absolute chance refuted by experiential evidence, mixed with as clear
_assertions_ of the same things, when taken together, have the appearance
of an attempt, as the politicians say, to “straddle” the question.
§13. But the ingenious Doctor seeks to bolster up necessity by
introducing the confused notion of “causation.”
I do not know where the idea originated that a cause is an instantaneous
state of things, perfectly determinative of every subsequent state. It
seems to be at the bottom of Kant’s discourse on the subject; yet it
accords neither with the original conception of a cause, nor with the
principles of mechanics. The original idea of an efficient cause is
that of an agent, more or less like a man. It is prior to the effect,
in the sense of having come into being before the latter; but it is not
transformed into the effect. In this sense, it may happen that an event
is a cause of a subsequent event; seldom, however, is it the principal
cause. Far less are events the only causes. The modern mechanical
conception, on the other hand, is that the relative positions of
particles determine their accelerations at the instants when they occupy
those positions. In other words, if the positions of all the particles
are given at _two_ instants (together with the law of force), then
the positions at all other instants may be deduced.[109] This doctrine
conflicts with Kant’s second analogy of experience, as interpreted by
him, in no less than four essential particulars. In the first place, far
from involving any principle that could properly be termed generation, or
_Erzeugung_, which is Kant’s word for the sequence of effect from cause,
the modern mechanical doctrine is a doctrine of persistence, and, as I
have repeatedly explained, positively prohibits any real growth. In the
second place, one state of things (i. e. one configuration of the system)
is not sufficient to determine a second, it is two that determine a
third. To whomsoever may think that this is an inconsiderable divergence
of opinions, let me say, study the logic of relatives, and you will think
so no longer. In the third place, the two determining configurations,
according to mechanics, may be taken at almost any two instants, and the
determined configuration be taken at any third instant we like. _There is
no mechanical truth in saying that the past determines the future, rather
than the future the past._ We habitually follow tradition in continuing
to use that form of expression, but every mathematician knows that it is
nothing but a form of expression. We continue, for convenience, to talk
of mechanical phenomena as if they were regulated, in the same manner
in which our intentions regulate our actions (which is essentially a
determination of the future by the past), although we are quite aware
that it is not really so. Remark how Kant reasons:
“If it is a necessary law of our sensibility, and consequently
a _formal condition_ of all perceptions, that the preceding
time determines the following, (since I can only come to
the following through the preceding,) then is it also an
indispensable _law of the empirical representation_ of the
time-series that the appearances of the preceding time
determine every occurrence in the following.”
What this leads to is a causality like that of mental phenomena, where it
_is_ the past which determines the future, and _not_ (in the same sense)
the reverse; but the doctrine of the conservation of energy consists
precisely in the denial that anything like this occurs in the domain of
physics. Had Kant studied the psychological phenomena more attentively
and generalised them more broadly, he would have seen that in the mind
causation is not absolute, but follows such a curve as is traced in my
essay towards “The Law of Mind” (_The Monist_, Vol. II, 550). Does our
judicious editor deem it ungracious to find fault with Kant for not doing
so much more than he did, considering what that hero-like achievement
was? We must seem to carp, as long as thinkers can hold that achievement
for sufficient. In the fourth place, Kant’s “Analogy” ignores that
continuity which is the life-blood of mathematical thought. He deals
with those awkward chunks of phenomenon, called “events.” He represents
one such “event” as determined by certain others, definitely, while
the rest have nothing to do with it. It is impossible to cement such
thought as this into hermetic continuity with the refined conceptions of
modern dynamics. The statement that every instantaneous state of things
determines precisely all subsequent states, and not at all any previous
states, could, I rather think, be shown to involve a contradiction.
The notion which Dr. Carus holds of a cause seems to be that it is a
state, embracing all the positions and velocities of all the masses at
one instant, the effect being a similar state for any subsequent instant.
(¶¶ 21, 24.) This breaks at once with common parlance, with dynamics,
and with philosophical logic. In common parlance, we do not say that
the position and upward velocity of a missile is the cause of its being
at a subsequent instant lower down and moving with a greater downward
velocity.[110] In dynamics, it is the fixed force, gravitation, or
whatever else, together with those relative positions of the bodies that
determine the intensity and direction of the forces, that is regarded
as the cause. But these causes are not previous to, but simultaneous
with, their effects, which are the instantaneous accelerations. Finally,
logic opposes our calling one of two states which equally determine one
another (as any two states of a system do, if the velocities are taken to
be included in these states) _the_ determinator, or cause, simply because
of the circumstance that it precedes the other in time,—a circumstance
that is upon the principles of dynamics plainly insignificant and
irrelevant.
