authority. This method breaks down in time by the fact
| |
| − | that authority can not fix all beliefs in all their details, and
| |
| − | because of the conflict which arises between organized traditions.
| |
| − | There may then be recourse to what is “agreeable to reason”—a
| |
| − | method potent in formation of taste and in esthetic productions
| |
| − | and in the history of philosophy,—but a method which
| |
| − | again fails to secure permanent agreements in society, and so
| |
| − | leaves individual belief at the mercy of attack. Hence, finally,
| |
| − | recourse to science, whose fundamental hypothesis is this:
| |
| − | “There are real things, whose characters are entirely independent
| |
| − | of our opinions about them; those realities affect our senses
| |
| − | according to regular laws, and ... by taking advantage of the
| |
| − | laws of perception, we can ascertain by <i>reasoning</i> how things
| |
| − | really are, and any man if he have sufficient experience and reason
| |
| − | enough about it, will be led to the one true conclusion.”<a id='r81' /><a href='#f81' class='c011'><sup>[81]</sup></a></p>
| |
| − |
| |
| − | <p class='c005'>It will be noted that the quotation employs the terms
| |
| − | “reality” and “truth,” while it makes them a part of the statement
| |
| − | <span class='pageno' id='Page_306'>306</span>of the <i>hypothesis</i> entertained in scientific procedure. Upon
| |
| − | such a basis, what meanings attach to the terms “reality” and
| |
| − | “truth”? Since they are general terms, their meanings must be
| |
| − | determined on the basis of the effects, having practical bearings,
| |
| − | which the object of our conception has. Now the effect which
| |
| − | real things have is to cause beliefs; beliefs are then the consequences
| |
| − | which give the general term reality a “rational purport.”
| |
| − | And on the assumption of the scientific method, the <i>distinguishing</i>
| |
| − | character of the <i>real</i> object must be that it tends to produce a
| |
| − | single universally accepted belief. “All the followers of science
| |
| − | are fully persuaded that the processes of investigation, if only
| |
| − | pushed far enough, will give one certain solution to every question
| |
| − | to which they can be applied.” “This activity of thought
| |
| − | by which we are carried, not where we wish, but to a foreordained
| |
| − | goal, is like the operation of destiny.... This great
| |
| − | law is embodied in the conception of truth and reality. The
| |
| − | opinion which is fated to be ultimately agreed to by all <i>who
| |
| − | investigate</i>, is what we mean by the truth, and the object represented
| |
| − | in this opinion is the real.”<a id='r82' /><a href='#f82' class='c011'><sup>[82]</sup></a> In a subsequent essay
| |
| − | (on the “Probability of Induction”) Peirce expressly draws
| |
| − | the conclusion which follows from this statement; viz., that this
| |
| − | conception of truth and reality makes everything depend upon
| |
| − | the character of the methods of inquiry and inference by which
| |
| − | conclusions are reached. “In the case of synthetic inferences
| |
| − | we know only the degree of trustworthiness of our proceeding.
| |
| − | As all knowledge comes from synthetic inference, we must also
| |
| − | infer that all human certainty consists merely in our knowing
| |
| − | that the processes by which our knowledge has been derived
| |
| − | are such as must generally have led to true conclusions”<a id='r83' /><a href='#f83' class='c011'><sup>[83]</sup></a>—true
| |
| − | conclusions, once more, being those which command the
| |
| − | agreement of competent inquiries.</p>
| |
| − |
| |
| − | <p class='c005'>Summing up, we may say that Peirce’s pragmaticism is a
| |
| − | doctrine concerning the meaning, conception, or rational purport
| |
| − | of objects, namely, that these consist in the “effects, which
| |
| − | might conceivably have practical bearings, we conceive the object
| |
| − | <span class='pageno' id='Page_307'>307</span>of our conception to have. Then, our conception of these
| |
| − | effects is the whole of our conception of the object.”<a id='r84' /><a href='#f84' class='c011'><sup>[84]</sup></a> “Our
| |
| − | idea of anything is our idea of its sensible effects,” and if we have
| |
| − | any doubt as to whether we really believe the effects to be sensible
| |
| − | or no, we have only to ask ourselves whether or no we should
| |
| − | act any differently in their presence. In short, our own responses
| |
| − | to sensory stimuli are the ultimate, or testing, ingredients in our
| |
| − | conception of an object. In the literal sense of the word pragmatist,
| |
| − | therefore, Peirce is more of a pragmatist than James.</p>
| |
| − |
| |
| − | <p class='c005'>He is also less of a nominalist. That is to say, he emphasizes
| |
| − | much less the <i>particular</i> sensible consequence, and much more
| |
| − | the habit, the generic attitude of response, set up in consequence
| |
| − | of experiences with a thing. In the passage in the Dictionary
| |
| − | already quoted he speaks as if in his later life he attached less
| |
| − | importance to action, and more to “concrete reasonableness”
| |
| − | than in his earlier writing. It may well be that the relative emphasis
| |
| − | had shifted. But there is at most but a difference of
| |
| − | emphasis. For in his later doctrine, concrete rationality means a
| |
| − | change in existence brought about <i>through</i> action, and through
| |
| − | action which embodies conceptions whose own specific existence
| |
| − | consists in habitual attitudes of response. In his earlier writing,
| |
| − | the emphasis upon habits, as something generic, is explicit.
| |
| − | “What a thing means is simply what habits it involves.”<a id='r85' /><a href='#f85' class='c011'><sup>[85]</sup></a>
| |
| − | More elaborately, “Induction infers a rule. Now the belief of
| |
| − | a rule is a habit. That a habit is a rule, active in us, is evident.
| |
| − | That every belief is of the nature of a habit, in so far as it is
| |
| − | of a general character, has been shown in the earlier papers of
| |
| − | this series.”<a id='r86' /><a href='#f86' class='c011'><sup>[86]</sup></a></p>
| |
| − |
| |
| − | <p class='c005'>The difference between Peirce and James which next strikes
| |
| − | us is the greater emphasis placed by the former upon the method
| |
| − | of procedure. As the quotations already made show, everything
| |
| − | ultimately turned, for Peirce, upon the trustworthiness of the
| |
| − | procedures of inquiry. Hence his high estimate of logic, as compared
| |
| − | with James—at least James in his later days. Hence also
| |
| − | <span class='pageno' id='Page_308'>308</span>his definite rejection of the appeal to the Will to Believe—under
| |
| − | the form of what he calls the method of tenacity. Closely
| |
| − | associated with this is the fact that Peirce has a more explicit
| |
| − | dependence upon the social factor than has James. The appeal
| |
| − | in Peirce is essentially to the consensus of those who have investigated,
| |
| − | using methods which are capable of employment by
| |
| − | all. It is the need for social agreement, and the fact that in its
| |
| − | absence “the method of tenacity” will be exposed to disintegration
| |
| − | from without, which finally forces upon mankind the
| |
| − | wider and wider utilization of the scientific method.</p>
| |
| − |
| |
| − | <p class='c005'>Finally, both Peirce and James are realists. The reasonings of
| |
| − | both depend upon the assumption of real things which really
| |
| − | have effects or consequences. Of the two, Peirce makes clearer
| |
| − | the fact that in philosophy at least we are dealing with the
| |
| − | <i>conception</i> of reality, with reality as a term having rational purport,
| |
| − | and hence with something whose meaning is itself to be
| |
| − | determined in terms of consequences. That “reality” means
| |
| − | the object of those beliefs which have, after prolonged and
| |
| − | coöperative inquiry, becomes stable, and “truth” the quality of
| |
| − | these beliefs is a logical consequence of this position. Thus
| |
| − | while “we may define the real as that whose characters are
| |
| − | independent of what anybody may think them to be ... it
| |
| − | would be a great mistake to suppose that this definition makes
| |
| − | the idea of reality perfectly clear.”<a id='r87' /><a href='#f87' class='c011'><sup>[87]</sup></a> For it is only the outcome
| |
| − | of persistent and conjoint inquiry which enables us to give
| |
| − | intelligible meaning in the concrete to the expression “characters
| |
| − | independent of what anybody may think them to be.”
| |
| − | (This is the pragmatic way out of the egocentric predicament.)
| |
| − | And while my purpose is wholly expository I can not close without
| |
| − | inquiring whether recourse to Peirce would not have a most
| |
| − | beneficial influence in contemporary discussion. Do not a large
| |
| − | part of our epistemological difficulties arise from an attempt to
| |
| − | define the “real” as something given prior to reflective inquiry
| |
| − | instead of as that which reflective inquiry is forced to reach and
| |
| − | to which when it is reached belief can stably cling?</p>
| |
| − |
| |
| − | <div class='chapter'>
| |
| − | <span class='pageno' id='Page_309'>309</span>
| |
| − | <h2 class='c009'>BIBLIOGRAPHY OF PEIRCE’S PUBLISHED WRITINGS</h2>
| |
| − | </div>
| |
| − | <p class='c006'>I. Writings of General Interest.<a id='r88' /><a href='#f88' class='c011'><sup>[88]</sup></a></p>
| |
| − |
| |
| − | <p class='c007'><i>A.</i> Three papers in the <i>Journal of Speculative Philosophy</i>, Vol. 2
| |
| − | (1868).</p>
| |
| − |
| |
| − | <p class='c008'>1. “Questions Concerning Certain Faculties Claimed for
| |
| − | Man,” pp. 103-114.</p>
| |
| − |
| |
| − | <p class='c008'>2. “Some Consequences of Four Incapacities,” pp. 140-157.</p>
| |
| − |
| |
| − | <p class='c008'>3. “Ground of Validity of the Laws of Logic,” pp. 193-208.</p>
| |
| − |
| |
| − | <p class='c014'>These three papers, somewhat loosely connected, deal mainly with the
| |
| − | philosophy of discursive thought. The first deals with our power of intuition,
| |
| − | and holds that “every thought is a sign.” The second, one of the
| |
| − | most remarkable of Peirce’s writings, contains an acute criticism of the
| |
| − | Cartesian tradition and a noteworthy argument against the traditional
| |
| − | emphasis on “images” in thinking. The third contains, <i>inter alia</i>, a
| |
| − | refutation of Mill’s indictment of the syllogism. The same volume of the
| |
| − | <i>Journal</i> contains two unsigned communications on Nominalism and on the
| |
| − | Meaning of Determined.</p>
| |
| − |
| |
| − | <p class='c007'><i>B.</i> Review of Fraser’s “Berkeley,” in the <i>North American Review</i>,
| |
| − | Vol. 113 (1871), pp. 449-472.</p>
| |
| − |
| |
| − | <p class='c014'>This paper contains an important analysis on medieval realism, and of
| |
| − | Berkeley’s nominalism. (A Scotist realism continues to distinguish Peirce’s
| |
| − | work after this.)</p>
| |
| − |
| |
| − | <p class='c007'><i>C.</i> “Illustrations of the Logic of Science,” in <i>Popular Science
| |
| − | Monthly</i>, Vols. 12-13 (1877-1878). Reprinted in Pt. I
| |
| − | of this volume. The first and second papers were also
| |
| − | published in the <i>Revue Philosophique</i>, Vols. 6-7 (1879).</p>
| |
| − |
| |
| − | <p class='c008'><i>D.</i> Ten papers in the <i>Monist</i>, Vols. 1-3 (1891-1893), and 15-16
| |
| − | (1905-1906). The first five are reprinted in Pt. II of this
| |
| − | volume.</p>
| |
| − |
| |
| − | <p class='c014'>The sixth paper, “Reply to the Necessitarians,” Vol. 3, pp. 526-570, is
| |
| − | an answer to the criticism of the foregoing by the editor of the <i>Monist</i>,
| |
| − | Vol. 2, pp. 560ff.; cf. Vol. 3, pp. 68ff. and 571ff., and McCrie, “The Issues
| |
| − | of Synechism,” Vol. 3, pp. 380ff.</p>
| |
| − |
| |
| − | <p class='c007'><span class='pageno' id='Page_310'>310</span>7. “What Pragmatism Is?” Vol. 15, pp. 161-181.</p>
| |
| − |
| |
| − | <p class='c008'>8. “The Issues of Pragmaticism,” Vol. 15, pp. 481-499.</p>
| |
| − |
| |
| − | <p class='c008'>9. “Mr. Peterson’s Proposed Discussion,” Vol. 16, pp. 147ff.</p>
| |
| − |
| |
| − | <p class='c008'>10. “Prolegomena to an Apology for Pragmaticism,” Vol. 16,
| |
| − | pp. 492-546.</p>
| |
| − |
| |
| − | <p class='c014'>The last four papers develop Peirce’s thought by showing its agreement
| |
| − | and disagreement with the pragmatism of James and Schiller. The last
| |
| − | paper contains his Method of Existential Graphs.</p>
| |
| − |
| |
| − | <p class='c007'><i>E.</i> “The Reality of God,” in the <i>Hibbert Journal</i>, Vol. 7 (1908),
| |
| − | pp. 96-112. (This article contains brief indications of many
| |
| − | of Peirce’s leading ideas.)</p>
| |
| − |
| |
| − | <p class='c008'><i>F.</i> Six Papers in the <i>Open Court</i>, Vols. 6-7 (1893).</p>
| |
| − |
| |
| − | <p class='c008'>1. “Pythagorics” (on the Pythagorean brotherhood), pp.
