Chapter XVI: Part 16

Several anecdotes are told about the insensibility to pain. An old thief had his leg amputated with the greatest apathy: the operation done, he took the limb into his hand and joked about it. An inveterate murderer, his penal servitude being ended, was dismissed out of the bagnio of the island S. He asked the warden to be retained, because he did not know how to get food and shelter. His demand being refused, he opened his bowels with the handle of a spoon, went to bed as usual, and died without even a sigh. Mandrin, a criminal, shortly before his execution allowed himself to be cut in eight places without giving a sign of pain; criminal R. flayed the skin of his face with a piece of glass. In the penitentiary at Chatham during the years 1871 and 1872, 841 voluntary wounds and injuries were made. Among them 27 convicts had mutilated some limb, and in 17 cases the limb had to be amputated.

This obtusity of the sensory organs in criminals is supposed to be of a cortical origin and being similar to the phenomena of savage life is interpreted as atavism. Criminals show deficiencies in the senses of touch, smell, taste, and hearing, but not of sight. And this is analogous to the savage in whom the sense of sight is naturally very strong, and no criminal could execute numerous thefts or escape the arm of justice without a high development of the sense of sight.

In the second article on comparisons of tone-distances Gustav Engel, Professor at the Royal High-school of Music in Berlin, takes occasion to explain his views of the subject with reference to the severe criticism of C. Stumpf on Carl Lorenz’s theory. Wilhelm Wundt had taken part in the discussion in favor of Lorenz. The subject of the article lies in the border-land between the physiology of hearing and music; and Professor Engel comes to the conclusion that affinity of tones, i. e. the interval-sense in a melodious succession does not lead to the same accuracy and reliability of hearing as their concord. He objects to the idea of an arithmetical difference as proposed by Lorenz and Wundt, and proves it through the fact that the Pythagorean tierce in the unaccompanied scale makes a less noticeable disturbance than in a concord, while the approximately pure tierce (which is too low only by a small fracture of a comma) is excellent in the concord while it causes a slight disturbance in the melody. Musical intervals are not identical with the geometrical intervals, yet they are based upon them as a selection made among innumerable possibilities for certain purposes. Their acceptance is established only in harmonic music, but this fact too adds some difficulties to the investigations made in this field, for if two tones sound together, we can no longer distinguish them separately, as would be required for the investigation; and if we let the one succeed the other their geometrical relation is no longer discerned with the same precision. (Hamburg and Leipsic: Leopold Voss.)

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VIERTELJAHRSSCHRIFT FÜR WISSENSCHAFTLICHE PHILOSOPHIE. Vol. XV. Nos. 3 and 4.

CONTENTS of No. 3:

PSYCHISCHE UND PHYSISCHE ACTIVITÄT. By _H. Höffding_.

UEBER SPRACHREFLEX, NATIVISMUS UND ABSICHTLICHE SPRACHBILDUNG.
(Achter Artikel.) By _A. Marty_.

ZUR PHILOSOPHIE DER MATHEMATIK. By _Chr. v. Ehrenfels_.

DER FOLGERUNGSCALCUL UND DIE INHALTSLOGIK. By _E. G. Husserl_.

CONTENTS of No. 4:

DIE GESETZMÄSSIGKEIT DER PHYSISCHEN ACTIVITÄT. By _H. Höffding_.

ETHNOLOGIE UND ÆSTHETIK. By _E. Grosse_.

UEBER DIE FORTSCHREITENDE ENTWICKLUNG DES MENSCHENGESCHLECHTS.
(Erster Artikel.) By _F. Rosenberger_.

UEBER SPRACHREFLEX, NATIVISMUS UND ABSICHTLICHE SPRACHBILDUNG.
(Neunter Artikel). By _A. Marty_.

UEBER FERNWIRKUNG UND ANORMALE. WAHRNEHMUNGSFÄKHIGKEIT.
Methodologische Randglossen. By _M. Offner_.

