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<h1 class='c001'>Chance, Love, and Logic</h1>
</div>
<div class='chapter'>
<h2 class='c009'>PREFACE</h2>
</div>
<p class='c006'>In the essays gathered together in this volume we have
the most developed and coherent available account of the
philosophy of Charles S. Peirce, whom James, Royce,
Dewey, and leading thinkers in England, France, Germany
and Italy have placed in the forefront of the great
seminal minds of recent times. Besides their inherent
value as the expression of a highly original and fruitful
mind, unusually well trained and informed in the exact
sciences, these essays are also important as giving us the
sources of a great deal of contemporary American philosophy.
Because of this historical importance no omissions
or changes have been made in the text beyond the correction
of some obvious slips and the recasting of a few expressions
in the interest of intelligibility.</p>
<p class='c005'>In a subject which bristles with suggestions and difficulties
the temptation to add notes of explanation or dissent
is almost insuperable. But as such notes might easily
have doubled the size of this volume I have refrained from
all comment on the text except in a few footnotes (indicated,
as usual, in brackets). The introduction is intended
(and I hope it will) help the reader to concatenate the
various lines of thought contained in these essays. I cannot
pretend to have adequately indicated their significance.
Great minds like those of James and Royce have been
nourished by these writings and I am persuaded that they
<span class='pageno' id='Page_iv'>iv</span>still offer mines of fruitful suggestion. Prof. Dewey’s supplementary
essay indicates their value for the fundamental
question of metaphysics, viz. the nature of reality.</p>
<p class='c005'>Grateful acknowledgment is here made to Mrs. Paul
Carus and to the Open Court Publishing Co. for permission
to reprint the essays of Part II from the <i>Monist</i>. The late
Paul Carus was one of the very few who not only gave
Peirce an opportunity to publish, but publicly recognized
the importance of his writings.</p>
<p class='c005'>I must also acknowledge my obligation to Professor
Dewey for kind permission to reprint his essay on the
Pragmatism of Peirce from the Journal of Philosophy, and
to the editors of that Journal, Professors Woodbridge and
Bush, for permission to reprint some material of my own.
Part V of the Bibliography was compiled by Mr. Irving
Smith.</p>
<p class='c005'><span class='sc'>Morris R. Cohen</span></p>
<p class='c005'><span class='sc'>The College of the City of New York.</span></p>
<div class='chapter'>
<span class='pageno' id='Page_v'>v</span>
<h2 class='c009'>TABLE OF CONTENTS</h2>
</div>
<p class='c006'><a href='#intro' style='color:#FFFF;'><span class='sc'>Introduction</span> vii</a></p>
<p class='c005'><a href='#proem' style='color:#FFFF;'><span class='sc'>Proem. The Rules of Philosophy</span> 1</a></p>
<p class='c005'><a href='#part1' style='color:#FFFF;'><span class='sc'>Part I. Chance and Logic</span> (Illustrations of the Logic of Science.)</a></p>
<p class='c005'><a href='#chap1-1' style='color:#FFFF;'>1. The Fixation of Belief 7</a></p>
<p class='c005'><a href='#chap1-2' style='color:#FFFF;'>2. How to Make Our Ideas Clear 32</a></p>
<p class='c005'><a href='#chap1-3' style='color:#FFFF;'>3. The Doctrine of Chances 61</a></p>
<p class='c005'><a href='#chap1-4' style='color:#FFFF;'>4. The Probability of Induction 82</a></p>
<p class='c005'><a href='#chap1-5' style='color:#FFFF;'>5. The Order of Nature 106</a></p>
<p class='c005'><a href='#chap1-6' style='color:#FFFF;'>6. Deduction, Induction and Hypothesis 131</a></p>
<p class='c006'><a href='#part2' style='color:#FFFF;'><span class='sc'>Part II. Love and Chance</span></a></p>
<p class='c005'><a href='#chap2-1' style='color:#FFFF;'>1. The Architecture of Theories 157</a></p>
<p class='c005'><a href='#chap2-2' style='color:#FFFF;'>2. The Doctrine of Necessity Examined 179</a></p>
<p class='c005'><a href='#chap2-3' style='color:#FFFF;'>3. The Law of Mind 202</a></p>
<p class='c005'><a href='#chap2-4' style='color:#FFFF;'>4. Man’s Glassy Essence 238</a></p>
<p class='c005'><a href='#chap2-5' style='color:#FFFF;'>5. Evolutionary Love 267</a></p>
<p class='c006'><a href='#essay' style='color:#FFFF;'><span class='sc'>Supplementary Essay</span>—The Pragmatism of Peirce, by John Dewey 301</a></p>
<div class='chapter'>
<span class='pageno' id='Page_vii'>vii</span>
<h2 id='intro' class='c009'>INTRODUCTION</h2>
</div>
<p class='c006'>Many and diverse are the minds that form the philosophic
community. There are, first and foremost, the great
masters, the system builders who rear their stately palaces
towering to the moon. These architectonic minds are
served by a varied host of followers and auxiliaries. Some
provide the furnishings to make these mystic mansions of
the mind more commodious, while others are engaged in
making their façades more imposing. Some are busy
strengthening weak places or building much-needed additions,
while many more are engaged in defending these
structures against the impetuous army of critics who are
ever eager and ready to pounce down upon and destroy all
that is new or bears the mortal mark of human imperfection.
There are also the philologists, those who are in a
more narrow sense scholars, who dig not only for facts or
roots, but also for the stones which may serve either for
building or as weapons of destruction. Remote from all
these, however, are the intellectual rovers who, in their
search for new fields, venture into the thick jungle that
surrounds the little patch of cultivated science. They are
not gregarious creatures, these lonely pioneers; and in their
wanderings they often completely lose touch with those
who tread the beaten paths. Those that return to the community
often speak strangely of strange things; and it is
not always that they arouse sufficient faith for others to
follow them and change their trails into high roads.</p>
<p class='c005'><span class='pageno' id='Page_viii'>viii</span>Few nowadays question the great value of these pioneer
minds; and it is often claimed that universities are established
to facilitate their work, and to prevent it from being
lost. But universities, like other well-managed institutions,
can find place only for those who work well in harness.
The restless, impatient minds, like the socially or conventionally
unacceptable, are thus kept out, no matter how
fruitful their originality. Charles S. Peirce was certainly
one of these restless pioneer souls with the fatal gift of
genuine originality. In his early papers, in the <i>Journal of
Speculative Philosophy</i>, and later, in the <i>Monist</i> papers
reprinted as <a href='#part2'>Part II</a> of this volume, we get glimpses of a
vast philosophic system on which he was working with an
unusual wealth of material and apparatus. To a rich
imagination and extraordinary learning he added one of the
most essential gifts of successful system builders, the power
to coin an apt and striking terminology. But the admitted
incompleteness of these preliminary sketches of his philosophic
system is not altogether due to the inherent difficulty
of the task and to external causes such as neglect and
poverty. A certain inner instability or lack of self-mastery
is reflected in the outer moral or conventional waywardness
which, except for a few years at Johns Hopkins,
caused him to be excluded from a university career, and
thus deprived him of much needed stimulus to ordinary
consistency and intelligibility. As the years advanced,
bringing little general interest in, or recognition of, the brilliant
logical studies of his early years, Peirce became more
and more fragmentary, cryptic, and involved; so that
James, the intellectual companion of his youth, later found
<span class='pageno' id='Page_ix'>ix</span>his lectures on pragmatism, “flashes of brilliant light relieved
against Cimmerian darkness”—a statement not to
be entirely discounted by the fact that James had no interest
in or aptitude for formal logical or mathematical considerations.</p>
<p class='c005'>Despite these limitations, however, Peirce stands out as
one of the great founders of modern scientific logic; and in
the realm of general philosophy the development of some
of his pregnant ideas has led to the pragmatism and
radical empiricism of James, as well as to the mathematical
idealism of Royce, and to the anti-nominalism which characterizes
the philosophic movement known as Neo-Realism.