Everybody will make slips in the use of words that have been on his lips
from before the time when he learned to think; but the practice which
I endeavor to follow in regard to the word _cause_, is to use it in
the Aristotelian sense of an _efficient cause_, in all its crudeness.
In short, I refuse to use it at all as a philosophical word. When my
conception is of a dynamical character, I endeavor to employ the accepted
terminology of dynamics;[111] and when my idea is a more general and
logical one, I prefer to speak of the _explanation_.
§ 14. Dr. Carus thinks the element of necessity in causation can be
demonstrated by considering the process as a transformation. “It is a
sequence of two states which belong together as an initial and final
aspect of one and the same event.” (¶ 21. Compare ¶¶ 20, 24.) He neglects
to explain how he brings under this formula the inward causation of the
will and character, as set forth by him in ¶¶ 163-167.
It is unnecessary for me to reply, at length, to an argument so
manifestly inconclusive. On the one hand, it conflicts with the principle
that absolute necessity cannot be proved from experience; and on the
other hand, it leaves room for an imperfect necessity.
Professor Tait has done an ill office to thought in countenancing the
idea that the conservation of energy is of the same nature as the
“conservation,” or rather perduration, of matter. Dr. Carus says (¶ 121)
that
“The law of the conservation of matter and energy rests upon
the experience (corroborated by experiments) that causation
is transformation. It states that the total amount of matter
and the total amount of energy remain constant. There is no
creation out of nothing and no conversion of something into
nothing.”
The historical part of this statement contains only a small grain of
truth; but that I will not stop to criticise. The point I wish to make
is that the law of the conservation of energy is here represented under
a false aspect. The true substance of the law is that the accelerations,
or rates of change, of the motions of the particles at any instant depend
solely on their relative positions at those instants. The equation which
expresses the law under this form is a differential equation of the
second order; that is, it involves the rates of change of the rates of
change of positions, together with the positions themselves. Now, because
of the purely analytic proposition of the differential calculus that
Dₜ²s = ½Dₛ(Dₜs)²,
the first integral of the differential equation of the second order, that
is, the differential equation of the first order which expresses the same
state of things, equates half the sum of the masses, each multiplied by
the square of its velocity, to a function of the relative positions of
the particles _plus_ an arbitrary constant.[112] In order to fix our
ideas, let us take a very simple example, that of a single particle
accelerated towards an infinite plane, at a rate proportional to the
_n_ᵗʰ power of its distance from the plane. In this case, if _s_ be the
distance, the second differential equation will be
Dₜ²s = -asⁿ,
and the first integral of it will be
(Dₜs)² = -(²ᵃ⁄ₙ₊₁)sⁿ⁺¹ + C.
By the first law of motion, and the Pythagorean proposition, the part
of the velocity-square depending on the horizontal component is also
constant.
The arbitrary constant, _C_, plainly has its genesis in the fact that
forces do not determine velocities, but only accelerations. Its value
will be fixed as soon as the velocity at any instant is known. This
quantity would exist, just the same, and be independent of the time, and
would therefore be “conserved” whether the forces were “conservative,”
that is, simply positional, or not. Now, this constant is the energy;
or rather, the energy is composed of this constant increased by another
which is absolutely indeterminable, being merely supposed large enough to
make the sum positive.
Thus, the law of energy does not prescribe that the total amount of
energy shall remain constant; for this would be so in any case by virtue
of the second law of motion; but what it prescribes is that the total
energy diminished by the living force shall give a remainder which
depends upon the relative positions of the particles and not upon the
time or the velocities. It is also to be noticed that the energy has
no particular magnitude, or quantity. Furthermore, in transformations
of kinetical energy into positional energy, and the reverse, the
different portions of energy do not retain their identity, any more
than, in book-keeping, the identity of the amounts of different items
is preserved. In short, the conservation of energy, (I do not mean the
_law_ of conservation,) is a mere result of algebra. Very different is
it with the “conservation” of matter. For, in the first place, the total
mass is a perfectly definite quantity; and, in the second place, in all
its transformations, not only is the _total_ amount constant, but all the
different parts preserve their identity. To speak, therefore, of “the
conservation of matter and energy,” is to assimilate facts of essentially
contrary natures; and to say that the law of the conservation of energy
makes the total amount of energy constant is to attribute to this law
a phenomenon really due to another law, and to overlook what this law
really does determine, namely, _that the total energy less the kinetic
energy gives a remainder which is exclusively positional_.
§ 15. Dr. Carus does not make it clear what he means by _chance_. He
does, indeed, say (¶¶ 145, 146):
“What is chance?
“Chance is any event not especially intended, either not
calculated, or, with a given and limited stock of knowledge,
incalculable.”
This defines what he means by a chance event, in the concrete; what he
understands by probability, we are left to conjecture. But from what he
says in ¶ 147, I infer that he regards it as dependent upon the state of
our ignorance, and therefore nothing real.
