Chapter XXVIII: Part IX: , p. 475, 1890), Dr. Johnstone Stoney, F. R. S., published an (18)

Concerning points like this, Dr. Carus, in company with the general body of thinkers, is laboring under a great disadvantage from not understanding the logic of relatives. It is a subject I have been studying for a great many years, and I feel and know that I have an important report that I ought to make upon it. This branch of logic is, however, so abstruse, that I have never been able to find the leisure to translate my conclusions into a form in which their significance would be manifest even to a powerful thinker whose thoughts had not long been turned in that direction. I shall succeed in doing so, whenever I can find myself in a situation where I need think of nothing else for months, and not before. That may not be for thirty years; but I believe it is the intention of providence that it should be. Meantime, I will testify, and the reader can take my testimony for what he thinks it is worth, that all deductive reasoning, except that kind which is so childishly simple that acute minds have doubted whether there was any reasoning there,—I mean non-relative syllogism,—requires an act of choice; because from a given premise, several conclusions,—in some cases an infinite number,—can be drawn. Hence, Dr. Carus is altogether too hasty in his confidence (¶¶ 195, 196) that general thinking machines “are not impossibilities.” An act of original and arbitrary determination would be required; and it seems almost evident that no machine could perform such an act except within narrow limits, thought out beforehand and embodied in its construction. Moreover, positive observation is called for in all inference, even the simplest,—though in deduction it is only observation of an object of imagination. Moreover, a peculiar act which may properly be called _abstraction_[107] is usually required, consisting in seizing evanescent elements of thought and holding them before the mind as “substantive” objects, to borrow a phrase from William James. At the same time, the process I am describing, that is, relative deduction, is perfectly general and demonstrative, and depends upon the truth of the assumed premises, and not, like inductive reasoning, upon the manner in which those premises present themselves.

But the application of the logic of relatives shows that the propositions of arithmetic, which Dr. Carus usually adduces as examples of formal law (¶ 15), are, in fact, only corollaries from definitions. They are certain only as applied to ideal constructions, and in such application, they are merely analytical.

The truth is our ideas about the distinction between analytical and synthetical judgments is much modified by the logic of relatives, and by the logic of probable inference. An analytical proposition is a definition or a proposition _deducible_ from definitions; a synthetical proposition is a proposition not analytical. Deduction, or analytical reasoning, is, as I have shown in my “Theory of Probable Reasoning,” a reasoning in which the conclusion follows (necessarily, or probably) from the state of things expressed in the premises, in contradistinction to scientific, or synthetical, reasoning, which is a reasoning in which the conclusion follows probably and approximately from the premises, owing to the conditions under which the latter have been observed, or otherwise ascertained. The two classes of reasoning present, besides, some other contrasts that need not be insisted upon in this place. They also present some significant resemblances. Deduction is really a matter of perception and of experimentation, just as induction and hypothetic inference are; only, the perception and experimentation are concerned with imaginary objects instead of with real ones. The operations of perception and of experimentation are subject to error, and therefore it is only in a Pickwickian sense that mathematical reasoning can be said to be perfectly certain. It is so, only under the condition that no error creeps into it: yet, after all, it is susceptible of attaining a practical certainty. So, for that matter, is scientific reasoning; but not so readily. Again, mathematics brings to light results as truly occult[108] and unexpected as those of chemistry; only they are results dependent upon the action of reason in the depths of our own consciousness, instead of being dependent, like those of chemistry, upon the action of Cosmical Reason, or Law. Or, stating the matter under another aspect, analytical reasoning depends upon associations of similarity, synthetical reasoning upon associations of contiguity. The logic of relatives, which justifies these assertions, shows accordingly that deductive reasoning is really quite different from what it was supposed by Kant to be; and this explains how it is that he and others have taken various mathematical propositions to be synthetical which in their ideal sense, as propositions of pure mathematics, are in truth only analytical.