At any rate, the work of James, Royce, and Russell, as
well as that of logicians like Schroeder, brings us of the
present generation into a better position to appreciate the
significance of Peirce’s work, than were his contemporaries.</p>
<h3 class='c010'>I</h3>
<p class='c006'>Peirce was by antecedents, training, and occupation a
scientist. He was a son of Benjamin Peirce, the great
Harvard mathematician, and his early environment, together
with his training in the Lawrence Scientific School,
justified his favorite claim that he was brought up in a
laboratory. He made important contributions not only in
mathematical logic but also in photometric astronomy,
geodesy, and psychophysics, as well as in philology. For
many years Peirce worked on the problems of geodesy, and
his contribution to the subject, his researches on the pendulum,
was at once recognized by European investigators
in this field. The International Geodetic Congress, to
<span class='pageno' id='Page_x'>x</span>which he was the first American representative, gave unusual
attention to his paper, and men like Cellerier and
Plantamour acknowledged their obligations to him.<a id='r1' /><a href='#f1' class='c011'><sup>[1]</sup></a></p>
<p class='c005'>This and other scientific work involving fine measurement,
with the correlative investigations into the theory
of probable error, seem to have been a decisive influence
in the development of Peirce’s philosophy of chance.
Philosophers inexperienced in actual scientific measurement
may naïvely accept as absolute truth such statements as
“every particle of matter attracts every other particle
directly as the product of their masses and inversely as the
square of the distance,” or “when hydrogen and oxygen
combine to form water the ratio of their weights is 1 : 8.”
But to those who are actually engaged in measuring natural
phenomena with instruments of precision, nature shows no
such absolute constancy or simplicity. As every laboratory
worker knows, no two observers, and no one observer in
successive experiments, get absolutely identical results. To
the men of the heroic period of science this was no difficulty.
They held unquestioningly the Platonic faith that nature
was created on simple geometric lines, and all the minute
variations were attributable to the fault of the observer or
the crudity of his instruments. This heroic faith was,
and still is, a most powerful stimulus to scientific research
and a protection against the incursions of supernaturalism.
But few would defend it to-day in its explicit form, and
there is little empirical evidence to show that while the
observer and his instruments are always varying, the objects
<span class='pageno' id='Page_xi'>xi</span>which he measures never deviate in the slightest from
the simple law. Doubtless, as one becomes more expert in
the manipulation of physical instruments, there is a noticeable
diminution of the range of the personal “error,” but
no amount of skill and no refinement of our instruments
have ever succeeded in eliminating irregular, though
small, variations. “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 departure from
the law.”<a id='r2' /><a href='#f2' class='c011'><sup>[2]</sup></a> There is certainly nothing in our empirical information
to prevent us from saying that all the so-called
constants of nature are merely instances of variation between
limits so near each other that their differences
may be neglected for certain purposes. Moreover, the approach
to constancy is observed only in mass phenomena,
when we are dealing with very large numbers of particles;
but social statistics also approach constant ratios when
the numbers are very large. Hence, without denying discrepancies
due solely to errors of observation, Peirce contends
that “we must suppose far more minute discrepancies
to exist owing to the imperfect cogency of the law itself,
to a certain swerving of the facts from any definite
formula.”<a id='r3' /><a href='#f3' class='c011'><sup>[3]</sup></a></p>
<p class='c005'>It is usual to associate disbelief in absolute laws of nature
with sentimental claims for freedom or theological
miracles. It is, therefore, well to insist that Peirce’s attack
is entirely in the interests of exact logic and a rational
account of the physical universe. As a rigorous logician
familiar with the actual procedures by which our knowledge
<span class='pageno' id='Page_xii'>xii</span>of the various laws of nature is obtained, he could not
admit that experience could prove their claim to absoluteness.
All the physical laws actually known, like Boyle’s
law or the law of gravitation, involve excessive simplification
of the phenomenal course of events, and thus a large
element of empirical inaccuracy. But a more positive
objection against the traditional assumption of absolute or
invariable laws of nature, is the fact that such assumption
makes the regularities of the universe ultimate, and thus
cuts us off from the possibility of ever explaining them or
how there comes to be as much regularity in the universe
as there is. But in ordinary affairs, the occurrence of any
regularity is the very thing to be explained. Moreover,
modern statistical mechanics and thermodynamics (theory
of gases, entropy, etc.) suggest that the regularity in the
universe is a matter of gradual growth; that the whole of
physical nature is a growth from a chaos of diversity to a
maximum of uniformity or entropy. A leading physicist of
the 19th Century, Boltzmann, has suggested that the
process of the whole physical universe is like that of a
continuous shaking up of a hap-hazard or chance mixture
of things, which thus gradually results in a progressively
more uniform distribution. Since Duns Scotus, students
of logic have known that every real entity has its individual
character (its <i>haecceitas</i> or <i>thisness</i>) which cannot be explained
or deduced from that which is uniform. Every
explanation, for example, of the moon’s path must take
particular existences for granted. Such original or underived
individuality and diversity is precisely what Peirce
means by chance; and from this point of view chance is
prior to law.</p>
<p class='c005'><span class='pageno' id='Page_xiii'>xiii</span>All that is necessary to visualize this is to suppose that
there is an infinitesimal tendency in things to acquire
habits, a tendency which is itself an accidental variation
grown habitual. We shall then be on the road to explain
the evolution and existence of the limited uniformities
actually prevailing in the physical world.</p>
<p class='c005'>A good deal of the foregoing may sound somewhat
mythologic. But even if it were so it would have the merit
of offering a rational alternative to the mechanical mythology
according to which all the atoms in the universe are
to-day precisely in the same condition in which they were
on the day of creation, a mythology which is forced to
regard all the empirical facts of spontaneity and novelty
as illusory, or devoid of substantial truth.</p>
<p class='c005'>The doctrine of the primacy of chance naturally suggests
the primacy of mind. Just as law is a chance habit so is
matter inert mind. The principal law of mind is that ideas
literally spread themselves continuously and become more
and more general or inclusive, so that people who form
communities of any sort develop general ideas in common.
When this continuous reaching-out of feeling becomes nurturing
love, such, e.g., which parents have for their offspring
or thinkers for their ideas, we have creative
evolution.</p>
<p class='c005'>James and Royce have called attention to the similarity
between Peirce’s doctrine of tychistic-agapism (chance and
love) and the creative evolution of Bergson. But while
both philosophies aim to restore life and growth in their
account of the nature of things, Peirce’s approach seems to
me to have marked advantages, owing to its being in closer
<span class='pageno' id='Page_xiv'>xiv</span>touch with modern physics. Bergson’s procedure is largely
based on the contention that mechanics cannot explain
certain empirical facts, such as the supposed identity of
the vertebrate eye and the eye of the scallop. But the fact
here is merely one of a certain resemblance of pattern, which
may well be explained by the mechanical principles of convergent
evolution. Peirce’s account involves no rejection
of the possibility of mechanical explanations. Indeed, by
carrying chance into the laws of mechanics he is enabled to
elaborate a positive and highly suggestive theory of protoplasm
to explain the facts of plasticity and habit.<a id='r4' /><a href='#f4' class='c011'><sup>[4]</sup></a> Instead
of postulating with Spencer and Bergson a continuous
growth of diversity, Peirce allows for growth of habits both
in diversity and in uniformity. The Spencerian mechanical
philosophy reduces all diversity to mere spatial differences.