| |
| − | 3375-3377.</p>
| |
| − |
| |
| − | <p class='c008'>2. “Dmesis” (on charity towards criminals), pp. 3399-3402.</p>
| |
| − |
| |
| − | <p class='c008'>3. “The Critic of Arguments (I.), Exact Thinking,” pp. 3391-3394.</p>
| |
| − |
| |
| − | <p class='c008'>4. “The Critic of Arguments (II.), The Reader is Introduced
| |
| − | to Relatives,” pp. 3415-3419. (The last two contain a
| |
| − | very clear succinct account of the general character of
| |
| − | Peirce’s logic.)</p>
| |
| − |
| |
| − | <p class='c008'>5. “What is Christian Faith?” pp. 3743-3745.</p>
| |
| − |
| |
| − | <p class='c008'>6. “The Marriage of Religion and Science,” pp. 3559-3560.</p>
| |
| − |
| |
| − | <p class='c008'><i>G.</i> Articles in Baldwin’s “Dictionary of Philosophy”: Individual,
| |
| − | kind, matter and form, possibility, pragmatism, priority,
| |
| − | reasoning, sign, scientific method, sufficient reason, synechism,
| |
| − | and uniformity.</p>
| |
| − |
| |
| − | <p class='c008'><i>H.</i> “Pearson’s Grammar of Science,” in <i>Popular Science Monthly</i>,
| |
| − | Vol. 58 (1901), pp. 296-306. (A critique of Pearson’s
| |
| − | conceptualism and of his utilitarian view as to the aim of
| |
| − | science.)</p>
| |
| − |
| |
| − | <p class='c014'>II. Writings of Predominantly Logical Interest.</p>
| |
| − |
| |
| − | <p class='c007'><i>A.</i> Five Papers on Logic, read before the American Academy of
| |
| − | Arts and Sciences. Published in the <i>Proceedings of the
| |
| − | Academy</i>, Vol. 7 (1867).</p>
| |
| − |
| |
| − | <p class='c008'>1. “On an Improvement in Boole’s Calculus of Logic,” pp.
| |
| − | 250-261. (Suggests improvements in Boole’s logic, especially
| |
| − | in the representation of particular propositions.
| |
| − | The association of probability with the notion of relative
| |
| − | frequency became a leading idea of Peirce’s
| |
| − | thought.)</p>
| |
| − |
| |
| − | <p class='c008'>2. “On the Natural Classification of Arguments,” pp. 261-287.
| |
| − | (A suggestive distinction between the leading
| |
| − | principle and the premise of an argument. Contains
| |
| − | also an interesting note (pp. 283-284) denying the positivistic
| |
| − | <span class='pageno' id='Page_311'>311</span>maxim that, “no hypothesis is admissible which
| |
| − | is not capable of verification by direct observation.”)</p>
| |
| − |
| |
| − | <p class='c008'>3. “On a New List of Categories,” pp. 287-298. The categories
| |
| − | are: Being, Quality (Reference to a Ground),
| |
| − | Relation (Reference to a Correlate), Representation
| |
| − | (Reference to an Interpretant), Substance. “Logic
| |
| − | has for its subject-genus all symbols and not merely
| |
| − | concepts.” Symbols include terms, propositions, and
| |
| − | arguments.</p>
| |
| − |
| |
| − | <p class='c008'>4. “Upon the Logic of Mathematics,” pp. 402-412. “There
| |
| − | are certain general propositions from which the truths
| |
| − | of mathematics follow syllogistically.”</p>
| |
| − |
| |
| − | <p class='c008'>5. “Upon Logical Comprehension and Extension,” pp. 416-432.
| |
| − | (Interesting historical references to the use of
| |
| − | these terms and an attack on the supposed rule as to
| |
| − | their inverse proportionality.)</p>
| |
| − |
| |
| − | <p class='c008'><i>B.</i> “Description of a Notation for the Logic of Relations,” in
| |
| − | <i>Memoires of the American Academy</i>, Vol. 9 (1870), pp.
| |
| − | 317-378. (Shows the relation of inclusion between classes
| |
| − | to be more fundamental than Boole’s use of equality. Extends
| |
| − | the Booleian calculus to DeMorgan’s logic of relative
| |
| − | terms.)</p>
| |
| − |
| |
| − | <p class='c008'><i>C.</i> “On the Algebra of Logic,” <i>American Journal of Mathematics</i>,
| |
| − | Vol. 3 (1880), pp. 15-57. (Referred to by Schroeder as
| |
| − | Peirce’s <i>Hauptwerk</i> in “Vorlesungen über die Algebra der
| |
| − | Logik,” Vol. 1., p. 107.)</p>
| |
| − |
| |
| − | <p class='c008'><i>D.</i> “On the Logic of Number,” <i>American Journal of Mathematics</i>,
| |
| − | Vol. 4 (1881), pp. 85-95.</p>
| |
| − |
| |
| − | <p class='c008'><i>E.</i> “Brief Description of the Algebra of Relatives,” Reprinted from
| |
| − | ??, pp. 1-6.</p>
| |
| − |
| |
| − | <p class='c008'><i>F.</i> “On the Algebra of Logic: A Contribution to the Philosophy of
| |
| − | Notation,” <i>American Journal of Mathematics</i>, Vol. 7 (1884),
| |
| − | pp. 180-202.</p>
| |
| − |
| |
| − | <p class='c008'><i>G.</i> “A Theory of Probable Inference” and notes “On a Limited
| |
| − | Universe of Marks” and on the “Logic of Relatives” in
| |
| − | “Studies in Logic by members of the Johns Hopkins
| |
| − | University,” Boston, 1883, pp. 126-203.</p>
| |
| − |
| |
| − | <p class='c008'><i>H.</i> “The Regenerated Logic,” <i>Monist</i>, Vol. 7, pp. 19-40.</p>
| |
| − |
| |
| − | <p class='c008'>“The Logic of Relatives,” <i>Monist</i>, Vol. 7, pp. 161-217. (An
| |
| − | elaborate development of his own logic of relatives, by way
| |
| − | of review of Schroeder’s book.)</p>
| |
| − |
| |
| − | <p class='c008'><i>I.</i> Miscellaneous Notes, etc.</p>
| |
| − |
| |
| − | <p class='c008'>1. Review of Venn’s “Logic of Chance,” <i>North American
| |
| − | Review</i>, July, 1867.</p>
| |
| − |
| |
| − | <p class='c008'>2. “On the Application of Logical Analysis to Multiple Algebra,”
| |
| − | <span class='pageno' id='Page_312'>312</span><i>Proceedings of the American Academy</i>, Vol. 10
| |
| − | (1875), pp. 392-394.</p>
| |
| − |
| |
| − | <p class='c008'>3. “Note on Grassman’s ‘Calculus of Extension,’” <i>Proceedings
| |
| − | of the American Academy</i>, Vol. 13 (1878), pp. 115-116.</p>
| |
| − |
| |
| − | <p class='c008'>4. “Note on Conversion,” <i>Mind</i>, Vol. 1, p. 424.</p>
| |
| − |
| |
| − | <p class='c008'>5. Notes and Additions to Benjamin Peirce’s “Linear Associative
| |
| − | Algebra,” <i>American Journal of Mathematics</i>,
| |
| − | Vol. 4 (1881), pp. 92ff., especially pp. 221-229.</p>
| |
| − |
| |
| − | <p class='c008'>6. “Logical Machines,” <i>American Journal of Psychology</i>,
| |
| − | Vol. 1 (1888).</p>
| |
| − |
| |
| − | <p class='c008'>7. “Infinitesimals,” <i>Science</i>, Vol. 11 (1900), p. 430.</p>
| |
| − |
| |
| − | <p class='c008'>8. “Some Amazing Mazes,” <i>Monist</i>, Vol. 18 (April and July,
| |
| − | 1908), and Vol. 19 (Jan., 1909).</p>
| |
| − |
| |
| − | <p class='c008'>9. “On Non-Aristotelian Logic” (Letter), <i>Monist</i>, Vol. 20.</p>
| |
| − |
| |
| − | <p class='c008'><i>J.</i> A Syllabus of Certain Topics of Logic. 1903. Boston. Alfred
| |
| − | Mudge & Son (a four page brochure).</p>
| |
| − |
| |
| − | <p class='c008'><i>K.</i> Articles in Baldwin’s “Dictionary of Philosophy” on: laws of
| |
| − | thought, leading principle, logic (exact and symbolic),
| |
| − | modality, negation, predicate and predication, probable inference,
| |
| − | quality, quantity, relatives, significant, simple, subject,
| |
| − | syllogism, theory, truth and falsity universal, universe,
| |
| − | validity, verification, whole and parts.</p>
| |
| − |
| |
| − | <p class='c014'>III. Researches in the Theory and Methods of Measurement.</p>
| |
| − |
| |
| − | <p class='c007'><i>A.</i> General and Astronomic.</p>
| |
| − |
| |
| − | <p class='c008'>1. “On the Theory of Errors of Observation,” <i>Report of the
| |
| − | Superintendent of the U. S. Coast Survey</i> for 1870, pp.
| |
| − | 220-224.</p>
| |
| − |
| |
| − | <p class='c008'>2. “Note on the Theory of Economy of Research,” <i>Report
| |
| − | of the U. S. Coast Survey</i> for 1876, pp. 197-201. (This
| |
| − | paper deals with the relation between the utility and
| |
| − | the cost of diminishing the probable error.)</p>
| |
| − |
| |
| − | <p class='c008'>3. “Apparatus for Recording a Mean of Observed Times,”
| |
| − | <i>U. S. Coast Survey</i>, 1877. Appendix No. 15 to <i>Report</i>
| |
| − | of 1875.</p>
| |
| − |
| |
| − | <p class='c008'>4. “Ferrero’s Metodo dei Minimi Quadrati,” <i>American Journal
| |
| − | of Mathematics</i>, Vol. 1 (1878), pp. 55-63.</p>
| |
| − |
| |
| − | <p class='c008'>5. “Photometric Researches,” <i>Annals of the Astronomical
| |
| − | Observatory of Harvard College</i>, Vol. 9 (1878), pp. 1-181.</p>
| |
| − |
| |
| − | <p class='c008'>6. “Methods and Results. Measurement of Gravity.” Washington.
| |
| − | 1879.</p>
| |
| − |
| |
| − | <p class='c008'>7. “Methods and Results. A Catalogue of Stars for Observations
| |
| − | of Latitude.” Washington. 1879.</p>
| |
| − |
| |
| − | <p class='c008'><span class='pageno' id='Page_313'>313</span>8. “On the Ghosts in Rutherford’s ‘Diffraction Spectra,’”
| |
| − | <i>American Journal of Mathematics</i>, Vol. 2 (1879), pp.