I am, therefore, much puzzled when I find him expressing a conviction
(¶¶ 88, 156) that chance plays an important part in the real world. He
explains very distinctly that “when we call a throw of the dice pure
chance, we mean that the incidents which condition the turning up of
these or those special faces of the dice have not been, or cannot be,
calculated.” (¶ 147.) This is the commonest, because the shallowest,
philosophy of chance. Even Venn might teach him better than that.
However, according to that view, when he writes of “the important part
that chance plays in the world,—not absolute chance ... but that same
chance of which the throw of the die is a typical instance” (¶ 88), he
can be understood to mean no more than that many things happen which we
are not in condition to calculate or predict. This is not playing a part
_in the world_, one would say—at least, not in the natural world; it is
only playing a part in our ignorance.
Dr. Carus frequently uses phrases which make us suspect he penetrates
deeper. Thus, he says, “we do not believe in absolute chance, but we
believe in chance” (¶ 144); and again, “Every man is the architect of
his own fortune—but not entirely. There are sometimes coincidences
determining the fates of men.” (¶ 161.) But when we remark the
consecution of ¶¶ 137-162, we feel pretty sure he really sees no
further. To do so would have been to perceive that indefinitely varied
specificalness _is_ chance.
For a long time, I myself strove to make chance that diversity in the
universe which laws leave room for, instead of a violation of law, or
lawlessness. That was truly believing in chance that was not absolute
chance. It was recognising that chance does play a part in the real
world, apart from what we may know or be ignorant of. But it was a
transitional belief which I have passed through, while Dr. Carus seems
not to have reached it.
As for absolute chance, Dr. Carus makes the momentous admission that
it is “not unimaginable” (¶ 150). If so, its negation, or absolute
necessity, cannot be a formal principle.
§ 16. But it is time for me to leave the consideration of Dr. Carus’s
system and to take up his strictures upon mine. His philosophy is one
eminently enlightened by modern ideas, which it synthetises to an
unusual extent. It is distinguished for its freedom from the vice of
one-sidedness, and displays every facet of the gem of philosophical
inquiry, except the one on which it rests, the question of absolute
law. Its prominent faults, which I feel sure must have struck every
competent reader, are that it shows little trace of meditation upon the
thoughts of the great idealists, and that there is a certain want of
congruity between different elements of it. How strangely it sounds,
for instance, to find an apriorian, and one who is dinging “formal
laws” so perpetually into our ears, one who holds that “in order to
weave the woof of the _a posteriori_ elements into coherent cloth, we
want the warp of the _a priori_” (¶ 15), to find this man declaring for
a positivism “which accepts no doctrine, theory, or law, unless it be
a formulation of facts,” and proclaiming that “the whole business of
science is to systematise the samenesses of experience, and to present
them in convenient formulas” (¶ 120). Now there is just one way of
bringing such warring elements into harmony, and curing the greatest
defect of the system,—and it is a way which would also bring the whole
into far better concordance with natural science. It is to lop off the
heads of all absolute propositions Whose subject is not the Absolute,
and reduce them to the level of probable and approximate statements.
Were that defalcation performed, Dr. Carus’s philosophy would, in its
general features, offer no violent opposition to my opinions. Moreover,
the Doctor has at heart the conciliation of religion and science. I
confess such serious concern makes me smile; for I think the atonement
he desires is a thing which will come to pass of itself when time is
ripe, and that our efforts to hasten it have just that slight effect
that our efforts to hasten the ripening of apples on a tree may have.
Besides, natural ripening is the best. Let science and religion each have
stout faith in itself, and refuse to compromise with alien and secondary
purposes, but push the development of its own thought on its own line;
and then, when reconcilement comes,—as come it surely will,—it will have
a positive value, and be an unmixed good. But since our accomplished
editor thinks himself called upon to assist in this birth of time, let
me ask him whether of all the conditions of such peace, the first is not
that religious thought should abandon that extravagant absoluteness of
assertion which is proper to the state of intellectual infancy, but which
it has so long been too timid to let go? This pragmatical and unneeded
absoluteness it is which is most deeply contrary to the method, the
results, and the whole spirit of science; and no error can be greater
than to fancy that science, or scientific men, rest upon it or readily
tolerate it.