There can be no substantial novelty; only new forms or
combinations can arise in time. The creative evolution of
Bergson though intended to support the claims of spontaneity
is still like the Spencerian in assuming all evolution
as proceeding from the simple to the complex. Peirce
allows for diversity and specificity as part of the original
character or endowment of things, which in the course of
time may increase in some respects and diminish in others.
Mind acquires the habit both of taking on, and also of laying
aside, habits. Evolution may thus lead to homogeneity
or uniformity as well as to greater heterogeneity.</p>
<p class='c005'>Not only has Peirce a greater regard than even Bergson
for the actual diversity and spontaneity of things, but he
is in a much better position than any other modern philosopher
<span class='pageno' id='Page_xv'>xv</span>to explain the order and coherence of the world.
This he effects by uniting the medieval regard for the
reality of universals with the modern scientific use of the
concept of continuity. The unfortunate war between the
pioneers of modern science and the adherents of the scholastic
doctrine of substantial forms, has been one of the
great misfortunes of human thought, in that it made absolute
atomism and nominalism the professed <i>creed</i> of physical
science. Now, extreme nominalism, the insistence on
the reality of the particular, leaves no room for the genuine
reality of law. It leaves, as Hume had the courage to
admit, nothing whereby the present can determine the
future; so that anything is as likely to happen as not.
From such a chaotic world, the <i>procedure</i> of modern natural
and mathematical science has saved us by the persistent
use of the principle of continuity; and no one has indicated
this more clearly than Peirce who was uniquely qualified
to do so by being a close student both of Duns Scotus and
of modern scientific methods.</p>
<p class='c005'>It is instructive in this respect to contrast the views of
Peirce and James. James, who so generously indicated his
indebtedness to Peirce for his pragmatism, was also largely
indebted to Peirce for his doctrine of radical empiricism.<a id='r5' /><a href='#f5' class='c011'><sup>[5]</sup></a>
The latter doctrine seeks to rescue the continuity and
fluidity of experience from the traditional British empiricism
or nominalism, which had resolved everything into a
number of mutually exclusive mental states. It is curious,
however, that while in his psychology James made extensive
use of the principle of continuity, he could not free himself
<span class='pageno' id='Page_xvi'>xvi</span>from British nominalism in his philosophy—witness the
extreme individualism of his social philosophy or the equally
extreme anthropomorphism of his religion. Certain of
Peirce’s suggestions as to the use of continuity in social
philosophy have been developed by Royce in his theory of
social consciousness and the nature of the community;<a id='r6' /><a href='#f6' class='c011'><sup>[6]</sup></a>
but much remains to be worked out and we can but repeat
Peirce’s own hope: “May some future student go over
this ground again and have the leisure to give his results
to the world.”</p>
<p class='c005'>It is well to note, however, that after writing the papers
included in this volume Peirce continued to be occupied
with the issues here raised. This he most significantly
indicated in the articles on logical topics contributed to
Baldwin’s Dictionary of Philosophy.<a id='r7' /><a href='#f7' class='c011'><sup>[7]</sup></a></p>
<p class='c005'>In these articles it is naturally the logical bearing of the
principles of tychism (chance), synechism (continuity), and
agapism (love) that is stressed. To use the Kantian terminology,
almost native to Peirce, the regulative rather
than the constitutive aspect of these principles is emphasized.
Thus the doctrine of chance is not only what it was
for James’ radical empiricism, a release from the blind
necessity of a “block universe,” but also a method of keeping
<span class='pageno' id='Page_xvii'>xvii</span>open a possible explanation of the genesis of the laws
of nature and an interpretation of them in accordance with
the theorems of probability, so fruitful in physical science
as well as in practical life. So the doctrine of love is not
only a cosmologic one, showing how chance feeling generates
order or rational diversity through the habit of generality
or continuity, but it also gives us the meaning of truth in
social terms, in showing that the test as to whether any
proposition is true postulates an indefinite number of co-operating
investigators. On its logical side the doctrine of
love (agapism) also recognized the important fact that
general ideas have a certain attraction which makes us divine
their nature even though we cannot clearly determine their
precise meaning before developing their possible consequences.</p>
<p class='c005'>Of the doctrine of continuity we are told expressly<a id='r8' /><a href='#f8' class='c011'><sup>[8]</sup></a> that
“synechism is not an ultimate absolute metaphysical
doctrine. It is a regulative principle of logic,” seeking the
thread of identity in diverse cases and avoiding hypotheses
that this or that is ultimate and, therefore, inexplicable.
(Examples of such hypotheses are: the existence of absolutely
accurate or uniform laws of nature, the eternity and
absolute likeness of all atoms, etc.) To be sure, the
synechist cannot deny that there is an element of the inexplicable
or ultimate, since it is directly forced upon him.
But he cannot regard it as a source of explanation. The
assumption of an inexplicability is a barrier on the road to
science. “The form under which alone anything can be
understood is the form of generality which is the same thing
<span class='pageno' id='Page_xviii'>xviii</span>as continuity.”<a id='r9' /><a href='#f9' class='c011'><sup>[9]</sup></a> This insistence on the generality of
intelligible form is perfectly consistent with due emphases
on the reality of the individual, which to a Scotist realist
connotes an element of will or will-resistence, but in logical
procedure means that the test of the truth or falsity of any
proposition refers us to particular perceptions.<a id='r10' /><a href='#f10' class='c011'><sup>[10]</sup></a> But
as no multitude of individuals can exhaust the meaning of
a continuum, which includes also organizing relations of
order, the full meaning of a concept cannot be in any
individual reaction, but is rather to be sought in the manner
in which all such reactions contribute to the development of
the concrete reasonableness of the whole evolutionary
process. In scientific procedure this means that integrity
of belief in general is more important than, because it is
the condition of, particular true beliefs.</p>
<h3 class='c010'>II</h3>
<p class='c006'>This insistence on the continuity so effectually used as a
heuristic principle in natural and mathematical science,
distinguishes the pragmatism of Peirce from that of his
follower James. Prof. Dewey has developed this point
authoritatively in the supplementary essay; but in view of
the general ignorance as to the sources of pragmatism which
prevails in this incurious age, some remarks on the actual
historical origin of pragmatism may be in order.</p>
<p class='c005'>There can be little doubt that Peirce was led to the formulation
of the principle of pragmatism through the influence
<span class='pageno' id='Page_xix'>xix</span>of Chauncey Wright.<a id='r11' /><a href='#f11' class='c011'><sup>[11]</sup></a> Wright who had first hand acquaintance
with creative scientific work in mathematics,
physics, and botany was led by the study of Mill and Bain
to reflect on the characteristics of scientific method. This
reflection led him to draw a distinction between the use of
popular scientific material, by men like Spencer, to construct
a myth or picture of the world, and the scientific
use of laws by men like Newton as means for extending our
knowledge of phenomena. Gravitation as a general fact
had interested metaphysicians long before Newton. What
made Newton’s contribution scientific was the formulation
of a mathematical law which has enabled us to deduce all
the then known facts of the solar system and to anticipate
or predict many more facts the existence of which would
not otherwise be even suspected, e.g., the existence of the
planet Neptune. Wright insists, therefore, that the principles
of modern mathematical and physical science are
the means through which nature is discovered, that scientific
<span class='pageno' id='Page_xx'>xx</span>laws are the finders rather than merely the summaries of
factual truths. This conception of the experimental scientist
as translating general propositions into prescriptions
for attaining new experimental truths, is the starting point
of Peirce’s pragmatism. The latter is embodied in the
principle that the meaning of a concept is to be found in
“all the conceivable experimental phenomena which the
affirmation or denial of the concept could imply.”<a id='r12' /><a href='#f12' class='c011'><sup>[12]</sup></a></p>
<p class='c005'>In the earlier statement of the pragmatic maxim,<a id='r13' /><a href='#f13' class='c011'><sup>[13]</sup></a>
Peirce emphasized the consequences for conduct that follow
from the acceptance or rejection of an idea; but the stoical
maxim that the end of man is action did not appeal to him
as much at sixty as it did at thirty.<a id='r14' /><a href='#f14' class='c011'><sup>[14]</sup></a> Naturally also Peirce
could not follow the development of pragmatism by Wm.