Descending from things I can demonstrate to things of which various facts, in the light of those demonstrations, fully persuade me, I will say that in my opinion there are many synthetical propositions which, if not _a priori_ in Dr. Carus’s sense, are, at least, innate (notwithstanding his frequent denials of this, as in ¶ 15) though he is quite right in saying that their abstract and distinct formulation comes very late (¶ 126). But turn the facts as I will, I cannot see that they afford the slightest reason for thinking that such propositions are ever absolutely universal, exact, or necessary in their truth. On the contrary, the principles of probable inference show this to be impossible.

Dr. Carus adduces the instance of a geometrical proposition, namely, “that two congruent regular tetrahedrons, when put together, will form a hexahedron.” (¶ 25.) This, he says, seems to be “a very wonderful thing”; for why should not a larger tetrahedron be formed, just as two heaps of flour make a large heap of flour? Yet, he continues, the probability that the two tetrahedrons do always make a hexahedron is 1, “which means certainty” (¶ 27). But as it happens, the proposition, in the form stated is quite erroneous. What is true is this. If two tetrahedra are so placed that one face of each is coincident with one face of the other, while all the other faces are inclined to one another, and if of the 8 faces, the 2 that are coincident are not counted, there remain to be counted 8-2=6 faces. But there is nothing more wonderful about this than that 8-2=6, which is an easy corollary from definitions. Very few propositions in mathematics that appear “marvellous” will hold water; and those few excite our astonishment only because the real complexity of the conditions are masked in an intuitional presentation of them.

Dr. Carus holds (¶ 15) that formal knowledge is absolutely universal, exact, and necessary. In some cases, as where he says that, given the number of dimensions of space, the entire geometry could be deduced (¶ 35), the boasted infallibility will prove on examination to be downright error. In all other cases, the propositions only relate to ideal constructions, and their applicability to the real world is at the best doubtful, and, as I think, false; while in their ideal purity, they are not synthetical.

Thus, my good friend and antagonist holds that the combination of oxygen and hydrogen to produce water is not “different in principle” from that of the tetrahedra to produce a hexahedron (¶ 26). There is all the difference between the ideal and the real; which to my Scotistic mind is very important. But this is not the only passage in which he speaks as if form were the principle of individuation.

§ 9. Dr. Carus’s position is even weaker than that of Kant, who makes space, for example, a necessary form of thought (in a broad sense of that term). But Dr. Carus appears to consider space as an absolute reality. For he says (¶ 119) that “every single point of space has its special and individual qualities.” Here again form is made the principle of individuation; whence the queer phrase, “individual qualities.”

§ 10. Dr. Carus argues that whatever is unequivocally determinate is necessary. (¶ 124.) Were the determination spoken of real dynamic determination, this would be a mere truism. But the expression used, _eindeutig bestimmt_, merely expresses a mathematical determination, and therefore no real necessity ensues. The equation

(Transcriber’s Note: Italics have been removed from the
formulæ for readability.)

x² - 23x + 132¼ = 0

determines _x_ to be either 11·477 or 11·523. In this sense, _x_ has necessarily one value or the other. The equation

x² - 12x + 6 = 0

determines _x_ to be either 11·477 or 0·523. Together, the two equations uniquely determine _x_ to be 11·477. This shows how much that argument amounts to.

§ 11. By “sameness,” Dr. Carus means equivalence for a given purpose. (¶¶ 102, 106.) By the “idea of sameness,” he means (¶¶ 77, 96) the principle that things having a common character are for some purpose equivalent. This, he says, “has a solid basis in the facts of experience.” By a “world of sameness” (¶ 113), he seems to mean one in which any two given concrete things are in some respect equivalent. He argues (¶ 122) that a “world of sameness is a world in which necessity rules.” I do not see this. It seems to me so bald a _non sequitur_, that I cannot but suppose the thought escapes my apprehension. If there were anything in the argument, it would seem to be a marvellously expeditious way of settling the whole dispute; and therefore it would have been worth the trouble of stating, so as to bring it within the purview of minds like mine.