| |
| − | 330-347.</p>
| |
| − |
| |
| − | <p class='c008'>9. “Note on a Comparison of a Wave-Length with a Meter,”
| |
| − | <i>American Journal of Science</i>, Vol. 18 (1879), p. 51.</p>
| |
| − |
| |
| − | <p class='c008'>10. “A Quincuncial Projection of the Sphere,” <i>American Journal
| |
| − | of Mathematics</i>, Vol. 2 (1879), pp. 394, 396.</p>
| |
| − |
| |
| − | <p class='c008'>11. “Numerical Measure of Success of Predictions,” <i>Science</i>,
| |
| − | Vol. 4 (1884), p. 453.</p>
| |
| − |
| |
| − | <p class='c008'>12. “Proceedings Assay Commission” Washington, 1888.
| |
| − | (Joint Reports on Weighing.)</p>
| |
| − |
| |
| − | <p class='c008'><i>B.</i> Geodetic Researches. The Pendulum.</p>
| |
| − |
| |
| − | <p class='c008'>1. “Measurement of Gravity at Initial Stations in America
| |
| − | and Europe,” <i>Report of the U. S. Coast Survey</i>, 1876,
| |
| − | pp. 202-237 and 410-416.</p>
| |
| − |
| |
| − | <p class='c008'>2. “De l’influence de la flexibilité du trépied sur l’oscillation
| |
| − | du pendule a réversion,” Conférence Geodesique Internationale
| |
| − | (1877) Comptes Rendus, Berlin, 1878, pp. 171-187.
| |
| − | (This paper was introduced by Plantamour and
| |
| − | was followed by the notes of Appolzer.)</p>
| |
| − |
| |
| − | <p class='c008'>3. “On the Influence of Internal Friction upon the Correction
| |
| − | of the Length of the Second’s Pendulum,” <i>Proceedings
| |
| − | of the American Academy</i>, Vol. 13 (1878), pp. 396-401.</p>
| |
| − |
| |
| − | <p class='c008'>4. “On a Method of Swinging Pendulums for the Determination
| |
| − | of Gravity proposed by M. Faye,” <i>American Journal
| |
| − | of Science</i>, Vol. 18 (1879), pp. 112-119.</p>
| |
| − |
| |
| − | <p class='c008'>5. “Results of Pendulum Experiments,” <i>American Journal of
| |
| − | Science</i>, Vol. 20 (1880).</p>
| |
| − |
| |
| − | <p class='c008'>6. “Flexure of Pendulum Supports,” <i>Report of the U. S.
| |
| − | Coast Survey</i>, 1881, pp. 359-441.</p>
| |
| − |
| |
| − | <p class='c008'>7. “On the Deduction of the Ellipticity of the Earth from
| |
| − | the Pendulum Experiment,” <i>Report of the U. S. Coast
| |
| − | Survey</i>, 1881, pp. 442-456.</p>
| |
| − |
| |
| − | <p class='c008'>8. “Determinations of Gravity at Stations in Pennsylvania,”
| |
| − | <i>Report of U. S. Coast Survey</i>, 1883, Appendix 19 and
| |
| − | pp. 473-486.</p>
| |
| − |
| |
| − | <p class='c008'>9. “On the Use of the Noddy,” <i>Report of the U. S. Coast
| |
| − | Survey</i>, 1884, pp. 475-482.</p>
| |
| − |
| |
| − | <p class='c008'>10. “Effect of the Flexure of a Pendulum upon the Period of
| |
| − | Oscillation,” <i>Report of the U. S. Coast Survey</i>, 1884,
| |
| − | pp. 483-485.</p>
| |
| − |
| |
| − | <p class='c008'>11. “On the Influence of a Noddy, and of Unequal Temperature
| |
| − | upon the Periods of a Pendulum,” <i>Report of the
| |
| − | U. S. Coast and Geodetic Survey</i> for 1885, pp. 509-512.</p>
| |
| − |
| |
| − | <p class='c008'><i>C.</i> Psychologic. “On Small Differences in Sensation” (in cooperation
| |
| − | <span class='pageno' id='Page_314'>314</span>with J. Jastrow), <i>National Academy of Sciences</i>,
| |
| − | Vol. 3 (1884), pp. 1-11.</p>
| |
| − |
| |
| − | <p class='c014'>IV. Philologic.</p>
| |
| − |
| |
| − | <p class='c007'>“Shakespearian Pronunciation” (in coöperation with J. B. Noyes),
| |
| − | <i>North American Review</i>, Vol. 98 (April, 1864), pp. 342-369.</p>
| |
| − |
| |
| − | <p class='c014'>V. Contributions to the <i>Nation</i>.</p>
| |
| − |
| |
| − | <p class='c007'>Lazelle, Capt. H. M., One Law in Nature. <i>Nation</i>, Vol. 17, No. 419.</p>
| |
| − |
| |
| − | <p class='c008'>Newcomb, S., Popular Astronomy. Vol. 27, No. 683.</p>
| |
| − |
| |
| − | <p class='c008'>Read, C., Theory of Logic, 1878. Vol. 28, No. 718.</p>
| |
| − |
| |
| − | <p class='c008'>Rood, O. N., Modern Chromatics, 1879. Vol. 29, No. 746.</p>
| |
| − |
| |
| − | <p class='c008'>Note on the <i>American Journal of Mathematics</i>. Vol. 29, No. 756.</p>
| |
| − |
| |
| − | <p class='c008'>Jevons, W. S., Studies in Deductive Logic, 1880. Vol. 32, No. 822.</p>
| |
| − |
| |
| − | <p class='c008'>Ribot, Th., The Psychology of Attention, 1890. Vol. 50, No. 1303.</p>
| |
| − |
| |
| − | <p class='c008'>James, W., The Principles of Psychology, 1890. Vol. 53, Nos. 1357 and
| |
| − | 1358.</p>
| |
| − |
| |
| − | <p class='c008'>Comte, A. (F. Harrison, editor), The New Calendar of Great Men, 1892.
| |
| − | Vol. 54, No. 1386.</p>
| |
| − |
| |
| − | <p class='c008'>Lobatchewsky, N. (Translator: G. B. Halsted), Geometrical Researches
| |
| − | on the Theory of Parallels, 1891. Vol. 54, No. 1389.</p>
| |
| − |
| |
| − | <p class='c008'>Lombroso, C., The Man of Genius, 1891. Vol. 54, No. 1391.</p>
| |
| − |
| |
| − | <p class='c008'>Note on William James’ abridgment of his Psychology, 1892. Vol. 54,
| |
| − | No. 1394.</p>
| |
| − |
| |
| − | <p class='c008'>McClelland, W. J., A Treatise on the Geometry of the Circle, 1891. Vol.
| |
| − | 54, No. 1395.</p>
| |
| − |
| |
| − | <p class='c008'>Buckley, Arabella B., Moral Teachings of Science, 1892. Vol. 54, No. 1405.</p>
| |
| − |
| |
| − | <p class='c008'>Hale, E. E., A New England Boyhood, 1893. Vol. 57, No. 1468.</p>
| |
| − |
| |
| − | <p class='c008'>Mach, E. (Translator: T. J. McCormack), The Science of Mechanics,
| |
| − | 1893. Vol. 57, No. 1475.</p>
| |
| − |
| |
| − | <p class='c008'>Ritchie, D. G., Darwin and Hegel, 1893. Vol. 57, No. 1482.</p>
| |
| − |
| |
| − | <p class='c008'>Huxley, T. H., Method and Results, 1893. Vol. 58, No. 1489.</p>
| |
| − |
| |
| − | <p class='c008'>Scott, Sir Walter, Familiar Letters of Sir Walter Scott. Vol. 58, No. 1493.</p>
| |
| − |
| |
| − | <p class='c008'>Gilbert, W. (Translator: P. F. Mottelay), Magnetic Bodies. Vol. 58, No.
| |
| − | 1494 and No. 1495.</p>
| |
| − |
| |
| − | <p class='c008'>Forsyth, A. R., Theory of Functions of a Complex Variable, 1893; and
| |
| − | Harkness, J., A Treatise on the Theory of Functions, 1893; and Picard,
| |
| − | E., Traité d’analyse, 1893. Vol. 58, No. 1498.</p>
| |
| − |
| |
| − | <p class='c008'>A Short Sketch of Helmholtz, Sept. 13, 1894. Vol. 59, No. 1524.</p>
| |
| − |
| |
| − | <p class='c008'>Windelband, W. (Translator: J. H. Tufts), A History of Philosophy; and
| |
| − | Falkenberg, R. (Translator: A. C. Armstrong), History of Modern
| |
| − | Philosophy; and Bascom, J., An Historical Interpretation of Philosophy;
| |
| − | and Burt, B. C., A History of Modern Philosophy. Vol. 59, Nos.
| |
| − | 1526 and 1527.</p>
| |
| − |
| |
| − | <p class='c008'><span class='pageno' id='Page_315'>315</span>Spinoza (Translators: W. H. White and Amelia H. Stirling), Ethics,
| |
| − | 1894. Vol. 59, No. 1532.</p>
| |
| − |
| |
| − | <p class='c008'>Watson, J., Comte, Mill, and Spencer, 1895. Vol. 60, No. 1554.</p>
| |
| − |
| |
| − | <p class='c008'>Jones, H., A Critical Account of the Philosophy of Lotze, 1895; and Eberhard,
| |
| − | V., Die Grundbegriffe der ebenen Geometrie, 1895; and Klein,
| |
| − | F. (Translator: A. Ziwet), Riemann and his Significance for the Development
| |
| − | of Modern Mathematics, 1895; and Davis, N. K., Elements
| |
| − | of Inductive Logic, 1895. Vol. 61, No. 1566.</p>
| |
| − |
| |
| − | <p class='c008'>Benjamin, P., The Intellectual Rise in Electricity, 1895. Vol. 62, No. 1592.</p>
| |
| − |
| |
| − | <p class='c008'>Baldwin, J. M., The Story of the Mind, 1898. Vol. 67, No. 1737.</p>
| |
| − |
| |
| − | <p class='c008'>Darwin, G. H., The Tides and Kindred Phenomena in the Solar System,
| |
| − | 1898. Vol. 67, No. 1747.</p>
| |
| − |
| |
| − | <p class='c008'>Marshall, H. R., Instinct and Reason, 1898. Vol. 68, No. 1774.</p>
| |
| − |
| |
| − | <p class='c008'>Britten, F. J., Old Clocks and Watches and their Makers, 1899. Vol. 69,
| |
| − | No. 1778.</p>
| |
| − |
| |
| − | <p class='c008'>Renouvier, Ch., et Prat, L. La Nouvelle Monadologie, 1899. Vol. 69,
| |
| − | No. 1779.</p>
| |
| − |
| |
| − | <p class='c008'>Mackintosh, R., From Comte to Benjamin Kidd, 1899; and Moore, J. H.,
| |
| − | Better-World Philosophy, 1899. Vol. 69, No. 1784.</p>
| |
| − |
| |
| − | <p class='c008'>Ford, P. L., The Many-sided Franklin, 1899. Vol. 69, No. 1793.</p>
| |
| − |
| |
| − | <p class='c008'>Avenel, G. d’, Le Mécanisme de la vie moderne, 1900. Vol. 70, No. 1805.</p>
| |
| − |
| |
| − | <p class='c008'>Reid, W., Memoirs and Correspondence of Lyon Playfair, 1899. Vol. 70,
| |
| − | No. 1806.</p>
| |
| − |
| |
| − | <p class='c008'>Stevenson, F. S., Robert Grosseteste, 1899. Vol. 70, No. 1816.</p>
| |
| − |
| |
| − | <p class='c008'>Thilly, F., Introduction to Ethics, 1900. Vol. 70, No. 1825.</p>
| |
| − |
| |
| − | <p class='c008'>Wallace, A. R., Studies, Scientific and Social, 1900. Vol. 72, No. 1854.</p>
| |
| − |
| |
| − | <p class='c008'>Sime, J., William Herschel and His Work, 1900. Vol. 72, No. 1856.</p>
| |
| − |
| |
| − | <p class='c008'>Rand, B. (Editor), The Life, Unpublished Letters, and Philosophical Regimen
| |
| − | of Anthony, Earl of Shaftesbury, 1900; and Robertson, J. M.