James who, like almost all modern psychologists, was a
thorough nominalist and always emphasized particular
sensible experience.<a id='r15' /><a href='#f15' class='c011'><sup>[15]</sup></a> It seemed to Peirce that such emphasis
<span class='pageno' id='Page_xxi'>xxi</span>on particular experiences endangered the principle
of continuity which in the hands of men like Weierstrass
had reformed modern mathematics. For this reason he
began to call his own doctrine pragmaticism, a sufficiently
unattractive name, he thought, to save it from kidnappers
and from popularity. He never, however, abandoned the
principle of pragmatism, that the meaning of an idea is
clarified (because constituted) by its conceivable experimental
consequences. Indeed, if we want to clarify the
meaning of the idea of pragmatism, let us apply the pragmatic
test to it. What will be the effect of accepting it?
Obviously it will be to develop certain general ideas or
habits of looking at things.</p>
<p class='c005'>Peirce’s pragmatism has, therefore, a decidedly intellectual
cast. The meaning of an idea or proposition is
found not by an intuition of it but by working out its implications.
It admits that thought does not constitute
reality. Categories can have no concrete being without
action or immediate feeling. But thought is none the less
an essential ingredient of reality; thought is “the melody
running through the succession of our sensations.” Pragmatism,
according to Peirce, seeks to define the rational
purport, not the sensuous quality. It is interested not in
the effect of our practical occupations or desires on our
ideas, but in the function of ideas as guides of action.
Whether a man is to pay damages in a certain lawsuit may
depend, in fact, on a term in the Aristotelian logic such as
proximate cause.</p>
<p class='c005'>It is of interest to observe that though Peirce is an ardent
admirer of Darwin’s method, his scientific caution makes
<span class='pageno' id='Page_xxii'>xxii</span>him refuse to apply the analogy of biologic natural selection
to the realm of ideas, in the wholesale and uncritical
manner that has lately become fashionable. Natural selection
may well favor the triumph of views which directly
influence biologic survival. But the pleasure of entertaining
congenial illusions may overbalance the inconvenience
resulting from their deceptive character. Thus rhetorical
appeals may long prevail over scientific evidence.</p>
<h3 class='c010'>III</h3>
<p class='c006'>Peirce preferred to call himself a logician, and his contributions
to logic have so far proved his most generally
recognized achievement. For a right perspective of these
contributions we may well begin with the observation that
though few branches of philosophy have been cultivated as
continuously as logic, Kant was able to affirm that the
science of logic had made no substantial progress since the
time of Aristotle. The reason for this is that Aristotle’s
logic, the logic of classes, was based on his own scientific
procedure as a zoologist, and is still in essence a valid
method so far as classification is part of all rational procedure.
But when we come to describe the mathematical
method of physical science, we cannot cast it into the
Aristotelian form without involving ourselves in such complicated
artificialities as to reduce almost to nil the value
of Aristotle’s logic as an organon. Aristotle’s logic enables
us to make a single inference from two premises. But the
vast multitude of theorems that modern mathematics has
derived from a few premises as to the nature of number,
shows the need of formulating a logic or theory of inference
<span class='pageno' id='Page_xxiii'>xxiii</span>that shall correspond to the modern, more complicated, practice
as Aristotle’s logic did to simple classificatory zoology.
To do this effectively would require the highest constructive
logical genius, together with an intimate knowledge
of the methods of the great variety of modern sciences.
This is in the nature of the case a very rare combination,
since great investigators are not as critical in examining
their own procedure as they are in examining the subject
matter which is their primary scientific interest. Hence,
when great investigators like Poincaré come to describe
their own work, they fall back on the uncritical assumptions
of the traditional logic which they learned in their school
days. Moreover, “For the last three centuries thought
has been conducted in laboratories, in the field, or otherwise
in the face of the facts, while chairs of logic have been
filled by men who breathe the air of the seminary.”<a id='r16' /><a href='#f16' class='c011'><sup>[16]</sup></a> The
great Leibnitz had the qualifications, but here, as elsewhere,
his worldly occupations left him no opportunity
except for very fragmentary contributions. It was not until
the middle of the 19th century that two mathematicians,
Boole and DeMorgan, laid the foundations for a more generalized
logic. Boole developed a general logical algorithm
or calculus, while DeMorgan called attention to non-syllogistic
inference and especially to the importance of the logic of
relations. Peirce’s great achievement is to have recognized
the possibilities of both and to have generalized and developed
them into a general theory of scientific inference.
The extent and thoroughness of his achievement has been
obscured by his fragmentary way of writing and by a rather
<span class='pageno' id='Page_xxiv'>xxiv</span>unwieldy symbolism. Still, modern mathematical logic,
such as that of Russell’s <i>Principles of Mathematics</i>, is but a
development of Peirce’s logic of relatives.</p>
<p class='c005'>This phase of Peirce’s work is highly technical and an
account of it is out of place here. Such an account will
be found in Lewis’ <i>Survey of Symbolic Logic</i>.<a id='r17' /><a href='#f17' class='c011'><sup>[17]</sup></a> I refer to
it here only to remind the reader that the <i>Illustrations of
the Logic of the Sciences</i> (<a href='#part1'>Part I</a> of this volume) have a
background of patient detailed work which is still being
developed to-day.</p>
<p class='c005'>Symbolic logic has been held in rather low esteem by
the followers of the old classical methods in philosophy.
Their stated objection to it has been mainly that it is
concerned with the minutiae of an artificial language and is
of no value as a guide to the interpretation of reality.