§ 12. My candid opponent sometimes endorses emphatically the Leibnizian principle. “Necessitarianism must be founded on something other than observation. Observation is _a posteriori_; it has reference to single facts, to particulars; yet the doctrine of necessity ... is of universal application. The doctrine of necessity ... is of an _a priori_ nature.” (¶ 11.) “Millions of single experiences ... cannot establish a solid belief in necessity.” (¶ 14.) “No amount of experience is sufficient to constitute causation by a mere synthesis of sequences.” (¶ 22.) “Millions of millions of cases” constitute “no proof” that a proposition “is always so.” (¶ 29.)

Nevertheless, he holds that the law of “the conservation of matter and energy” so conclusively proves necessary causation, that the obstinacy of Hume, himself, could not have withstood the argument. (¶ 23.) One wonders, then, what is supposed to prove this “law of the conservation of matter and energy,” if no amount of experience can prove it.

But the _a priori_ itself can “be based on the firm ground of experience.” (¶ 14.) In that case, it is not prior to experience, after all! “The idea of necessity is based upon the conception of sameness, and ... the existence of sameness is a fact of experience.” (¶ 87.) If absolute necessity can be irrefragably demonstrated from the fact that two things are alike, it is a pity Dr. Carus should not state this demonstration in a form, that I, and men like me, can understand. That would be more to the purpose than merely saying it can be proved. Absolute chance is rejected as “involving a violation of laws well established by _positive evidence_.” (¶ 149.)

All these _denials_ that absolute necessity can be established and 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.

I now found myself forced by a great many different indications to the conclusion that an evolutionary philosophy of some kind must be accepted,—including among such philosophies systems like those of Aristotle and of Hegel. From this point the reasoning was more rapid. Evolution had been a prominent study for half a generation; and much light had been thrown upon the conditions for a fruitful evolutionary philosophy. The first question was, how far shall this evolution go back? What shall we suppose _not_ to be a product of growth? I fancy it is this cautious reflectiveness of my procedure which especially displeases Dr. Carus. It is not positivistic: it is architectonic. But the answer to the question was not far to seek. If an evolutionary explanation is to be adopted, philosophy, logic, and the economy of research all dictate that in the first essay, at least, that style of explanation be carried as far back as explanation is called for. What elements of the universe require no explanation? This was a simple question, capable of being decided by logic with as much facility and certainty as a suitable problem is solved by differential calculus. Being, and the uniformity in which being consists, require to be explained. The only thing that does not require it is non-existent spontaneity. This was soon seen to mean absolute chance. The conclusion so reached was clinched by a careful reëxamination of the office of chance in science generally, and especially in the doctrines of evolution. Arrived at this point, the next question was, what is the principle by which the development is to proceed? It was a difficult inquiry, and involved researches from different points of view.

But I will not trouble the reader with further autobiographical details. I have given enough to show that my method has neither been in theory purely empirical, nor in practice mere brain-spinning; and that, in short, my friend Dr. Carus’s account of it has been as incorrect as can be.

§ 18. The learned doctor (¶¶ 6, 7, 8) pronounces me to be an imitator of David Hume, or, at least, classes my opinions as closely allied to his. Yet be it known that never, during the thirty years in which I have been writing on philosophical questions, have I failed in my allegiance to realistic opinions and to certain Scotistic ideas; while all that Hume has to say is said at the instance and in the interest of the extremest nominalism. Moreover, instead of being a purely negative critic, like Hume, seeking to annul a fundamental conception generally admitted, I am a positive critic, pleading for the admission to a place in our scheme of the universe for an idea generally rejected. In the first paper of this series, in which I gave a preliminary sketch of such of my ideas as could be so presented, I carefully recorded my opposition to all philosophies which deny the reality of the Absolute, and asserted that “the one intelligible theory of the universe is that of objective idealism, that matter is effete mind.” This is as much as to say that I am a Schellingian, of some stripe; so that, on the whole, I do not think Dr. Carus has made a very happy hit in likening me to Hume, to whose whole method and style of philosophising I have always been perhaps too intensely averse. Yet, notwithstanding my present disclaimer, I have little doubt apriorians will continue to describe me as belonging to the sceptical school. They have their wonderful ways of arriving at truth, without stooping to confront their conclusions with facts; and it is amusing to see how sincerely they are convinced that nobody can have science at heart, without denying all they uphold.[117]