| |
| − | (Editor), Characteristics of Men, <i>etc.</i>, by Shaftesbury, 1900. Vol. 72,
| |
| − | No. 1857.</p>
| |
| − |
| |
| − | <p class='c008'>Bacon, Rev. J. M., By Land and Sea, 1901. Vol. 72, No. 1865.</p>
| |
| − |
| |
| − | <p class='c008'>Jordan, W. L., Essays in Illustration of the Action of Astral Gravitation
| |
| − | in Natural Phenomena, 1900. Vol. 72, No. 1876.</p>
| |
| − |
| |
| − | <p class='c008'>Goblot, E., Le Vocabulaire Philosophique, 1901. Vol. 72, No. 1877.</p>
| |
| − |
| |
| − | <p class='c008'>Fraser, A. C. (Editor), The Works of George Berkeley, 1901. Vol. 73,
| |
| − | No. 1883.</p>
| |
| − |
| |
| − | <p class='c008'>Frazer, P., Bibliotics, 1901. Vol. 73, No. 1883.</p>
| |
| − |
| |
| − | <p class='c008'>Caldecott, A., The Philosophy of Religion in England and America, 1901.
| |
| − | Vol. 73, No. 1885.</p>
| |
| − |
| |
| − | <p class='c008'>Review of four physical books. Vol. 73, No. 1887.</p>
| |
| − |
| |
| − | <p class='c008'>Maher, M., Psychology: Empirical and Rational, 1901. Vol. 73, No.
| |
| − | 1892.</p>
| |
| − |
| |
| − | <p class='c008'>Mezes, S. E., Ethics, 1901. Vol. 73, No. 1895.</p>
| |
| − |
| |
| − | <p class='c008'>Report of the Meeting of the National Academy of Sciences, Philadelphia,
| |
| − | 1901. Vol. 73, No. 1899.</p>
| |
| − |
| |
| − | <p class='c008'><span class='pageno' id='Page_316'>316</span>Crozier, J. B., History of Intellectual Developments on the Lines of Modern
| |
| − | Evolution. Vol. III., 1901, Vol. 74, No. 1908.</p>
| |
| − |
| |
| − | <p class='c008'>Richardson, E. C., Classification, Theoretical and Practical, 1901. Vol. 74,
| |
| − | No. 1913.</p>
| |
| − |
| |
| − | <p class='c008'>Vallery-Radot, R. (Translator: Mrs. R. L. Devonshire), The Life of
| |
| − | Pasteur. Vol. 74, No. 1914.</p>
| |
| − |
| |
| − | <p class='c008'>Giddings, F. H., Inductive Sociology, 1902. Vol. 74, No. 1918.</p>
| |
| − |
| |
| − | <p class='c008'>Report on the Meeting of the National Academy of Sciences, Washington,
| |
| − | D. C., 1902. Vol. 74, No. 1921.</p>
| |
| − |
| |
| − | <p class='c008'>Emerson, E. R., The Story of the Vine, 1902. Vol. 74, No. 1926.</p>
| |
| − |
| |
| − | <p class='c008'>Joachim, H. H., A Study of the Ethics of Spinoza, 1901. Vol. 75, No.
| |
| − | 1932.</p>
| |
| − |
| |
| − | <p class='c008'>Review of four chemistry text-books, 1902. Vol. 75, No. 1934.</p>
| |
| − |
| |
| − | <p class='c008'>Royce, J., The World and the Individual, Vol. II., 1901. Vol. 75, No.
| |
| − | 1935. (For a review of Vol. I., probably by Peirce, see 1900, Vol. 70,
| |
| − | No. 1814.)</p>
| |
| − |
| |
| − | <p class='c008'>Thorpe, T. E., Essays in Historical Chemistry, 1902. Vol. 75, No. 1938.</p>
| |
| − |
| |
| − | <p class='c008'>Paulsen, F., Immanuel Kant: His Life and Doctrine, 1902. Vol. 75, No.
| |
| − | 1941.</p>
| |
| − |
| |
| − | <p class='c008'>Aikens, H. A., The Principles of Logic, 1902. Vol. 75, No. 1942.</p>
| |
| − |
| |
| − | <p class='c008'>Drude, P., The Theory of Optics, 1902. Vol. 75, No. 1944.</p>
| |
| − |
| |
| − | <p class='c008'>Valentine, E. S., Travels in Space, 1902; and Walker, F., Aerial Navigation,
| |
| − | 1902. Vol. 75, No. 1947.</p>
| |
| − |
| |
| − | <p class='c008'>Baillie, J. B., The Origin and Significance of Hegel’s Logic, 1901. Vol. 75,
| |
| − | No. 1950.</p>
| |
| − |
| |
| − | <p class='c008'>Forsyth, A. R., Theory of Differential Equations, Vol. IV., 1902. Vol. 75,
| |
| − | No. 1952.</p>
| |
| − |
| |
| − | <p class='c008'>Ellwanger, G. W., The Pleasures of the Table, 1902. Vol. 75, No. 1955.</p>
| |
| − |
| |
| − | <p class='c008'>Earle, Alice M., Sundials and Roses of Yesterday, 1902. Vol. 75, No.
| |
| − | 1956.</p>
| |
| − |
| |
| − | <p class='c008'>Smith, Rev. T., Euclid: His Life and System, 1902. Vol. 76, No. 1961.</p>
| |
| − |
| |
| − | <p class='c008'>Report on the Meeting of the National Academy of Sciences, Washington,
| |
| − | D. C., 1903. Vol. 76, No. 1974.</p>
| |
| − |
| |
| − | <p class='c008'>Hibben, J. G., Hegel’s Logic, 1902. Vol. 76, No. 1977.</p>
| |
| − |
| |
| − | <p class='c008'>Mellor, J. W., Higher Mathematics for Students of Chemistry and Physics,
| |
| − | 1903. Vol. 76, No. 1977.</p>
| |
| − |
| |
| − | <p class='c008'>Sturt, H. C. (Editor), Personal Idealism, 1902. Vol. 76, No. 1979.</p>
| |
| − |
| |
| − | <p class='c008'>Baldwin, J. M., Dictionary of Philosophy and Psychology, Vol. II., 1902.
| |
| − | Vol. 76, No. 1980.</p>
| |
| − |
| |
| − | <p class='c008'>Note on Kant’s Prolegomene edited in English by Dr. P. Carus, 1903.
| |
| − | Vol. 76, No. 1981.</p>
| |
| − |
| |
| − | <p class='c008'>Smith, N., Studies in the Cartesian Philosophy, 1902. Vol. 77, No. 1985.</p>
| |
| − |
| |
| − | <p class='c008'>Hinds, J. I. D., Inorganic Chemistry, 1902. Vol. 77, No. 1986.</p>
| |
| − |
| |
| − | <p class='c008'>Clerke, Agnes M., Problems in Astrophysics, 1903. Vol. 77, No. 1987.</p>
| |
| − |
| |
| − | <p class='c008'>Michelson, A. A., Light Waves and their Uses, 1903; and Fleming, J. A.,
| |
| − | Waves and Ripples in Water, 1902. Vol. 77, No. 1989.</p>
| |
| − |
| |
| − | <p class='c008'><span class='pageno' id='Page_317'>317</span>Note on Sir Norman Lockyer. Vol. 77, No. 1794.</p>
| |
| − |
| |
| − | <p class='c008'>Note on British and American Science, 1903. Vol. 77, No. 1996.</p>
| |
| − |
| |
| − | <p class='c008'>Welby, Lady Victoria, What is Meaning? 1903; and Russell, B., The Principles
| |
| − | of Mathematics, 1903. Vol. 77, No. 1998.</p>
| |
| − |
| |
| − | <p class='c008'>Note on the Practical Application of the Theory of Functions, 1903. Vol.
| |
| − | 77, No. 1999.</p>
| |
| − |
| |
| − | <p class='c008'>Fahie, J. J., Galileo. Vol. 78, No. 2015.</p>
| |
| − |
| |
| − | <p class='c008'>Halsey, F. A., The Metric Fallacy, and Dale, S. S., The Metric Failure in
| |
| − | the Textile Industry. Vol. 78, No. 2020.</p>
| |
| − |
| |
| − | <p class='c008'>Newcomb, S., The Reminiscences of an Astronomer, 1903. Vol. 78, No.
| |
| − | 2021.</p>
| |
| − |
| |
| − | <p class='c008'>Boole, Mrs. M. E., Lectures on the Logic of Arithmetic, 1903; and Bowden,
| |
| − | J., Elements of the Theory of Integers, 1903. Vol. 78, No. 2024.</p>
| |
| − |
| |
| − | <p class='c008'>Report on the Meeting of the National Academy of Sciences, Washington,
| |
| − | D. C., 1904. Vol. 78, No. 2026.</p>
| |
| − |
| |
| − | <p class='c008'>Lévy-Bruhl, L. (Translator: Kathleen de Beaumont-Klein), The Philosophy
| |
| − | of Auguste Comte, 1903. Vol. 78, No. 2026.</p>
| |
| − |
| |
| − | <p class='c008'>Turner, W., History of Philosophy, 1903. Vol. 79, No. 2036.</p>
| |
| − |
| |
| − | <p class='c008'>Duff, R. A., Spinoza’s Political and Ethical Philosophy. Vol. 79, No.
| |
| − | 2038.</p>
| |
| − |
| |
| − | <p class='c008'>Allbutt, T. C., Notes on the Composition of Scientific Papers, 1904. Vol.
| |
| − | 79, No. 2039.</p>
| |
| − |
| |
| − | <p class='c008'>Sylvester, J. J., The Collected Mathematical Papers of, Vol. I. Vol. 79,
| |
| − | No. 2045.</p>
| |
| − |
| |
| − | <p class='c008'>Renouvier, Ch., Les Derniers Entretiens, 1904, and Dewey, J., Studies in
| |
| − | Logical Theory, 1903. Vol. 79, No. 2046.</p>
| |
| − |
| |
| − | <p class='c008'>Royce, J., Outlines of Psychology. Vol. 79, No. 2048.</p>
| |
| − |
| |
| − | <p class='c008'>Straton, G. M., Experimental Psychology and its Bearing upon Culture.
| |
| − | Vol. 79, No. 2055.</p>
| |
| − |
| |
| − | <p class='c008'>Report on the Meeting of the National Academy of Sciences, New York,
| |
| − | 1904. Vol. 79, No. 2057.</p>
| |
| − |
| |
| − | <p class='c008'>Boole, Mrs. M. E., The Preparation of the Child for Science, 1904. Vol.
| |
| − | 80, No. 2062.</p>
| |
| − |
| |
| − | <p class='c008'>Royce, J., Herbert Spencer, 1904. Vol. 80, No. 2065.</p>
| |
| − |
| |
| − | <p class='c008'>Strutt, R. J., The Becquerel Rays and the Properties of Radium, 1904.
| |
| − | Vol. 80, No. 2066.</p>
| |
| − |
| |
| − | <p class='c008'>Schuster, A., An Introduction to the Theory of Optics, 1904. Vol. 80,
| |
| − | No. 2071.</p>
| |
| − |
| |
| − | <p class='c008'>Findlay, A., The Phase Rule and its Application, 1904. Vol. 80, No. 2074.</p>
| |
| − |
| |
| − | <p class='c008'>Report on the Meeting of the National Academy of Sciences, Washington,
| |
| − | D. C., 1905. Vol. 80, No. 2078.</p>
| |
| − |
| |
| − | <p class='c008'>Flint, R., Philosophy as Scientia Scientiarum, 1904; and Peirce, C. S., A
| |
| − | Syllabus of Certain Topics of Logic, 1903. Vol. 80, No. 2079.</p>
| |
| − |
| |
| − | <p class='c008'>Arnold, R. B., Scientific Fact and Metaphysical Reality, 1904, also a Note
| |
| − | on Mendeleeff’s Principles of Chemistry. Vol. 80, No. 2083.</p>
| |
| − |
| |
| − | <p class='c008'><span class='pageno' id='Page_318'>318</span>Note on Ida Freund’s The Study of Chemical Composition. Vol. 80, No.