Now it should be readily admitted that preoccupation with
symbolic logic is rather apt to retard the irresponsible
flight of philosophic fancy. Yet this is by no means always
an evil. By insisting on an accuracy that is painful to those
impatient to obtain sweeping and comforting, though hasty,
conclusions, symbolic logic is well calculated to remove the
great scandal of traditional philosophy—the claim of absolutely
certain results in fields where there is the greatest
conflict of opinion. This scandalous situation arises in part
from the fact that in popular exposition we do not have to
make our premises or assumptions explicit; hence all sorts
of dubious prejudices are implicitly appealed to as absolutely
<span class='pageno' id='Page_xxv'>xxv</span>necessary principles. Also, by the use of popular
terms which have a variety of meanings, one easily slides
from one meaning to another, so that the most improbable
conclusions are thus derived from seeming truisms. By
making assumptions and rules explicit, and by using technical
terms that do not drag wide penumbras of meaning
with them, the method of symbolic logic may cruelly reduce
the sweeping pretensions of philosophy. But there is no
reason for supposing that pretentiousness rather than
humility is the way to philosophic salvation. Man is bound
to speculate about the universe beyond the range of his
knowledge, but he is not bound to indulge the vanity of
setting up such speculations as absolutely certain dogmas.</p>
<p class='c005'>There is, however, no reason for denying that greater
rigor and accuracy of exposition can really help us to discern
new truth. Modern mathematics since Gauss and
Weierstrass has actually been led to greater fruitfulness by
increased rigor which makes such procedure as the old
proofs of Taylor’s theorem no longer possible. The substitution
of rigorous analytic procedures for the old Euclidean
proofs based on intuition, has opened up vast fields
of geometry. Nor has this been without any effect on
philosophy. Where formerly concepts like infinity and continuity
were objects of gaping awe or the recurrent occasions
for intellectual violence,<a id='r18' /><a href='#f18' class='c011'><sup>[18]</sup></a> we are now beginning to
use them, thanks to Peirce and Royce, in accurate and
definable senses. Consider, for instance, the amount of
a priori nonsense which Peirce eliminates by pointing out
<span class='pageno' id='Page_xxvi'>xxvi</span>that the application of the concept of continuity to a span
of consciousness removes the necessity for assuming a first
or last moment; so likewise the range of vision on a large
unobstructed ground has no line between the visible and the
invisible. These considerations will be found utterly destructive
of the force of the old arguments (fundamental
to Kant and others) as to the necessary infinity of time and
space. Similar enlightenment is soon likely to result from
the more careful use of terms like relative and absolute,
which are bones of contention in philosophy but Ariadne
threads of exploration in theoretical physics, because of
the definite symbolism of mathematics. Other important
truths made clear by symbolic logic is the hypothetical
character of universal propositions and the consequent insight
that no particulars can be deduced from universals
alone, since no number of hypotheses can without given data
establish an existing fact.</p>
<p class='c005'>There is, however, an even more positive direction in
which symbolic logic serves the interest of philosophy, and
that is in throwing light on the nature of symbols and on
the relation of meaning. Philosophers have light-heartedly
dismissed questions as to the nature of significant signs as
‘merely’ (most fatal word!) a matter of language. But
Peirce in the paper on Man’s Glassy [Shakespearian for
Mirror-Like] Essence, endeavors to exhibit man’s whole
nature as symbolic.<a id='r19' /><a href='#f19' class='c011'><sup>[19]</sup></a> This is closely connected with his
logical doctrine which regards signs or symbols as one of
<span class='pageno' id='Page_xxvii'>xxvii</span>the fundamental categories or aspects of the universe
(Thoughts and things are the other two). Independently
of Peirce but in line with his thought another great and
neglected thinker, Santayana, has shown that the whole life
of man that is bound up with the institutions of civilization,
is concerned with symbols.</p>
<p class='c005'>It is not altogether accidental that, since Boole and
DeMorgan, those who have occupied themselves with symbolic
logic have felt called upon to deal with the problem
of probability. The reason is indicated by Peirce when he
formulates the problem of probable inference in such a way
as to make the old classic logic of absolutely true or false
conclusions, a limiting case (i.e., of values 1 and 0) of the
logic of probable inference whose values range all the way
between these two limits. This technical device is itself
the result of applying the principle of continuity to throw
two hitherto distinct types of reasoning into the same class.
The result is philosophically significant.</p>
<p class='c005'>Where the classical logic spoke of major and minor
premises without establishing any really important difference
between the two, Peirce draws a distinction between
the premises and the guiding principle of our argument.
All reasoning is from some concrete situation to another.
The propositions which represent the first are the premises
in the strict sense of the word. But the feeling that certain
conclusions follow from these premises is conditioned by an
implicit or explicit belief in some guiding principle which
connects the premises and the conclusions. When such a
leading principle results in true conclusions in all cases of
true premises, we have logical deduction of the orthodox
<span class='pageno' id='Page_xxviii'>xxviii</span>type. If, however, such a principle brings about a true conclusion
only in a certain proportion of cases, then we have
probability.</p>
<p class='c005'>This reduction of probability to the relative frequency
of true propositions in a class of propositions, was suggested
to Peirce by Venn’s <i>Logic of Chance</i>. Peirce uses it to
establish some truths of greatest importance to logic and
philosophy.</p>
<p class='c005'>He eliminates the difficulties of the old conceptualist
view, which made probability a measure of our ignorance
and yet had to admit that almost all fruitfulness of our
practical and scientific reasoning depended on the theorems
of probability. How could we safely predict phenomena by
measuring our ignorance?</p>
<p class='c005'>Probability being reduced to a matter of the relative frequency
of a class in a larger class or genus, it becomes,
strictly speaking, inapplicable to single cases by themselves.
A single penny will fall head or it will fall tail every time;
to-morrow it will rain, or it will not rain at all. The
probability of 1/2 or any other fraction means nothing in
the single case. It is only because we feel the single event
as representative of a class, as something which repeats
itself, that we speak elliptically of the probability of a
single event. Hence follows the important corollary that
reasoning with respect to the probability of this or that arrangement
of the universe would be valid only if universes
were as plentiful as blackberries.</p>
<p class='c005'>To be useful at all, theories must be simpler than the
complex facts which they seek to explain. Hence, it is
often convenient to employ a principle of certainty where
<span class='pageno' id='Page_xxix'>xxix</span>the facts justify only a principle of some degree of probability.
In such cases we must be cautious in accepting
any extreme consequence of these principles, and also be
on guard against apparent refutations based on such extreme
consequences.</p>
<p class='c005'>Finally I should like to emphasize the value of Peirce’s
theory of inference for a philosophy of civilization. To the
old argument that logic is of no importance because people
learn to reason, as to walk, by instinct and habit and not by
scientific instruction, Peirce admits<a id='r20' /><a href='#f20' class='c011'><sup>[20]</sup></a> that “all human
knowledge up to the highest flights of science is but the
development of our inborn animal instincts.” But though
logical rules are first felt implicitly, bringing them into
explicit consciousness helps the process of analysis and
thus makes possible the recognition of old principles in novel
situations. This increases our range of adaptability to such
an extent as to justify a general distinction between the
slave of routine or habit and the freeman who can anticipate
and control nature through knowledge of principles. Peirce’s
analysis of the method of science as a method of attaining
stability of beliefs by free inquiry inviting all possible
doubt, in contrast with the methods of iteration (“will to
believe”) and social authority, is one of the best introductions
to a theory of liberal or Hellenic civilization, as
opposed to those of despotic societies. Authority has its
roots in the force of habit, but it cannot prevent new and
unorthodox ideas from arising; and in the effort to defend
authoritative social views men are apt to be far more ruthless
than in defending their own personal convictions.</p>
<div>
<span class='pageno' id='Page_xxx'>xxx</span>
<h3 class='c010'>IV</h3>
</div>
<p class='c006'>Not only the pragmatism and the radical empiricism of
James, but the idealism of Royce and the more recent
movement of neo-realism are largely indebted to Peirce.</p>
<p class='c005'>It may seem strange that the same thinker should be
claimed as foster-father of both recent idealism and realism,
and some may take it as another sign of his lack of consistency.