My opponent has a habit of throwing out surprising opinions without the least attempt to illuminate them with the effulgence of reason. Thus he says (¶ 8): “If Kant’s answer to Hume had been satisfactory, Mr. Peirce would probably not have renewed the attack.” What attack? All that Hume attacked I defend, namely, law as a reality. How could a defence of that which I defend as essential to my position, cause me to surrender that position, namely, that real regularity is imperfect? In any sense in which Hume could have admitted the possibility of law, it must be precisely followed; since its existence could consist only in the conformity of facts unto it. But perhaps Dr. Carus means that if one question had been completely settled, I should probably have confined myself to talking about that, instead of broaching a new one.

§ 19. Another misunderstanding of my position on the part of Dr. Carus (¶¶ 12, 13) is simply due to “boldly” having been twice printed where the reading should have been “baldly,” in my paper on “The Doctrine of Necessity.” (_The Monist_, Vol. II, p. 336, lines 20 and 25.) I wish printers would learn that I never use the word _bold_. I have so little of the quality, that I don’t know what it means. As I read the “revise,” as usual, it was presumably my fault that the _erratum_ occurred. At any rate, had my meaning been clearly expressed, the proof-reader would not have been misled by my defective chirography. What I was trying to say was, in substance, this: Absolute chance is a hypothesis; and, like every hypothesis, can only be defended as explaining certain phenomena.[118] Yet to suppose that an event is brought about by absolute chance is utterly illogical, since as a hypothesis it could only be admitted on the ground of its explaining observed facts; now from mere non-law nothing necessarily follows, and therefore nothing can be explained; for to explain a fact is to show that it is a necessary, or, at least, a probable, result from another fact, known or supposed. Why is not this a complete refutation of the theory of absolute chance? _Answer_: because the _existence_ of absolute chance, as well as many of its characters, are not themselves absolute chances, or sporadic events, unsubject to general law. On the contrary, these things _are_ general laws. Everybody is familiar with the fact that chance has laws, and that statistical results follow therefrom. Very well: I do not propose to explain anything as due to the action of chance, that is, as being lawless. I do not countenance the idea that Bible stories, for instance, show that nature’s laws were violated;—though they may help to show that nature’s laws are not so mechanical as we are accustomed to think. But I only propose to explain the regularities of nature as consequences of the only uniformity, or general fact, there was in the chaos, namely, the general absence of any, determinate law.[119] In fact, after the first step is taken, I only use _chance_ to give room for the development of law by means of the law of habits.

§ 20. In ¶ 28, I read: “Mr. Peirce does not object to necessity in certain cases; he objects to necessity being a universal feature of the world.” This is correctly stated, and so it is in ¶ 203. I object to necessity being universal, as well as to its ever being exact. In short, I object to absolute universality, absolute exactitude, absolute necessity, being attributed to any proposition that does not deal with the Α and the Ω, in the which I do not include any object of ordinary knowledge. But it is careless to write (¶ 193) that I “describe the domain of mind as the absence of law.” Is not one of my papers entitled “The Law of Mind”? It is true that I make the law of mind essentially different in its mode of action from the law of mechanics, inasmuch as it requires its own violation; but it is law, not chance uncontrolled. That it is not “an undetermined and indeterminable sporting” should have been obvious from my expressly stating that its ultimate result must be the entire elimination of chance from the universe. That directly negatives the adjective “indeterminable,” and hence also the adjective “undetermined.” Still more unwarranted is the statement (¶ 205) that I deny “that there are samenesses in this world.” If the slightest excuse for such an accusation can be found in all my writings I shall be mightily surprised.