| |
| − | 2086.</p>
| |
| − |
| |
| − | <p class='c008'>Carnegie, A., James Watt, 1905. Vol. 80, No. 2087.</p>
| |
| − |
| |
| − | <p class='c008'>Ross, E. A., Foundations of Sociology, 1905, and Sociological Papers, 1905,
| |
| − | published by the Sociological Society. Vol. 81, No. 2089.</p>
| |
| − |
| |
| − | <p class='c008'>Wundt, W. (Translator: E. B. Titchener), Principles of Physiological
| |
| − | Psychology, 1904. Vol. 81, No. 2090.</p>
| |
| − |
| |
| − | <p class='c008'>Roscoe, H. E., A Treatise on Chemistry, Vol. I., 1905, and de Fleury, M.,
| |
| − | Nos Enfants au Collège, 1905. Vol. 81, No. 2097.</p>
| |
| − |
| |
| − | <p class='c008'>Varigny, H. de, La Nature et la Vie, 1905. Vol. 81, No. 2101.</p>
| |
| − |
| |
| − | <p class='c008'>Note on Mr. G. W. Hill’s Moon Theory. Vol. 81, 2103.</p>
| |
| − |
| |
| − | <p class='c008'>Report on the Meeting of the National Academy of Sciences, New Haven,
| |
| − | 1905. Vol. 81, No. 2108.</p>
| |
| − |
| |
| − | <p class='c008'>Gosse, E., Sir Thomas Browne, 1905. Vol. 81, No. 2111.</p>
| |
| − |
| |
| − | <p class='c008'>Rutherford, E., Radio-Activity, 1905. Vol. 82, No. 2116.</p>
| |
| − |
| |
| − | <p class='c008'>Wallace, A. R., My Life, 1905. Vol. 82, No. 2121.</p>
| |
| − |
| |
| − | <p class='c008'>Haldane, Elizabeth S., Descartes. Vol. 82, No. 2125.</p>
| |
| − |
| |
| − | <p class='c008'>Report on the Meeting of the National Academy of Sciences, Washington,
| |
| − | D. C., 1906. Vol. 82, No. 2130.</p>
| |
| − |
| |
| − | <p class='c008'>Rogers, H. J. (Editor), Congress of Arts and Sciences, Universal Exposition,
| |
| − | St. Louis, 1904. Vol. 82, No. 2136.</p>
| |
| − |
| |
| − | <p class='c008'>Loeb, J., The Dynamics of Living Matter; and Mann, G., Chemistry of
| |
| − | the Proteids. Vol. 83, No. 2140.</p>
| |
| − |
| |
| − | <p class='c008'>Roscoe, H. E., The Life and Experiences of Sir Henry Enfield Roscoe.
| |
| − | Vol. 83, No. 2141.</p>
| |
| − |
| |
| − | <p class='c008'>Marshall, T., Aristotle’s Theory of Conduct. Vol. 83, No. 2150.</p>
| |
| − |
| |
| − | <p class='c008'>Joseph, H. W. B., An Introduction to Logic. Vol. 83, No. 2156.</p>
| |
| − |
| |
| − | <p class='c014'><span class='sc'>Other Articles and Reviews</span></p>
| |
| − |
| |
| − | <p class='c007'>Old Stone Mill at Newport, <i>Science</i>, 4, 1884, 512.</p>
| |
| − |
| |
| − | <p class='c008'>Criticism on “Phantasms of the Living,” <i>Proc. Am. Soc. Psychical Research</i>,
| |
| − | Vol. 1, No. 3 (1887).</p>
| |
| − |
| |
| − | <p class='c008'>Napoleon Intime, <i>The Independent</i>, December 21 and December 28, 1893.</p>
| |
| − |
| |
| − | <p class='c008'>Decennial Celebration of Clark University, <i>Science</i>, 11 (1900), p. 620.</p>
| |
| − |
| |
| − | <p class='c008'>Century’s Great Men of Science, <i>Smithsonian Institute Reports</i>, 1900.</p>
| |
| − |
| |
| − | <p class='c008'>Campanus <i>Science</i>, 13 (1901), p. 809.</p>
| |
| − |
| |
| − | <p class='c008'>French Academy of Science, N. Y. Evening <i>Post</i>, March 5, 1904.</p>
| |
| − |
| |
| − | <div class='nf-center-c1'>
| |
| − | <div class='nf-center c000'>
| |
| − | <div><span class='large'>Footnotes</span></div>
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <div class='footnote' id='f1'>
| |
| − | <p class='c005'><span class='label'><a href='#r1'>1</a>. </span>See Plantamour’s “<i>Recherches Experimentales sur le mouvement
| |
| − | simultané d’un pendule et de ses supports</i>,” Geneva, 1878, pp. 3-4.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f2'>
| |
| − | <p class='c005'><span class='label'><a href='#r2'>2</a>. </span>P. <a href='#Page_190'>190</a>.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f3'>
| |
| − | <p class='c005'><span class='label'><a href='#r3'>3</a>. </span>Pp. <a href='#Page_162'>162</a>-163.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f4'>
| |
| − | <p class='c005'><span class='label'><a href='#r4'>4</a>. </span>Pp. <a href='#Page_249'>249</a> ff.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f5'>
| |
| − | <p class='c005'><span class='label'><a href='#r5'>5</a>. </span>James, <i>Pluralistic Universe</i>, pp. 398-400.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f6'>
| |
| − | <p class='c005'><span class='label'><a href='#r6'>6</a>. </span>Royce, <i>Studies in Good and Evil</i>, and <i>The Problem of Christianity</i>,
| |
| − | esp. Vol. 2. Baldwin (<i>Mental Development</i>) is heavily indebted to Royce
| |
| − | in this respect.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f7'>
| |
| − | <p class='c005'><span class='label'><a href='#r7'>7</a>. </span>These articles are by-products or fragments of a comprehensive work
| |
| − | on <i>Logic</i> on which Peirce was engaged for many years. For the writing
| |
| − | of this book, Royce declared, no greater mind or greater erudition has
| |
| − | appeared in America. Only several chapters seem to have been finished,
| |
| − | and will doubtless be included with other hitherto unpublished manuscripts
| |
| − | in the complete edition of Peirce’s writings that is now being
| |
| − | prepared by Harvard University.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f8'>
| |
| − | <p class='c005'><span class='label'><a href='#r8'>8</a>. </span>Baldwin’s <i>Dictionary</i>, article Synechism.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f9'>
| |
| − | <p class='c005'><span class='label'><a href='#r9'>9</a>. </span><i>Ib.</i></p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f10'>
| |
| − | <p class='c005'><span class='label'><a href='#r10'>10</a>. </span>Baldwin’s <i>Dictionary</i>, art. Individual: “Everything whose identity
| |
| − | consists in a continuity of reactions will be a single logical individual.”</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f11'>
| |
| − | <p class='c005'><span class='label'><a href='#r11'>11</a>. </span>The personal relations between Peirce and Wright were thus described
| |
| − | by Peirce in a letter to Mrs. Ladd-Franklin (<i>Journal of Philosophy</i>,
| |
| − | Vol. 13, p. 719): “It must have been about 1857 when I first made
| |
| − | the acquaintance of Chauncey Wright, a mind about on the level of
| |
| − | J. S. Mill. He was a thorough mathematician. He had a most penetrating
| |
| − | intellect.—He and I used to have long and very lively and close
| |
| − | disputations lasting two or three hours daily for many years. In the
| |
| − | sixties I started a little club called ‘The Metaphysical Club.’—Wright
| |
| − | was the strongest member and probably I was next.—Then there were
| |
| − | Frank Abbott, William James and others.” “It was there that the name
| |
| − | and the doctrine of pragmatism saw the light.” It might be added that
| |
| − | Peirce’s tychism is indebted to Wright’s doctrine of accidents and “cosmic
| |
| − | weather,” a doctrine which maintained against LaPlace that a mind knowing
| |
| − | nature from moment to moment is bound to encounter genuine novelty
| |
| − | in phenomena, which no amount of knowledge would enable us to foresee.
| |
| − | See Wright’s <i>Philosophical Discussions</i>—1876, also Cambridge <i>Hist. of
| |
| − | American Literature</i>, Vol. 3, p. 234.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f12'>
| |
| − | <p class='c005'><span class='label'><a href='#r12'>12</a>. </span><i>Monist</i>, Vol. 15, p. 180.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f13'>
| |
| − | <p class='c005'><span class='label'><a href='#r13'>13</a>. </span>This volume, pp. <a href='#Page_43'>43</a>-45.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f14'>
| |
| − | <p class='c005'><span class='label'><a href='#r14'>14</a>. </span>“To say that we live for the sake of action would be to say that
| |
| − | there is no such thing as a rational purport.” <i>Monist</i>, Vol. XV, p. 175.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f15'>
| |
| − | <p class='c005'><span class='label'><a href='#r15'>15</a>. </span>The letter to Mrs. Ladd-Franklin quoted before, explains why
| |
| − | James, though always loyal to Peirce and anxious to give him credit whenever
| |
| − | possible, could not understand the latter’s lectures on pragmatism.
| |
| − | Peirce’s incidental judgments on others is worth quoting here:</p>
| |
| − |
| |
| − | <p class='c005'>“Modern psychologists are so soaked with sensationalism that they
| |
| − | cannot understand anything that does not mean that. How can I, to
| |
| − | whom nothing seems so thoroughly real as generals, and who regards
| |
| − | Truth and Justice as <i>literally</i> the most powerful powers in the world,
| |
| − | expect to be understood by the thoroughgoing Wundtian? But the curious
| |
| − | thing is to see absolute idealists tainted with this disease,—or men who,
| |
| − | like John Dewey, hover between Absolute Idealism and Sensationalism.
| |
| − | Royce’s opinions as developed in his <i>World and Individualism</i> are extremely
| |
| − | near to mine. His insistence on the elements of purpose in
| |
| − | intellectual concepts is essentially the pragmatic position.”</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f16'>
| |
| − | <p class='c005'><span class='label'><a href='#r16'>16</a>. </span>Baldwin’s <i>Dictionary</i>, art. Method.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f17'>
| |
| − | <p class='c005'><span class='label'><a href='#r17'>17</a>. </span>“Peirce anticipated the most important procedures of his successors
| |
| − | even when he did not work them out himself. Again and again one finds
| |
| − | the clue to the most recent developments in the writings of Peirce,”
| |
| − | Lewis’ <i>Survey of Symbolic Logic</i>, p. 79.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f18'>
| |
| − | <p class='c005'><span class='label'><a href='#r18'>18</a>. </span>Hans Breitmann is symbolic of those who “solved the infinite as one
| |
| − | eternal sphere.”</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f19'>
| |
| − | <p class='c005'><span class='label'><a href='#r19'>19</a>. </span>See <i>Journal of Speculative Philosophy</i>, Vol. 2, pp. 155-157, article on
| |
| − | A New List of Categories in the Proceedings of the American Academy
| |
| − | of Arts and Sciences, Vol. 7, 287-298 and article on <i>Sign</i>, in Baldwin’s
| |
| − | <i>Dictionary</i>.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f20'>
| |
| − | <p class='c005'><span class='label'><a href='#r20'>20</a>. </span><i>Studies in Logic</i>, p. 181.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f21'>
| |
| − | <p class='c005'><span class='label'><a href='#r21'>21</a>. </span><i>Monist</i>, Vol. 7, p. 27. <i>Cf.</i> <i>Journal of Speculative Philosophy</i>,
| |
| − | Vol. 2, p. 207; <i>Popular Science Monthly</i>, Vol. 58, pp. 305-306.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f22'>
| |
| − | <p class='c005'><span class='label'><a href='#r22'>22</a>. </span>This vol., p. <a href='#Page_15'>15</a>.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f23'>
| |
| − | <p class='c005'><span class='label'><a href='#r23'>23</a>. </span>Suggestive for a theory of the metaphysics of fictions is the suggestion
| |
| − | (p. 46) “that the question of what would occur under circumstances
| |
| − | which do not actually arise, is not a question of fact, but only of the
| |
| − | most perspicuous arrangement of them.” This arrangement is, of course,
| |
| − | not merely subjective.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f24'>
| |
| − | <p class='c005'><span class='label'><a href='#r24'>24</a>. </span>Pp. 128-129, <i>cf.</i> <i>Monist</i>, Vol. 7, p. 206, and <i>Logical Studies</i>, pp.