But this seeming strangeness is really due to
the looseness with which the antithesis between realism and
idealism has generally been put. If by idealism we denote
the nominalistic doctrine of Berkeley, then Peirce is clearly
not an idealist; and his work in logic as a study of types
of order (in which Royce followed him) is fundamental
for a logical realism. But if idealism means the old
Platonic doctrine that “ideas,” genera, or forms are not
merely mental but the real conditions of existence, we need
not wonder that Peirce was both idealist and realist.</p>
<p class='c005'>Royce’s indebtedness to Peirce is principally in the use
of modern mathematical material, such as the recent development
of the concepts of infinity and continuity, to
throw light on fundamental questions of philosophy, such
as relation of the individual to God or the Universe. At
the end of the nineteenth century mathematics had almost
disappeared from the repertory of philosophy (cf. Külpe’s
<i>Introduction to Philosophy</i>), and Peirce’s essay on the
<i>Law of Mind</i> opened a new way which Royce followed in
his <i>World and the Individual</i>, to the great surprise of his
idealistic brethren. In his <i>Problem of Christianity</i> Royce
has also indicated his indebtedness to Peirce for his doctrine
<span class='pageno' id='Page_xxxi'>xxxi</span>of social consciousness, the mind of the community,
and the process of interpretation. It may be that a great
deal of the similarity between the thoughts of these two
men is due to common sources, such as the works of Kant
and Schelling; but it is well to note that not only in his
later writings but also in his lectures and seminars Royce
continually referred to Peirce’s views.</p>
<p class='c005'>The ground for the neo-realist movement in American
philosophy was largely prepared by the mathematical work
of Russell and by the utilization of mathematics to which
Royce was led by Peirce. The logic of Mr. Russell is
based, as he himself has pointed out, on a combination of
the work of Peirce and Peano. In this combination the
notation of Peano has proved of greater technical fluency,
but all of Peano’s results can also be obtained by Peirce’s
method as developed by Schroeder and Mrs. Ladd-Franklin.
But philosophically Peirce’s influence is far greater in
insisting that logic is not a branch of psychology, that it
is not concerned with merely mental processes, but with
objective relations. To the view that the laws of logic
represent “the necessities of thought,” that propositions
are true because “we can not help thinking so,” he answers:
“Exact logic will say that <i>C</i>’s following logically from <i>A</i> is
a state of things which no impotence of thought alone can
bring about.”<a id='r21' /><a href='#f21' class='c011'><sup>[21]</sup></a> “The question of validity is purely one
of fact and not of thinking.... It is not in the least the
question whether, when the premises are accepted by the
mind, we feel an impulse to accept the conclusion also.
<span class='pageno' id='Page_xxxii'>xxxii</span>The true conclusion would remain true if we had no impulse
to accept it, and the false one would remain false
though we could not resist the tendency to believe in it.”<a id='r22' /><a href='#f22' class='c011'><sup>[22]</sup></a></p>
<p class='c005'>Since the days of Locke modern philosophy has been
almost entirely dominated by the assumption that one must
study the process of knowing before one can find out the
nature of things known; in other words, that psychology is
<i>the</i> central philosophic science. The result of this has been
an almost complete identification of philosophy with mental
science. Nor did the influence of biologic studies of the
middle of the nineteenth century shake the belief in that
banal dictum of philosophic mediocrity: “The proper
study of mankind is man.” The recent renaissance of
logical studies, and the remarkable progress of physics in
our own day bid fair to remind us that while the Lockian
way has brought some gains to philosophy, the more ancient
way of philosophy is by no means exhausted of promise.
Man cannot lose his interest in the great cosmic play.
Those who have faith in the ancient and fruitful approach
to philosophy through the doors of mathematics and physics
will find the writings of Charles S. Peirce full of suggestions.
That such an approach can also throw light on the
vexed problem of knowledge needs no assurance to those
acquainted with Plato and Aristotle. But I may conclude
by referring to Peirce’s doctrine of ideal as opposed to
sensible experiment,<a id='r23' /><a href='#f23' class='c011'><sup>[23]</sup></a> and to his treatment of the question
<span class='pageno' id='Page_xxxiii'>xxxiii</span>how it is that in spite of an infinity of possible hypotheses,
mankind has managed to make so many successful inductions.<a id='r24' /><a href='#f24' class='c011'><sup>[24]</sup></a>
And for the bearing of mathematical studies on the
wisdom of life, the following is certainly worth serious reflection:
“All human affairs rest upon probabilities. If
man were immortal [on earth] he could be perfectly sure
of seeing the day when everything in which he had trusted
should betray his trust. He would break down, at last, as
every great fortune, as every dynasty, as every civilization
does. In place of this we have death.” The recognition
that the death of the individual does not destroy the logical
meaning of his utterances, that this meaning involves the
ideal of an unlimited community, carries us into the heart
of pure religion.</p>
<div class='chapter'>
<span class='pageno' id='Page_1'>1</span>
<h2 id='proem' class='c009'>PROEM <br /> THE RULES OF PHILOSOPHY<a id='r25' /><a href='#f25' class='c011'><sup>[25]</sup></a></h2>
</div>
<p class='c006'>Descartes is the father of modern philosophy, and the
spirit of Cartesianism—that which principally distinguishes
it from the scholasticism which it displaced—may
be compendiously stated as follows:</p>
<p class='c005'>1. It teaches that philosophy must begin with universal
doubt; whereas scholasticism had never questioned fundamentals.</p>
<p class='c005'>2. It teaches that the ultimate test of certainty is to be
found in the individual consciousness; whereas scholasticism
had rested on the testimony of sages and of the Catholic
Church.</p>
<p class='c005'>3. The multiform argumentation of the middle ages is
replaced by a single thread of inference depending often
upon inconspicuous premises.</p>
<p class='c005'>4. Scholasticism had its mysteries of faith, but undertook
to explain all created things. But there are many facts
which Cartesianism not only does not explain but renders
absolutely inexplicable, unless to say that “God makes them
so” is to be regarded as an explanation.</p>
<p class='c005'>In some, or all of these respects, most modern philosophers
have been, in effect, Cartesians. Now without wishing
<span class='pageno' id='Page_2'>2</span>to return to scholasticism, it seems to me that modern
science and modern logic require us to stand upon a very
different platform from this.</p>
<p class='c005'>1. We cannot begin with complete doubt. We must begin
with all the prejudices which we actually have when we
enter upon the study of philosophy. These prejudices are
not to be dispelled by a maxim, for they are things which
it does not occur to us can be questioned. Hence this
initial skepticism will be a mere self-deception, and not real
doubt; and no one who follows the Cartesian method will
ever be satisfied until he has formally recovered all those
beliefs which in form he has given up. It is, therefore, as
useless a preliminary as going to the North Pole would be
in order to get to Constantinople by coming down regularly
upon a meridian. A person may, it is true, in the course
of his studies, find reason to doubt what he began by believing;
but in that case he doubts because he has a positive
reason for it, and not on account of the Cartesian maxim.
Let us not pretend to doubt in philosophy what we do not
doubt in our hearts.</p>
<p class='c005'>2. The same formalism appears in the Cartesian criterion,
which amounts to this: “Whatever I am clearly convinced
of, is true.” If I were really convinced, I should have done
with reasoning and should require no test of certainty.
But then to make single individuals absolute judges of truth
is most pernicious. The result is that metaphysics has
reached a pitch of certainty far beyond that of the physical
sciences;—only they can agree upon nothing else. In
sciences in which men come to agreement, when a theory
<span class='pageno' id='Page_3'>3</span>has been broached it is considered to be on probation until
this agreement is reached. After it is reached, the question
of certainty becomes an idle one, because there is no one
left who doubts it. We individually cannot reasonably
hope to attain the ultimate philosophy which we pursue;
we can only seek it, therefore, for the community of philosophers.
Hence, if disciplined and candid minds carefully
examine a theory and refuse to accept it, this ought to create
doubts in the mind of the author of the theory himself.</p>
<p class='c005'>3. Philosophy ought to imitate the successful sciences in
its methods, so far as to proceed only from tangible premises
which can be subjected to careful scrutiny, and to trust
rather to the multitude and variety of its arguments than
to the conclusiveness of any one. Its reasoning should not
form a chain which is no stronger than its weakest link,
but a cable whose fibers may be ever so slender, provided
they are sufficiently numerous and intimately connected.</p>
<p class='c005'>4. Every unidealistic philosophy supposes some absolutely
inexplicable, unanalyzable ultimate; in short, something
resulting from mediation itself not susceptible of mediation.