§ 17. Dr. Carus (¶¶ 56-64) condemns my method of investigation as
contrary to that by which science has been advanced; and holds that a
radically different, and thoroughly positivistic method is requisite,—a
method so intensely positivistic as to exclude all originality. I suppose
he will not object to my forming an opinion concerning the methods of
science. I was brought up in an atmosphere of scientific inquiry, and
have all my life chiefly lived among scientific men. For the last thirty
years, the study which has constantly been before my mind has been upon
the nature, strength, and history of methods of scientific thought. I
have no space here to argue the question. In its logical aspect, I have
partly considered it in various publications; and in its historical
aspect, I have long been engaged upon a treatise about it. My critic says
(¶ 57) that 1 am “very positivistic in my logic of science.” This is a
singular misapprehension. Few of the great scientific minds with whom
I have come into personal contact, and from whom I endeavored to learn
were disposed to contemn originality or the ideal part of the mind’s work
in investigation; and those few, it was easy to see, really breathed an
atmosphere of ideas which were so incessantly present that they were
unconscious of them. Were I to name those of my teachers who were most
positivistic in theory, a smile would be excited. My own historical
studies, which have been somewhat minutely critical, have, on the whole
confirmed the views of Whewell, the only man of philosophical power
conjoined with scientific training who had made a comprehensive survey
of the whole course of science, that progress in science depends upon
the observation of the right facts by minds _furnished with appropriate
ideas_. Finally, my long investigation of the logical process, of
scientific reasoning led me many years ago to the conclusion that science
is nothing but a development of our natural instincts. So much for my
_theory_ of scientific logic. It is as totally opposed as anything can
be to Dr. Carus’s theory (¶ 69, note; and “Ursache, Grund und Zweck,” p.
2) that originality is out of place in science.
But in my _practice_ of scientific reasoning, Dr. Carus accuses me of
being what he calls a “constructionist”; that is, a theoriser unguided by
indications from observation or accepted facts. To a mind upon whom that
celebrated and splendid chapter of Kant upon the architectonical method
failed to make a deep impression, I may appear so; but _travesty_ is in
truth hardly too strong a word to describe the account of my method by
Dr. Carus.
Perhaps exaggeration is not without its value. If so, let me sum up the
method Dr. Carus recommends. Eschew originality, is its pious formula;
do not think for yourself, nor countenance results obtained by original
minds. Distrust them; they are not safe men. Leave originality to
mathematicians and their breed, to poets, and to all those who seek the
sad notoriety of having unsettled belief.[113] Flee all philosophies
which smack of this aberrant nineteenth century.[114] This theory of Dr.
Carus condemns itself; for it is highly original, and soars into the free
ether untrammelled by historic facts.
Keppler comes very close to realising my ideal of the scientific method;
and he is one of the few thinkers who have taken their readers fully into
their confidence as to what their method really has been.[115] I should
not feel justified in inflicting upon mine an autobiographical account
of my own course of thought; but some things Dr. Carus’s accusation
forces me to mention. My method of attacking all problems has ever been
to begin with an historical and rational inquiry into the special method
adapted to the special problem. This is the essence of my architectonical
proceeding upon which Dr. Carus has commented very severely. To look an
inch before one’s nose involves originality: therefore, it is wrong to
have a conscious method. But further, in regard to philosophy, not only
the methods, but the elementary ideas which are to enter into those
methods, should be subjected to careful preliminary examination. This,
especially, Dr. Carus finds very unscientific. (¶ 64, and elsewhere.)
It is, undoubtedly, the most characteristic feature of my procedure.
Certainly it was not a notion hastily or irreflectively caught up; but
is the maturest fruit of a lifetime of reflection upon the methods of
science, including those of philosophy; and if it shall be found that one
contribution to thought on my part has proved of permanent service, that,
I expect, will be the one. This method in no wise teaches that the method
and materials for thought are not to be modified in the course of the
study of the subject-matter. But instead of taking ideas at haphazard, or
being satisfied with those that have been handed down from the good old
times, as a mind keenly alive to the dangers of originality would have
done, I have undertaken to make a systematic survey of human knowledge
(a very slight sketch of which composed the substance of my paper on
the “Architecture of Theories,”) in order to find what ideas have, as a
fact, proved most fruitful, and to observe the special utilities they
have severally fulfilled. A subsidiary object of this survey was to note
what the great obstacles are to-day in the way of the further advance of
the different branches of science. In my “Architecture of Theories,” I
never professed to do more than make a slight sketch of a small portion
of my preliminary studies, devoting thirteen lines to some hints as to
the nature of the results. In the four following papers I have given
a selection of a few of these results. Among those which remain to be
reported are some of much more immediate importance than any of those
hitherto set forth. If anybody has been surprised to find my subsequent
papers developing thoughts which they were unable to foresee from my
first, it is only what I warned people from the outset that they would
find to happen. Nor have the greatest of these surprises yet been
reached.[116]
The next series of facts reviewed was that of the history of philosophy.
I waded right into this fearful slough of “originality,” in order to
gather what seemed to throw a light upon the subject. Finally, I reviewed
the general facts of the universe.