§ 21. Dr. Carus fully admits (¶ 9) the justice of my first reply to the argument that necessity is postulated in all scientific reasoning, which reply is that to postulate necessity does not make it true. As this reply, if correct is complete, Dr. Carus was bound after that admission to drop the postulate-argument in favor of necessity.[120] But he takes no notice, at all, of my four-page argument to show that scientific reasoning does _not_ postulate absolute universality, exactitude, or necessity (_The Monist_, Vol. II, pp. 324-327); but calmly asserts, four or five times over (¶¶ 5, 11, 16, 62, 79), without one scintilla of argumentation, that that postulate _is_ made, and uses this as an argument in favor of necessity.

§ 22. He also fully admits (¶¶ 11, 14, 22) the justice of my argument that the absoluteness of universality, exactitude, and necessity, cannot be proved, nor rendered probable, by arguments from observation. That argument consisted in assuming that all arguments from observation are probable arguments, and in showing that probable inferences are always affected with probable errors.

Had I deemed it requisite, I might easily have fortified that argument by a more profound analysis of scientific reasoning. Such an analysis I had formerly given in my “Theory of Probable Inference” (in “Studies in Logic,” Boston: Little and Brown).

But, notwithstanding his admissions, Dr. Carus sets up his _ipse dixit_ against my argumentation. “We deny most positively,” says the editorial Elohim, “that the calculus of probabilities is applicable to the order of the world, as to whether it may or may not be universal.” (¶¶ 27, 31.)

To support this, he cites (¶¶ 31-34) four passages from articles written by me sixteen years ago. I hope my mind has not been stationary during all these years; yet there is little in those old articles which I now think positively erroneous, and nothing in the passages cited. My present views had, at that time, already begun to urge themselves on my mind; but they were not ripe for public avowal. In the first of the passages cited, I express the opinion, which I first uttered in my earlier lectures before the Lowell Institute, in 1866, afterwards in the _Popular Science Monthly_ in 1877, in still fuller elaboration in my “Theory of Probable Inference” in 1882, and maintain now as strongly as ever, that no definite probability can be assigned to any general arrangement of nature. To speak of an _antecedent_ probability would imply that there was a statistical science of different universes; and a _deduced_ probability requires an antecedent probability for one of its data.[121] This consideration only goes to fortify my present position, that we cannot conclude from observed facts with any degree of probability, and therefore _a fortiori_ not with certainty, that any proposition is absolutely universal, exact, or necessary. In the absence of any weight of probability in favor of any particular exact statement, the formal presumption is altogether against any one out of innumerable possible statements of that kind.

The second passage cited is one in which I argue that the universe is not a chaos, or chance-medley. Now Dr. Carus admits (¶ 28) that I do not to-day maintain that it is a chance-medley.

The third passage cited is this: “A contradiction is involved in the very idea of a chance-world.” This is in entire harmony with my present position that “a chaos ... being without connection or regularity would properly be without existence.” (“Architecture of Theories,” _The Monist_, Vol. I, p. 176.)

The fourth passage is to the effect that “the interest which the uniformities of nature have for an animal measures his place in the scale of intelligence.” This I still believe.

So much for my supposed contradictions. If I am not mistaken, our amiable editor, whose admirable editorship springs so largely out of his amiability, in copying out these passages was really not half so much intent on showing me to be wrong at present, as on showing me to have been right formerly. However hard he hits, he contrives to honey his sockdologers, and sincerely cares more to make the reader admire his antagonist when he is right than to condemn him when he is wrong. There is a touch of art in this that proclaims the born editor, and which I can hardly hope to imitate.