Now that anything is thus inexplicable, can only be known
by reasoning from signs. But the only justification of an
inference from signs is that the conclusion explains the fact.
To suppose the fact absolutely inexplicable, is not to explain
it, and hence this supposition is never allowable.</p>
<div class='chapter'>
<span class='pageno' id='Page_5'>5</span>
<h2 id='part1' class='c009'>PART I <br /> CHANCE AND LOGIC <br /> (ILLUSTRATIONS OF THE LOGIC OF SCIENCE)</h2>
</div>
<div>
<span class='pageno' id='Page_7'>7</span>
<h3 id='chap1-1' class='c001'>CHANCE AND LOGIC <br /> FIRST PAPER <br /> THE FIXATION OF BELIEF<a id='r26' /><a href='#f26' class='c011'><sup>[26]</sup></a></h3>
</div>
<h4 class='c012'>I</h4>
<p class='c006'>Few persons care to study logic, because everybody conceives
himself to be proficient enough in the art of reasoning
already. But I observe that this satisfaction is limited to
one’s own ratiocination, and does not extend to that of
other men.</p>
<p class='c005'>We come to the full possession of our power of drawing
inferences the last of all our faculties, for it is not so much
a natural gift as a long and difficult art. The history of
its practice would make a grand subject for a book. The
medieval schoolman, following the Romans, made logic the
earliest of a boy’s studies after grammar, as being very
easy. So it was as they understood it. Its fundamental
principle, according to them, was, that all knowledge rests
on either authority or reason; but that whatever is deduced
by reason depends ultimately on a premise derived from
authority. Accordingly, as soon as a boy was perfect in
the syllogistic procedure, his intellectual kit of tools was
held to be complete.</p>
<p class='c005'><span class='pageno' id='Page_8'>8</span>To Roger Bacon, that remarkable mind who in the middle
of the thirteenth century was almost a scientific man, the
schoolmen’s conception of reasoning appeared only an obstacle
to truth. He saw that experience alone teaches anything—a
proposition which to us seems easy to understand,
because a distinct conception of experience has been handed
down to us from former generations; which to him also
seemed perfectly clear, because its difficulties had not yet
unfolded themselves. Of all kinds of experience, the best,
he thought, was interior illumination, which teaches many
things about Nature which the external senses could never
discover, such as the transubstantiation of bread.</p>
<p class='c005'>Four centuries later, the more celebrated Bacon, in the
first book of his “Novum Organum,” gave his clear account
of experience as something which must be open to verification
and reëxamination. But, superior as Lord Bacon’s
conception is to earlier notions, a modern reader who is not
in awe of his grandiloquence is chiefly struck by the inadequacy
of his view of scientific procedure. That we have
only to make some crude experiments, to draw up briefs
of the results in certain blank forms, to go through these
by rule, checking off everything disproved and setting down
the alternatives, and that thus in a few years physical
science would be finished up—what an idea! “He wrote
on science like a Lord Chancellor,”<a id='r27' /><a href='#f27' class='c011'><sup>[27]</sup></a> indeed.</p>
<p class='c005'>The early scientists, Copernicus, Tycho Brahe, Kepler,
Galileo and Gilbert, had methods more like those of their
modern brethren. Kepler undertook to draw a curve
<span class='pageno' id='Page_9'>9</span>through the places of Mars;<a id='r28' /><a href='#f28' class='c011'><sup>[28]</sup></a> and his greatest service to
science was in impressing on men’s minds that this was the
thing to be done if they wished to improve astronomy;
that they were not to content themselves with inquiring
whether one system of epicycles was better than another
but that they were to sit down by the figures and find out
what the curve, in truth, was. He accomplished this by his
incomparable energy and courage, blundering along in the
most inconceivable way (to us), from one irrational hypothesis
to another, until, after trying twenty-two of these,
he fell, by the mere exhaustion of his invention, upon the
orbit which a mind well furnished with the weapons of
modern logic would have tried almost at the outset.<a id='r29' /><a href='#f29' class='c011'><sup>[29]</sup></a></p>
<p class='c005'>In the same way, every work of science great enough to
be remembered for a few generations affords some
exemplification of the defective state of the art of reasoning
of the time when it was written; and each chief step in
science has been a lesson in logic. It was so when Lavoisier
and his contemporaries took up the study of Chemistry.
The old chemist’s maxim had been, “Lege, lege, lege,
labora, ora, et relege.” Lavoisier’s method was not to read
and pray, not to dream that some long and complicated
chemical process would have a certain effect, to put it into
practice with dull patience, after its inevitable failure to
dream that with some modification it would have another
result, and to end by publishing the last dream as a fact:
his way was to carry his mind into his laboratory, and to
make of his alembics and cucurbits instruments of thought,
<span class='pageno' id='Page_10'>10</span>giving a new conception of reasoning as something which
was to be done with one’s eyes open, by manipulating real
things instead of words and fancies.</p>
<p class='c005'>The Darwinian controversy is, in large part, a question
of logic. Mr. Darwin proposed to apply the statistical
method to biology. The same thing has been done in a
widely different branch of science, the theory of gases.
Though unable to say what the movement of any particular
molecule of gas would be on a certain hypothesis regarding
the constitution of this class of bodies, Clausius and Maxwell
were yet able, by the application of the doctrine of
probabilities, to predict that in the long run such and such
a proportion of the molecules would, under given circumstances,
acquire such and such velocities; that there would
take place, every second, such and such a number of collisions,
etc.; and from these propositions they were able to
deduce certain properties of gases, especially in regard to
their heat-relations. In like manner, Darwin, while unable
to say what the operation of variation and natural selection
in every individual case will be, demonstrates that in the
long run they will adapt animals to their circumstances.
Whether or not existing animal forms are due to such action,
or what position the theory ought to take, forms the
subject of a discussion in which questions of fact and
questions of logic are curiously interlaced.</p>
<h4 class='c012'>II</h4>
<p class='c006'>The object of reasoning is to find out, from the consideration
of what we already know, something else which we do
<span class='pageno' id='Page_11'>11</span>not know. Consequently, reasoning is good if it be such
as to give a true conclusion from true premises, and not
otherwise. Thus, the question of validity is purely one of
fact and not of thinking. A being the premises and B being
the conclusion, the question is, whether these facts are
really so related that if A is B is. If so, the inference is
valid; if not, not. It is not in the least the question
whether, when the premises are accepted by the mind, we
feel an impulse to accept the conclusion also. It is true
that we do generally reason correctly by nature. But that
is an accident; the true conclusion would remain true if we
had no impulse to accept it; and the false one would remain
false, though we could not resist the tendency to believe
in it.</p>
<p class='c005'>We are, doubtless, in the main logical animals, but we
are not perfectly so. Most of us, for example, are naturally
more sanguine and hopeful than logic would justify.
We seem to be so constituted that in the absence of any
facts to go upon we are happy and self-satisfied; so that the
effect of experience is continually to counteract our hopes
and aspirations. Yet a lifetime of the application of this
corrective does not usually eradicate our sanguine disposition.