| |
| − | 175 ff.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f25'>
| |
| − | <p class='c005'><span class='label'><a href='#r25'>25</a>. </span>From the <i>Journal of Speculative Philosophy</i>, vol. 2, p. 140.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f26'>
| |
| − | <p class='c005'><span class='label'><a href='#r26'>26</a>. </span><i>Popular Science Monthly</i>, November, 1877.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f27'>
| |
| − | <p class='c005'><span class='label'><a href='#r27'>27</a>. </span>[This is substantially the dictum of Harvey to John Aubrey. See
| |
| − | the latter’s <i>Brief Lives</i> (Oxford ed. 1898) I 299.]</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f28'>
| |
| − | <p class='c005'><span class='label'><a href='#r28'>28</a>. </span>Not quite so, but as nearly so as can be told in a few words.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f29'>
| |
| − | <p class='c005'><span class='label'><a href='#r29'>29</a>. </span>[This modern logic, however, is largely the outcome of Kepler’s work.]</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f30'>
| |
| − | <p class='c005'><span class='label'><a href='#r30'>30</a>. </span>I am not speaking of secondary effects occasionally produced by the
| |
| − | interference of other impulses.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f31'>
| |
| − | <p class='c005'><span class='label'><a href='#r31'>31</a>. </span><i>Popular Science Monthly</i>, January, 1878.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f32'>
| |
| − | <p class='c005'><span class='label'><a href='#r32'>32</a>. </span>Possibly the velocities also have to be taken into account.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f33'>
| |
| − | <p class='c005'><span class='label'><a href='#r33'>33</a>. </span>Fate means merely that which is sure to come true, and can nohow
| |
| − | be avoided. It is a superstition to suppose that a certain sort of events
| |
| − | are ever fated, and it is another to suppose that the word fate can never
| |
| − | be freed from its superstitious taint. We are all fated to die.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f34'>
| |
| − | <p class='c005'><span class='label'><a href='#r34'>34</a>. </span><i>Popular Science Monthly</i>, March, 1878.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f35'>
| |
| − | <p class='c005'><span class='label'><a href='#r35'>35</a>. </span>[Later, pp. <a href='#Page_170'>170</a> ff. and <a href='#Page_215'>215</a> ff., it is shown that continuity is also at
| |
| − | the basis of mathematical generalization. See also article on Synechism
| |
| − | in <i>Baldwin’s Dictionary of Philosophy</i>.]</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f36'>
| |
| − | <p class='c005'><span class='label'><a href='#r36'>36</a>. </span>This mode of thought is so familiarly associated with all exact numerical
| |
| − | consideration, that the phrase appropriate to it is imitated by
| |
| − | shallow writers in order to produce the appearance of exactitude where
| |
| − | none exists. Certain newspapers which affect a learned tone talk of “the
| |
| − | average man,” when they simply mean <i>most men</i>, and have no idea of
| |
| − | striking an average.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f37'>
| |
| − | <p class='c005'><span class='label'><a href='#r37'>37</a>. </span><i>Cf.</i> pp. <a href='#Page_179'>179</a> ff. below.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f38'>
| |
| − | <p class='c005'><span class='label'><a href='#r38'>38</a>. </span>The conception of probability here set forth is substantially that first
| |
| − | developed by Mr. Venn, in his <i>Logic of Chance</i>. Of course, a vague
| |
| − | apprehension of the idea had always existed, but the problem was to make
| |
| − | it perfectly clear, and to him belongs the credit of first doing this.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f39'>
| |
| − | <p class='c005'><span class='label'><a href='#r39'>39</a>. </span>I do not here admit an absolutely unknowable. Evidence could show
| |
| − | us what would probably be the case after any given lapse of time; and
| |
| − | though a subsequent time might be assigned which that evidence might
| |
| − | not cover, yet further evidence would cover it.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f40'>
| |
| − | <p class='c005'><span class='label'><a href='#r40'>40</a>. </span><i>Popular Science Monthly</i>, April, 1878.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f41'>
| |
| − | <p class='c005'><span class='label'><a href='#r41'>41</a>. </span>Strictly we should need an infinite series of numbers each depending
| |
| − | on the probable error of the last.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f42'>
| |
| − | <p class='c005'><span class='label'><a href='#r42'>42</a>. </span>“Perfect indecision, belief inclining neither way, an even chance.”—<span class='sc'>De
| |
| − | Morgan</span>, p. 182.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f43'>
| |
| − | <p class='c005'><span class='label'><a href='#r43'>43</a>. </span><i>Logique</i>. The same is true, according to him, of every performance
| |
| − | of a differentiation, but not of integration. He does not tell us whether
| |
| − | it is the supernatural assistance which makes the former process so
| |
| − | much the easier.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f44'>
| |
| − | <p class='c005'><span class='label'><a href='#r44'>44</a>. </span><i>Popular Science Monthly</i>, June, 1878.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f45'>
| |
| − | <p class='c005'><span class='label'><a href='#r45'>45</a>. </span>[See Santayana, <i>Reason in Religion</i>.]</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f46'>
| |
| − | <p class='c005'><span class='label'><a href='#r46'>46</a>. </span>For the present purpose, the negative of a character is to be considered
| |
| − | as much a character as the positive, for a uniformity may either
| |
| − | be affirmative or negative. I do not say that no distinction can be drawn
| |
| − | between positive and negative uniformities.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f47'>
| |
| − | <p class='c005'><span class='label'><a href='#r47'>47</a>. </span>There being 5 simple characters, with their negatives, they could
| |
| − | be compounded in various ways so as to make 241 characters in all, without
| |
| − | counting the characters <i>existence</i> and <i>non-existence</i>, which make up
| |
| − | 243 or 3<sup>5</sup>.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f48'>
| |
| − | <p class='c005'><span class='label'><a href='#r48'>48</a>. </span>This principle was, I believe, first stated by Mr. De Morgan.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f49'>
| |
| − | <p class='c005'><span class='label'><a href='#r49'>49</a>. </span>Not in every idea but only in the one so formulated.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f50'>
| |
| − | <p class='c005'><span class='label'><a href='#r50'>50</a>. </span>[Note that this corollary is itself a theoretical inference and not an
| |
| − | empirical rule.]</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f51'>
| |
| − | <p class='c005'><span class='label'><a href='#r51'>51</a>. </span><i>Popular Science Monthly</i>, August, 1878.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f52'>
| |
| − | <p class='c005'><span class='label'><a href='#r52'>52</a>. </span>[Later Pierce called it <i>presumptive inference</i>. See Baldwin’s <i>Dictionary</i>
| |
| − | art. <i>Probable Inference</i>.]</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f53'>
| |
| − | <p class='c005'><span class='label'><a href='#r53'>53</a>. </span>This division was first made in a course of lectures by the author
| |
| − | before the Lowell Institute, Boston, in 1866, and was printed in the
| |
| − | <i>Proceedings of the American Academy of Arts and Sciences</i>, for April 9,
| |
| − | 1867.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f54'>
| |
| − | <p class='c005'><span class='label'><a href='#r54'>54</a>. </span><i>The Monist</i>, January, 1891.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f55'>
| |
| − | <p class='c005'><span class='label'><a href='#r55'>55</a>. </span>The neo-Darwinian, Weismann, has shown that mortality would
| |
| − | almost necessarily result from the action of the Darwinian principle.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f56'>
| |
| − | <p class='c005'><span class='label'><a href='#r56'>56</a>. </span>A feeling may certainly be compound, but only in virtue of a perception
| |
| − | which is not that feeling nor any feeling at all.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f57'>
| |
| − | <p class='c005'><span class='label'><a href='#r57'>57</a>. </span>[The reader will find further light on the following illustration in
| |
| − | any text-book of projective geometry, e.g., Reye, <i>Geometry of Position</i>,
| |
| − | I, pp. 17-24, or <i>Encyc. Britannica</i>, XI, p. 689.]</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f58'>
| |
| − | <p class='c005'><span class='label'><a href='#r58'>58</a>. </span>[A more familiar example of this is the introduction of irrational or
| |
| − | absurd numbers like √2. After it was proved that no ratio of two integers
| |
| − | could possibly equal √2 the idea of number was generalized to include the
| |
| − | latter. Fractions and the so-called imaginary numbers illustrate the same
| |
| − | process of generalization for the sake of making certain operations (i.e.
| |
| − | division and finding the root) continuously applicable.]</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f59'>
| |
| − | <p class='c005'><span class='label'><a href='#r59'>59</a>. </span><i>The Monist</i>, April, 1892.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f60'>
| |
| − | <p class='c005'><span class='label'><a href='#r60'>60</a>. </span><i>Continuous</i> is not exactly the right word, but I let it go to avoid a
| |
| − | long and irrelevant discussion.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f61'>
| |
| − | <p class='c005'><span class='label'><a href='#r61'>61</a>. </span><i>The Monist</i>, July, 1892.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f62'>
| |
| − | <p class='c005'><span class='label'><a href='#r62'>62</a>. </span>This proposition is substantially the same as a theorem of Cantor,
| |
| − | though it is enunciated in a much more general form.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f63'>
| |
| − | <p class='c005'><span class='label'><a href='#r63'>63</a>. </span><i>The Monist</i>, October, 1892.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f64'>
| |
| − | <p class='c005'><span class='label'><a href='#r64'>64</a>. </span>I am rejoiced to find, since my last paper was printed, that a philosopher
| |
| − | as subtle and profound as Dr. Edmund Montgomery has long
| |
| − | been arguing for the same element in the universe. Other world-renowned
| |
| − | thinkers, as M. Renouvier and M. Delbœuf, appear to share this opinion.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f65'>
| |
| − | <p class='c005'><span class='label'><a href='#r65'>65</a>. </span>By a <i>vera causa</i>, in the logic of science, is meant a state of things
| |
| − | known to exist in some cases and supposed to exist in other cases, because
| |
| − | it would account for observed phenomena.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f66'>
| |
| − | <p class='c005'><span class='label'><a href='#r66'>66</a>. </span>Wiedemann, <i>Annalen</i>, 1887-1889.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f67'>
| |
| − | <p class='c005'><span class='label'><a href='#r67'>67</a>. </span>See Maxwell on Spherical Harmonics, in his <i>Electricity and
| |
| − | Magnetism</i>.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f68'>
| |
| − | <p class='c005'><span class='label'><a href='#r68'>68</a>. </span>The word <i>system</i> has three peculiar meanings in mathematics. (<i>A.</i>)
| |
| − | It means an orderly exposition of the truths of astronomy, and hence
| |
| − | a theory of the motions of the stars; as the Ptolemaic <i>system</i>, the Copernican
| |
| − | <i>system</i>. This is much like the sense in which we speak of the
| |
| − | Calvinistic <i>system</i> of theology, the Kantian <i>system</i> of philosophy, etc.