Though Dr. Carus admits over and over again that necessity cannot be based on observation, he often slips back to the idea that it can be so based. He says, (¶ 30) that “form is a quality of this world, not of some samples of it, but throughout, so far as we know of existence in even the most superficial way.” But does he not see that all we _do_ know, and all we _shall_ to-morrow, or at any date know, is nothing but a sample of our possible experience,—nay, is but a sample of what we are in the future to have already experienced? I have characterised inductive inference as reasoning from samples; but the most usual way of sampling a class is by examining _all_ the instances of it that have come under our observation, or which we can at once collect.

§ 23. Dr. Carus (¶¶ 44, 46) holds that from my social theory of reality, namely, that the real is the idea in which the community ultimately settles down, the existence of something inevitable is to be inferred. I confess I never anticipated that anybody would urge that. I thought just the reverse might be objected, namely, that all absoluteness was removed from reality by that theory, and it was many years ago that, in my “Theory of Probable Inference,” I admitted the obvious justice, as it seemed to me, of that objection. We cannot be quite sure that the community ever will settle down to an unalterable conclusion upon any given question. Even if they do so for the most part, we have no reason to think the unanimity will be quite complete, nor can we rationally presume any overwhelming _consensus_ of opinion will be reached upon every question. All that we are entitled to assume is in the form of a _hope_ that such conclusion may be substantially reached concerning the particular questions with which our inquiries are busied.

Such, at least, are the results to which the consideration of the doctrine of probability brings my mind irresistibly. So that, the social theory of reality, far from being incompatible with tychism, inevitably leads up to that form of philosophy. Socialistic, or as I prefer to term it, agapastic ontology seems to me likely to find favor with many minds at an early day, because it is a natural path by which the nominalist may be led into the realistic ways of thought, ways toward which many facts and inward forces impel him. It is well, therefore, to call attention to the circumstances that the realism to which it leads is a doctrine which declares general truths to be real,—independent of the opinions of any particular collection of minds,—but not to be destined, in a strictly universal, exact, and sure acceptation, to be so settled, and established. Now to assert that general truths are objectively real, but to deny that they are strictly universal, exact, and certain, is to embrace the doctrine of absolute chance. Thus it is that the agapastic ontologist who endeavors to escape tychism will find himself “led into” that “inextricable confusion” which Dr. Carus (¶ 4) has taken a contract to show that I am led into.

§ 24. Conservatism is wholesome and necessary; the most convinced radical must admit the wisdom of it, in the abstract; and a conservative will be in no haste to espouse the doctrine of absolute chance. I, myself, pondered over it for long years before doing so. But I am persuaded, at length, that mankind will before very long take up with it; and I do not believe philosophers will be found tagging on to the tail of the general procession.

My little dialogue between the tychist and the necessitarian (_The Monist_, Vol. II, pp. 331-333) seems to have represented pretty fairly the views of the latter; for Dr. Carus, in ¶¶ 151-155, does little more than reiterate them, without much, if at all, reinforcing them. His ¶¶ 158-160 merely work out, in a form perhaps not quite clear, what is manifest from the elementary principles of dynamics, and was considered in my dialogue.

His arguments in this connection, apart from those already noticed, are that absolute chance is something which if it existed would require explanation, that the manifold specificalness of nature is explained by law without any aid from chance, and that absolute chance if it existed, in the sense in which it is supposed to exist in my chaos, could not possibly breed law as supposed by me. To the consideration of these arguments I proceed to apply myself.

§ 25. One of the architectonic—and, therefore, I suppose, by Dr. Carus considered as highly reprehensible—features of my theory, is that, instead of saying off-hand what elements strike me as requiring explanation and what as not doing so, which seems to be his way, I have devoted a long time to the study of the whole logical doctrine of explanation, and of the history of explanations, and have based upon the general principles so ascertained my conclusions as to what things do and what do not require to be explained.