Where hope is unchecked by any experience, it is
likely that our optimism is extravagant. Logicality in regard
to practical matters is the most useful quality an animal
can possess, and might, therefore, result from the
action of natural selection; but outside of these it is probably
of more advantage to the animal to have his mind
filled with pleasing and encouraging visions, independently
of their truth; and thus, upon unpractical subjects, natural
<span class='pageno' id='Page_12'>12</span>selection might occasion a fallacious tendency of thought.</p>
<p class='c005'>That which determines us, from given premises, to draw
one inference rather than another, is some habit of mind,
whether it be constitutional or acquired. The habit is good
or otherwise, according as it produces true conclusions from
true premises or not; and an inference is regarded as valid
or not, without reference to the truth or falsity of its conclusion
specially, but according as the habit which determines
it is such as to produce true conclusions in general
or not. The particular habit of mind which governs this
or that inference may be formulated in a proposition whose
truth depends on the validity of the inferences which the
habit determines; and such a formula is called a <i>guiding
principle</i> of inference. Suppose, for example, that we observe
that a rotating disk of copper quickly comes to rest
when placed between the poles of a magnet, and we infer
that this will happen with every disk of copper. The guiding
principle is, that what is true of one piece of copper is
true of another. Such a guiding principle with regard to
copper would be much safer than with regard to many other
substances—brass, for example.</p>
<p class='c005'>A book might be written to signalize all the most important
of these guiding principles of reasoning. It would
probably be, we must confess, of no service to a person
whose thought is directed wholly to practical subjects, and
whose activity moves along thoroughly beaten paths. The
problems which present themselves to such a mind are
matters of routine which he has learned once for all to
handle in learning his business. But let a man venture into
an unfamiliar field, or where his results are not continually
<span class='pageno' id='Page_13'>13</span>checked by experience, and all history shows that the most
masculine intellect will ofttimes lose his orientation and
waste his efforts in directions which bring him no nearer to
his goal, or even carry him entirely astray. He is like a
ship on the open sea, with no one on board who understands
the rules of navigation. And in such a case some general
study of the guiding principles of reasoning would be sure
to be found useful.</p>
<p class='c005'>The subject could hardly be treated, however, without
being first limited; since almost any fact may serve as a
guiding principle. But it so happens that there exists a
division among facts, such that in one class are all those
which are absolutely essential as guiding principles, while
in the other are all those which have any other interest as
objects of research. This division is between those which
are necessarily taken for granted in asking whether a certain
conclusion follows from certain premises, and those
which are not implied in that question. A moment’s thought
will show that a variety of facts are already assumed when
the logical question is first asked. It is implied, for instance,
that there are such states of mind as doubt and
belief—that a passage from one to the other is possible,
the object of thought remaining the same, and that this
transition is subject to some rules which all minds are alike
bound by. As these are facts which we must already know
before we can have any clear conception of reasoning at all,
it cannot be supposed to be any longer of much interest to
inquire into their truth or falsity. On the other hand, it
is easy to believe that those rules of reasoning which are
deduced from the very idea of the process are the ones
<span class='pageno' id='Page_14'>14</span>which are the most essential; and, indeed, that so long as it
conforms to these it will, at least, not lead to false conclusions
from true premises. In point of fact, the importance
of what may be deduced from the assumptions involved
in the logical question turns out to be greater than might
be supposed, and this for reasons which it is difficult to exhibit
at the outset. The only one which I shall here mention
is, that conceptions which are really products of logical
reflections, without being readily seen to be so, mingle with
our ordinary thoughts, and are frequently the causes of
great confusion. This is the case, for example, with the
conception of quality. A quality as such is never an object
of observation. We can see that a thing is blue or green,
but the quality of being blue and the quality of being green
are not things which we see; they are products of logical
reflections. The truth is, that common-sense, or thought
as it first emerges above the level of the narrowly practical,
is deeply imbued with that bad logical quality to which the
epithet <i>metaphysical</i> is commonly applied; and nothing can
clear it up but a severe course of logic.</p>
<h4 class='c012'>III</h4>
<p class='c006'>We generally know when we wish to ask a question and
when we wish to pronounce a judgment, for there is a dissimilarity
between the sensation of doubting and that of
believing.</p>
<p class='c005'>But this is not all which distinguishes doubt from belief.
There is a practical difference. Our beliefs guide our desires
and shape our actions. The Assassins, or followers
<span class='pageno' id='Page_15'>15</span>of the Old Man of the Mountain, used to rush into death at
his least command, because they believed that obedience
to him would insure everlasting felicity. Had they doubted
this, they would not have acted as they did. So it is with
every belief, according to its degree. The feeling of believing
is a more or less sure indication of there being established
in our nature some habit which will determine our
actions. Doubt never has such an effect.</p>
<p class='c005'>Nor must we overlook a third point of difference. Doubt
is an uneasy and dissatisfied state from which we struggle
to free ourselves and pass into the state of belief; while the
latter is a calm and satisfactory state which we do not wish
to avoid, or to change to a belief in anything else.<a id='r30' /><a href='#f30' class='c011'><sup>[30]</sup></a> On
the contrary, we cling tenaciously, not merely to believing,
but to believing just what we do believe.</p>
<p class='c005'>Thus, both doubt and belief have positive effects upon us,
though very different ones. Belief does not make us act at
once, but puts us into such a condition that we shall behave
in a certain way, when the occasion arises. Doubt has not
the least effect of this sort, but stimulates us to action until
it is destroyed. This reminds us of the irritation of a nerve
and the reflex action produced thereby; while for the analogue
of belief, in the nervous system, we must look to what
are called nervous associations—for example, to that habit
of the nerves in consequence of which the smell of a peach
will make the mouth water.</p>
<div>
<span class='pageno' id='Page_16'>16</span>
<h4 class='c012'>IV</h4>
</div>
<p class='c006'>The irritation of doubt causes a struggle to attain a state
of belief. I shall term this struggle <i>inquiry</i>, though it must
be admitted that this is sometimes not a very apt
designation.</p>
<p class='c005'>The irritation of doubt is the only immediate motive for
the struggle to attain belief. It is certainly best for us
that our beliefs should be such as may truly guide our
actions so as to satisfy our desires; and this reflection will
make us reject any belief which does not seem to have been
so formed as to insure this result. But it will only do so
by creating a doubt in the place of that belief. With the
doubt, therefore, the struggle begins, and with the cessation
of doubt it ends. Hence, the sole object of inquiry is the
settlement of opinion. We may fancy that this is not
enough for us, and that we seek not merely an opinion,
but a true opinion. But put this fancy to the test, and it
proves groundless; for as soon as a firm belief is reached
we are entirely satisfied, whether the belief be false or true.
And it is clear that nothing out of the sphere of our knowledge
can be our object, for nothing which does not affect
the mind can be a motive for a mental effort. The most
that can be maintained is, that we seek for a belief that we
shall <i>think</i> to be true. But we think each one of our beliefs
to be true, and, indeed, it is mere tautology to say so.</p>
<p class='c005'>That the settlement of opinion is the sole end of inquiry
is a very important proposition. It sweeps away, at once,
various vague and erroneous conceptions of proof. A few
of these may be noticed here.</p>
<p class='c005'><span class='pageno' id='Page_17'>17</span>1. Some philosophers have imagined that to start an inquiry
it was only necessary to utter or question or set it
down on paper, and have even recommended us to begin
our studies with questioning everything! But the mere
putting of a proposition into the interrogative form does
not stimulate the mind to any struggle after belief. There
must be a real and living doubt, and without all this discussion
is idle.</p>
<p class='c005'>2. It is a very common idea that a demonstration must
rest on some ultimate and absolutely indubitable propositions.
These, according to one school, are first principles
of a general nature; according to another, are first sensations.
But, in point of fact, an inquiry, to have that completely
satisfactory result called demonstration, has only
to start with propositions perfectly free from all actual
doubt. If the premises are not in fact doubted at all, they
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>
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