| |
| − | (<i>B.</i>) It means the aggregate of the planets considered as all moving in
| |
| − | somewhat the same way, as the solar <i>system</i>; and hence any aggregate
| |
| − | of particles moving under mutual forces. (<i>C.</i>) It means a number of
| |
| − | forces acting simultaneously upon a number of particles.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f69'>
| |
| − | <p class='c005'><span class='label'><a href='#r69'>69</a>. </span>But, in fact, an inspection of these curves is sufficient to show that
| |
| − | they are of a higher degree than the third. For they have the line <i>V</i> = O,
| |
| − | or some line <i>V</i> a constant for an asymptote, while for small values of
| |
| − | <i>P</i>, the values of <i>d</i><sup>2</sup><i>p</i>/(<i>dV</i>)<sup>2</sup> are positive.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f70'>
| |
| − | <p class='c005'><span class='label'><a href='#r70'>70</a>. </span>Anticipated by Clausius as long ago as 1857; and by Williamson in
| |
| − | 1851.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f71'>
| |
| − | <p class='c005'><span class='label'><a href='#r71'>71</a>. </span>“Physiologically, ... accommodation means the breaking up of a
| |
| − | habit.... Psychologically, it means reviving consciousness.” Baldwin,
| |
| − | <i>Psychology</i>, Part III, ch. i., § 5.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f72'>
| |
| − | <p class='c005'><span class='label'><a href='#r72'>72</a>. </span><i>The Monist</i>, January, 1893.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f73'>
| |
| − | <p class='c005'><span class='label'><a href='#r73'>73</a>. </span>How can a writer have any respect for science, as such, who is
| |
| − | capable of confounding with the scientific propositions of political economy,
| |
| − | which have nothing to say concerning what is “beneficent,” such
| |
| − | brummagem generalisations as this?</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f74'>
| |
| − | <p class='c005'><span class='label'><a href='#r74'>74</a>. </span>I am happy to find that Dr. Carus, too, ranks Weismann among the
| |
| − | opponents of Darwin, notwithstanding his flying that flag.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f75'>
| |
| − | <p class='c005'><span class='label'><a href='#r75'>75</a>. </span>See <i>Draper’s History of Intellectual Development</i>, chap. x.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f76'>
| |
| − | <p class='c005'><span class='label'><a href='#r76'>76</a>. </span>Thomson, himself, in his article <i>Heat</i> in the <i>Encyclopedia Britannica</i>,
| |
| − | never once mentions the name of Clausius.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f77'>
| |
| − | <p class='c005'><span class='label'><a href='#r77'>77</a>. </span>See article on “Pragmatism,” in <i>Baldwin’s Dictionary</i>, Vol. 2., p.
| |
| − | 322, and the <i>Monist</i>, Vol. 15, p. 162.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f78'>
| |
| − | <p class='c005'><span class='label'><a href='#r78'>78</a>. </span>Kant discriminates the laws of morality, which are <i>a priori</i>, from
| |
| − | rules of skill, having to do with technique or art, and counsels of prudence,
| |
| − | having to do with welfare. The latter he calls pragmatic; the <i>a priori</i>
| |
| − | laws practical. See <i>Metaphysics of Morals</i>, Abbott’s trans., pp. 33 and 34.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f79'>
| |
| − | <p class='c005'><span class='label'><a href='#r79'>79</a>. </span>See the article in the <i>Monist</i> already mentioned, and another one
| |
| − | in the same volume, p. 481, “The Issues of Pragmaticism.”</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f80'>
| |
| − | <p class='c005'><span class='label'><a href='#r80'>80</a>. </span>It is probably fair to see here an empirical rendering of the Kantian
| |
| − | generality of moral action, while the distinction and connection of “rational
| |
| − | purport” and “sensible particular” have also obvious Kantian
| |
| − | associations.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f81'>
| |
| − | <p class='c005'><span class='label'><a href='#r81'>81</a>. </span>P. 26.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f82'>
| |
| − | <p class='c005'><span class='label'><a href='#r82'>82</a>. </span>P. 56-57.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f83'>
| |
| − | <p class='c005'><span class='label'><a href='#r83'>83</a>. </span>P. 105.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f84'>
| |
| − | <p class='c005'><span class='label'><a href='#r84'>84</a>. </span>P. 45.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f85'>
| |
| − | <p class='c005'><span class='label'><a href='#r85'>85</a>. </span>P. 43.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f86'>
| |
| − | <p class='c005'><span class='label'><a href='#r86'>86</a>. </span>P. 151.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f87'>
| |
| − | <p class='c005'><span class='label'><a href='#r87'>87</a>. </span>P. 53.</p>
| |
| − | </div>
| |
| − | <div class='footnote' id='f88'>
| |
| − | <p class='c005'><span class='label'><a href='#r88'>88</a>. </span>The following classification is arbitrary, as some of Peirce’s most significant
| |
| − | reflections occur in papers under headings II. and III. It may,
| |
| − | however, be useful.</p>
| |
| − | </div>
| |
| − | <div>
| |
| − |
| |
| − | <ul class='ul_1 c002'>
| |
| − | <li>Transcriber’s Notes:
| |
| − | <ul class='ul_2'>
| |
| − | <li>Footnotes have been collected at the end of the text, and are linked for ease of
| |
| − | reference.
| |
| − | </li>
| |
| − | </ul>
| |
| − | </li>
| |
| − | </ul>
| |
| − |
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin-top:4em'>*** END OF THE PROJECT GUTENBERG EBOOK CHANCE, LOVE, AND LOGIC ***</div>
| |
| − | <div style='text-align:left'>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | Updated editions will replace the previous one—the old editions will
| |
| − | be renamed.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | Creating the works from print editions not protected by U.S. copyright
| |
| − | law means that no one owns a United States copyright in these works,
| |
| − | so the Foundation (and you!) can copy and distribute it in the United
| |
| − | States without permission and without paying copyright
| |
| − | royalties. Special rules, set forth in the General Terms of Use part
| |
| − | of this license, apply to copying and distributing Project
| |
| − | Gutenberg™ electronic works to protect the PROJECT GUTENBERG™
| |
| − | concept and trademark. Project Gutenberg is a registered trademark,
| |
| − | and may not be used if you charge for an eBook, except by following
| |
| − | the terms of the trademark license, including paying royalties for use
| |
| − | of the Project Gutenberg trademark. If you do not charge anything for
| |
| − | copies of this eBook, complying with the trademark license is very
| |
| − | easy. You may use this eBook for nearly any purpose such as creation
| |
| − | of derivative works, reports, performances and research. Project
| |
| − | Gutenberg eBooks may be modified and printed and given away--you may
| |
| − | do practically ANYTHING in the United States with eBooks not protected
| |
| − | by U.S. copyright law. Redistribution is subject to the trademark
| |
| − | license, especially commercial redistribution.
| |
| − | </div>
| |
| − |
| |
| − | <div style='margin:0.83em 0; font-size:1.1em; text-align:center'>START: FULL LICENSE<br />
| |
| − | <span style='font-size:smaller'>THE FULL PROJECT GUTENBERG LICENSE<br />
| |
| − | PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK</span>
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | To protect the Project Gutenberg™ mission of promoting the free
| |
| − | distribution of electronic works, by using or distributing this work
| |
| − | (or any other work associated in any way with the phrase “Project
| |
| − | Gutenberg”), you agree to comply with all the terms of the Full
| |
| − | Project Gutenberg™ License available with this file or online at
| |
| − | www.gutenberg.org/license.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; font-size:1.1em; margin:1em 0; font-weight:bold'>
| |
| − | Section 1. General Terms of Use and Redistributing Project Gutenberg™ electronic works
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | 1.A. By reading or using any part of this Project Gutenberg™
| |
| − | electronic work, you indicate that you have read, understand, agree to
| |
| − | and accept all the terms of this license and intellectual property
| |
| − | (trademark/copyright) agreement. If you do not agree to abide by all
| |
| − | the terms of this agreement, you must cease using and return or
| |
| − | destroy all copies of Project Gutenberg™ electronic works in your
| |
| − | possession. If you paid a fee for obtaining a copy of or access to a
| |
| − | Project Gutenberg™ electronic work and you do not agree to be bound
| |
| − | by the terms of this agreement, you may obtain a refund from the person
| |
| − | or entity to whom you paid the fee as set forth in paragraph 1.E.8.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | 1.B. “Project Gutenberg” is a registered trademark. It may only be
| |
| − | used on or associated in any way with an electronic work by people who
| |
| − | agree to be bound by the terms of this agreement. There are a few
| |
| − | things that you can do with most Project Gutenberg™ electronic works
| |
| − | even without complying with the full terms of this agreement. See
| |
| − | paragraph 1.C below. There are a lot of things you can do with Project
| |
| − | Gutenberg™ electronic works if you follow the terms of this
| |
| − | agreement and help preserve free future access to Project Gutenberg™
| |
| − | electronic works. See paragraph 1.E below.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | 1.C. The Project Gutenberg Literary Archive Foundation (“the
| |
| − | Foundation” or PGLAF), owns a compilation copyright in the collection
| |
| − | of Project Gutenberg™ electronic works. Nearly all the individual
| |
| − | works in the collection are in the public domain in the United
| |
| − | States. If an individual work is unprotected by copyright law in the
| |
| − | United States and you are located in the United States, we do not
| |
| − | claim a right to prevent you from copying, distributing, performing,
| |
| − | displaying or creating derivative works based on the work as long as
| |
| − | all references to Project Gutenberg are removed. Of course, we hope
| |
| − | that you will support the Project Gutenberg™ mission of promoting
| |
| − | free access to electronic works by freely sharing Project Gutenberg™
| |
| − | works in compliance with the terms of this agreement for keeping the
| |
| − | Project Gutenberg™ name associated with the work. You can easily
| |
| − | comply with the terms of this agreement by keeping this work in the
| |
| − | same format with its attached full Project Gutenberg™ License when
| |
| − | you share it without charge with others.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | 1.D. The copyright laws of the place where you are located also govern
| |
| − | what you can do with this work. Copyright laws in most countries are
| |
| − | in a constant state of change. If you are outside the United States,
| |
| − | check the laws of your country in addition to the terms of this
| |
| − | agreement before downloading, copying, displaying, performing,
| |
| − | distributing or creating derivative works based on this work or any
| |
| − | other Project Gutenberg™ work. The Foundation makes no
| |
| − | representations concerning the copyright status of any work in any
| |
| − | country other than the United States.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | 1.E. Unless you have removed all references to Project Gutenberg:
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | 1.E.1. The following sentence, with active links to, or other
| |
| − | immediate access to, the full Project Gutenberg™ License must appear
| |
| − | prominently whenever any copy of a Project Gutenberg™ work (any work
| |
| − | on which the phrase “Project Gutenberg” appears, or with which the
| |
| − | phrase “Project Gutenberg” is associated) is accessed, displayed,
| |
| − | performed, viewed, copied or distributed:
| |
| − | </div>
| |
| − |
| |
| − | <blockquote>
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | This eBook is for the use of anyone anywhere in the United States and most
| |
| − | other parts of the world at no cost and with almost no restrictions
| |
| − | whatsoever. You may copy it, give it away or re-use it under the terms
| |
| − | of the Project Gutenberg License included with this eBook or online
| |
| − | at <a href="https://www.gutenberg.org">www.gutenberg.org</a>. If you
| |
| − | are not located in the United States, you will have to check the laws
| |
| − | of the country where you are located before using this eBook.
| |
| − | </div>
| |
| − | </blockquote>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | 1.E.2. If an individual Project Gutenberg™ electronic work is
| |
| − | derived from texts not protected by U.S. copyright law (does not
| |
| − | contain a notice indicating that it is posted with permission of the
| |
| − | copyright holder), the work can be copied and distributed to anyone in
| |
| − | the United States without paying any fees or charges. If you are
| |
| − | redistributing or providing access to a work with the phrase “Project
| |
| − | Gutenberg” associated with or appearing on the work, you must comply
| |
| − | either with the requirements of paragraphs 1.E.1 through 1.E.7 or
| |
| − | obtain permission for the use of the work and the Project Gutenberg™
| |
| − | trademark as set forth in paragraphs 1.E.8 or 1.E.9.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | 1.E.3. If an individual Project Gutenberg™ electronic work is posted
| |
| − | with the permission of the copyright holder, your use and distribution
| |
| − | must comply with both paragraphs 1.E.1 through 1.E.7 and any
| |
| − | additional terms imposed by the copyright holder. Additional terms
| |
| − | will be linked to the Project Gutenberg™ License for all works
| |
| − | posted with the permission of the copyright holder found at the
| |
| − | beginning of this work.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | 1.E.4. Do not unlink or detach or remove the full Project Gutenberg™
| |
| − | License terms from this work, or any files containing a part of this
| |
| − | work or any other work associated with Project Gutenberg™.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | 1.E.5. Do not copy, display, perform, distribute or redistribute this
| |
| − | electronic work, or any part of this electronic work, without
| |
| − | prominently displaying the sentence set forth in paragraph 1.E.1 with
| |
| − | active links or immediate access to the full terms of the Project
| |
| − | Gutenberg™ License.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | 1.E.6. You may convert to and distribute this work in any binary,
| |
| − | compressed, marked up, nonproprietary or proprietary form, including
| |
| − | any word processing or hypertext form. However, if you provide access
| |
| − | to or distribute copies of a Project Gutenberg™ work in a format
| |
| − | other than “Plain Vanilla ASCII” or other format used in the official
| |
| − | version posted on the official Project Gutenberg™ website
| |
| − | (www.gutenberg.org), you must, at no additional cost, fee or expense
| |
| − | to the user, provide a copy, a means of exporting a copy, or a means
| |
| − | of obtaining a copy upon request, of the work in its original “Plain
| |
| − | Vanilla ASCII” or other form. Any alternate format must include the
| |
| − | full Project Gutenberg™ License as specified in paragraph 1.E.1.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | 1.E.7. Do not charge a fee for access to, viewing, displaying,
| |
| − | performing, copying or distributing any Project Gutenberg™ works
| |
| − | unless you comply with paragraph 1.E.8 or 1.E.9.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | 1.E.8. You may charge a reasonable fee for copies of or providing
| |
| − | access to or distributing Project Gutenberg™ electronic works
| |
| − | provided that:
| |
| − | </div>
| |
| − |
| |
| − | <div style='margin-left:0.7em;'>
| |
| − | <div style='text-indent:-0.7em'>
| |
| − | • You pay a royalty fee of 20% of the gross profits you derive from
| |
| − | the use of Project Gutenberg™ works calculated using the method
| |
| − | you already use to calculate your applicable taxes. The fee is owed
| |
| − | to the owner of the Project Gutenberg™ trademark, but he has
| |
| − | agreed to donate royalties under this paragraph to the Project
| |
| − | Gutenberg Literary Archive Foundation. Royalty payments must be paid
| |
| − | within 60 days following each date on which you prepare (or are
| |
| − | legally required to prepare) your periodic tax returns. Royalty
| |
| − | payments should be clearly marked as such and sent to the Project
| |
| − | Gutenberg Literary Archive Foundation at the address specified in
| |
| − | Section 4, “Information about donations to the Project Gutenberg
| |
| − | Literary Archive Foundation.”
| |
| − | </div>
| |
| − |
| |
| − | <div style='text-indent:-0.7em'>
| |
| − | • You provide a full refund of any money paid by a user who notifies
| |
| − | you in writing (or by e-mail) within 30 days of receipt that s/he
| |
| − | does not agree to the terms of the full Project Gutenberg™
| |
| − | License. You must require such a user to return or destroy all
| |
| − | copies of the works possessed in a physical medium and discontinue
| |
| − | all use of and all access to other copies of Project Gutenberg™
| |
| − | works.
| |
| − | </div>
| |
| − |
| |
| − | <div style='text-indent:-0.7em'>
| |
| − | • You provide, in accordance with paragraph 1.F.3, a full refund of
| |
| − | any money paid for a work or a replacement copy, if a defect in the
| |
| − | electronic work is discovered and reported to you within 90 days of
| |
| − | receipt of the work.
| |
| − | </div>
| |
| − |
| |
| − | <div style='text-indent:-0.7em'>
| |
| − | • You comply with all other terms of this agreement for free
| |
| − | distribution of Project Gutenberg™ works.
| |
| − | </div>
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | 1.E.9. If you wish to charge a fee or distribute a Project
| |
| − | Gutenberg™ electronic work or group of works on different terms than
| |
| − | are set forth in this agreement, you must obtain permission in writing
| |
| − | from the Project Gutenberg Literary Archive Foundation, the manager of
| |
| − | the Project Gutenberg™ trademark. Contact the Foundation as set
| |
| − | forth in Section 3 below.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | 1.F.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | 1.F.1. Project Gutenberg volunteers and employees expend considerable
| |
| − | effort to identify, do copyright research on, transcribe and proofread
| |
| − | works not protected by U.S. copyright law in creating the Project
| |
| − | Gutenberg™ collection. Despite these efforts, Project Gutenberg™
| |
| − | electronic works, and the medium on which they may be stored, may
| |
| − | contain “Defects,” such as, but not limited to, incomplete, inaccurate
| |
| − | or corrupt data, transcription errors, a copyright or other
| |
| − | intellectual property infringement, a defective or damaged disk or
| |
| − | other medium, a computer virus, or computer codes that damage or
| |
| − | cannot be read by your equipment.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | 1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the “Right
| |
| − | of Replacement or Refund” described in paragraph 1.F.3, the Project
| |
| − | Gutenberg Literary Archive Foundation, the owner of the Project
| |
| − | Gutenberg™ trademark, and any other party distributing a Project
| |
| − | Gutenberg™ electronic work under this agreement, disclaim all
| |
| − | liability to you for damages, costs and expenses, including legal
| |
| − | fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT
| |
| − | LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE
| |
| − | PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE THAT THE FOUNDATION, THE
| |
| − | TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE
| |
| − | LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR
| |
| − | INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH
| |
| − | DAMAGE.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | 1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a
| |
| − | defect in this electronic work within 90 days of receiving it, you can
| |
| − | receive a refund of the money (if any) you paid for it by sending a
| |
| − | written explanation to the person you received the work from. If you
| |
| − | received the work on a physical medium, you must return the medium
| |
| − | with your written explanation. The person or entity that provided you
| |
| − | with the defective work may elect to provide a replacement copy in
| |
| − | lieu of a refund. If you received the work electronically, the person
| |
| − | or entity providing it to you may choose to give you a second
| |
| − | opportunity to receive the work electronically in lieu of a refund. If
| |
| − | the second copy is also defective, you may demand a refund in writing
| |
| − | without further opportunities to fix the problem.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | 1.F.4. Except for the limited right of replacement or refund set forth
| |
| − | in paragraph 1.F.3, this work is provided to you ‘AS-IS’, WITH NO
| |
| − | OTHER WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT
| |
| − | LIMITED TO WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PURPOSE.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | 1.F.5. Some states do not allow disclaimers of certain implied
| |
| − | warranties or the exclusion or limitation of certain types of
| |
| − | damages. If any disclaimer or limitation set forth in this agreement
| |
| − | violates the law of the state applicable to this agreement, the
| |
| − | agreement shall be interpreted to make the maximum disclaimer or
| |
| − | limitation permitted by the applicable state law. The invalidity or
| |
| − | unenforceability of any provision of this agreement shall not void the
| |
| − | remaining provisions.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | 1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the
| |
| − | trademark owner, any agent or employee of the Foundation, anyone
| |
| − | providing copies of Project Gutenberg™ electronic works in
| |
| − | accordance with this agreement, and any volunteers associated with the
| |
| − | production, promotion and distribution of Project Gutenberg™
| |
| − | electronic works, harmless from all liability, costs and expenses,
| |
| − | including legal fees, that arise directly or indirectly from any of
| |
| − | the following which you do or cause to occur: (a) distribution of this
| |
| − | or any Project Gutenberg™ work, (b) alteration, modification, or
| |
| − | additions or deletions to any Project Gutenberg™ work, and (c) any
| |
| − | Defect you cause.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; font-size:1.1em; margin:1em 0; font-weight:bold'>
| |
| − | Section 2. Information about the Mission of Project Gutenberg™
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | Project Gutenberg™ is synonymous with the free distribution of
| |
| − | electronic works in formats readable by the widest variety of
| |
| − | computers including obsolete, old, middle-aged and new computers. It
| |
| − | exists because of the efforts of hundreds of volunteers and donations
| |
| − | from people in all walks of life.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | Volunteers and financial support to provide volunteers with the
| |
| − | assistance they need are critical to reaching Project Gutenberg™’s
| |
| − | goals and ensuring that the Project Gutenberg™ collection will
| |
| − | remain freely available for generations to come. In 2001, the Project
| |
| − | Gutenberg Literary Archive Foundation was created to provide a secure
| |
| − | and permanent future for Project Gutenberg™ and future
| |
| − | generations. To learn more about the Project Gutenberg Literary
| |
| − | Archive Foundation and how your efforts and donations can help, see
| |
| − | Sections 3 and 4 and the Foundation information page at www.gutenberg.org.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; font-size:1.1em; margin:1em 0; font-weight:bold'>
| |
| − | Section 3. Information about the Project Gutenberg Literary Archive Foundation
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | The Project Gutenberg Literary Archive Foundation is a non-profit
| |
| − | 501(c)(3) educational corporation organized under the laws of the
| |
| − | state of Mississippi and granted tax exempt status by the Internal
| |
| − | Revenue Service. The Foundation’s EIN or federal tax identification
| |
| − | number is 64-6221541. Contributions to the Project Gutenberg Literary
| |
| − | Archive Foundation are tax deductible to the full extent permitted by
| |
| − | U.S. federal laws and your state’s laws.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | The Foundation’s business office is located at 809 North 1500 West,
| |
| − | Salt Lake City, UT 84116, (801) 596-1887. Email contact links and up
| |
| − | to date contact information can be found at the Foundation’s website
| |
| − | and official page at www.gutenberg.org/contact
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; font-size:1.1em; margin:1em 0; font-weight:bold'>
| |
| − | Section 4. Information about Donations to the Project Gutenberg Literary Archive Foundation
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | Project Gutenberg™ depends upon and cannot survive without widespread
| |
| − | public support and donations to carry out its mission of
| |
| − | increasing the number of public domain and licensed works that can be
| |
| − | freely distributed in machine-readable form accessible by the widest
| |
| − | array of equipment including outdated equipment. Many small donations
| |
| − | ($1 to $5,000) are particularly important to maintaining tax exempt
| |
| − | status with the IRS.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | The Foundation is committed to complying with the laws regulating
| |
| − | charities and charitable donations in all 50 states of the United
| |
| − | States. Compliance requirements are not uniform and it takes a
| |
| − | considerable effort, much paperwork and many fees to meet and keep up
| |
| − | with these requirements. We do not solicit donations in locations
| |
| − | where we have not received written confirmation of compliance. To SEND
| |
| − | DONATIONS or determine the status of compliance for any particular state
| |
| − | visit <a href="https://www.gutenberg.org/donate/">www.gutenberg.org/donate</a>.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | While we cannot and do not solicit contributions from states where we
| |
| − | have not met the solicitation requirements, we know of no prohibition
| |
| − | against accepting unsolicited donations from donors in such states who
| |
| − | approach us with offers to donate.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | International donations are gratefully accepted, but we cannot make
| |
| − | any statements concerning tax treatment of donations received from
| |
| − | outside the United States. U.S. laws alone swamp our small staff.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | Please check the Project Gutenberg web pages for current donation
| |
| − | methods and addresses. Donations are accepted in a number of other
| |
| − | ways including checks, online payments and credit card donations. To
| |
| − | donate, please visit: www.gutenberg.org/donate
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; font-size:1.1em; margin:1em 0; font-weight:bold'>
| |
| − | Section 5. General Information About Project Gutenberg™ electronic works
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | Professor Michael S. Hart was the originator of the Project
| |
| − | Gutenberg™ concept of a library of electronic works that could be
| |
| − | freely shared with anyone. For forty years, he produced and
| |
| − | distributed Project Gutenberg™ eBooks with only a loose network of
| |
| − | volunteer support.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | Project Gutenberg™ eBooks are often created from several printed
| |
| − | editions, all of which are confirmed as not protected by copyright in
| |
| − | the U.S. unless a copyright notice is included. Thus, we do not
| |
| − | necessarily keep eBooks in compliance with any particular paper
| |
| − | edition.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | Most people start at our website which has the main PG search
| |
| − | facility: <a href="https://www.gutenberg.org">www.gutenberg.org</a>.
| |
| − | </div>
| |
| − |
| |
| − | <div style='display:block; margin:1em 0'>
| |
| − | This website includes information about Project Gutenberg™,
| |
| − | including how to make donations to the Project Gutenberg Literary
| |
| − | Archive Foundation, how to help produce our new eBooks, and how to
| |
| − | subscribe to our email newsletter to hear about new eBooks.
| |
| − | </div>
| |
| − |
| |
| − | </div>
| |
| | | | |
| | </body> | | </body> |