Prof. H. Höffding’s article on psychical and physical activity is an answer to a criticism by Professor Kroman. Professor Höffding had proposed, concerning the relation of the psychical to the physical, a theory which he called the “identity hypothesis,” according to which the physical and psychical activities are not different in their nature but only in their phenomenal appearance. K. Kroman, a countryman and colleague of H. Höffding—both are professors at the University of Copenhagen—rejected in his recent work “Logic and Psychology” the identity hypothesis and characterised it as “Duplicism,” a name against which Höffding protests. Kroman’s objections are as follows: _a_) Natural science knows of no reason to conceive of the relation of the psychical to the material in the way expressed by the identity-hypothesis. _b_) On the basis of the identity-hypothesis it remains unexplained how we can know anything about the external world. _c_) It is inexplicable how an identity can obtain of two so different things as are the bodily multiplicity and the psychical unity. Professor Höffding investigates these three objections separately and comes to the conclusion that his identity-hypothesis shows the relation between the psychical and material nature in a clear and simple light. It excludes on the one hand materialism and on the other hand spiritualism. The question whether either phenomenon, spirit or matter, represents the absolute nature of existence, cannot, according to Höffding, be answered. It appears to us that Professor Höffding’s position is sound in all main points and may be considered as that view which is most prevalent among modern psychologists. However, concerning the question whether spirit or matter represents the absolute nature of existence, we refer the reader to the editorial article “Are there Things in Themselves?” section XII, “The Oneness of Subjectivity and Objectivity.” In our opinion the question itself is illegitimate. Neither the subjectivity of spirit, nor the objectivity of matter represents the absolute nature of existence; both together form the nature of existence; and we omit here the word “absolute” purposely. The question as to which abstract, matter or spirit, represents the absolute nature of existence seems to us similar to the question which of the two terms _A_ and _B_ represents in the relation _A:B_ the absolute nature of the relation. The obvious answer is neither.

The eighth article of A. Marty of Prague on Language-reflex is mainly of a controversial nature directed against L. Tobler’s article on the origin of language in the _Zeitschrift für Völker-Psychologie_. By Nativism, Marty understands the theory that certain involuntary articulate sounds are associated with certain ideas, while the so-called empirical theory attempts to explain the origin of the first words without such innate mechanical relations between sounds and concepts. Marty represents the empirical solution of the problem and objects to the extreme nativism, but he grants that Tobler’s modified nativism approaches very much to his own position.

The longest article of the present number (63 pp.) is an essay full of valuable hints by Chr. v. Ehrenfels on the Philosophy of Mathematics. The epistemological basis of mathematics demands a psychological investigation of its contents. Accordingly the author proposes to present a psychological characterisation of the number-conceptions, from which he derives some conclusions concerning the theory of cognition. He investigates the origin of the unity conception which is generally defined as “positing a unit” or as “conceiving as a unit.” We usually believe that we abstract numbers directly from the objects, when we look for instance at one house with two doors and five windows. But this process of abstraction is not quite so direct as it seems. The number-conception is not taken from external observation, but carried into the same; yet this is done involuntarily and inadvertently so that it appears as if they were _eo ipso_ contained in it.

What is the origin of the concepts “unity” and “multiplicity”? Two methods present themselves: 1) The concentration of attention and (2) the act of bringing into relation. The former produces a unity and, when successively directed to several objects, a series of units. The latter appears to be required by the consideration that the conception of a number is conditioned by acts of distinguishing. The number “two” requires two acts of distinguishing, “three” requires three, “four” requires six and the number _n_ requires _n_/2(_n_-1) acts of distinguishing. This explains why we can have clear and direct conceptions only of very low figures. The idea that a combination of both methods will explain the facts is by no means excluded. But there is a third source which may be used to explain the unity conception, viz. inner experience. “The unity of consciousness,” Ehrenfels says, “has been misused in philosophy to demonstrate the substantiality, simplicity, and indestructibility of the soul.” Nevertheless there is some truth in the unity idea, for the present psychical phenomena present themselves in a peculiar amalgamation, which admits of a comparison between two elements while it erects a barrier between the _ego_ and the _tu_. Our psychical contents will always appear to us as a unit; and on this basis we might declare that the unity conception is derived from this source. [Here Ehrenfels does not see that the concentration of attention is practically the same as the unity of consciousness, for attention means consciousness, and concentration produces unity.]

Number-conceptions originate by counting. We disjoin things; for instance, we throw a number of apples into a basket, or we let the finger slide over the division lines of a measuring stick naming each unit while proceeding in the act. From such processes the function of counting can be abstracted while the details are neglected as unimportant. Most of the higher numbers are never directly but only indirectly realised. So for instance twenty is to many that number which will be reached by counting up to twenty, yet the single units of the number are lost sight of entirely. Such number-conceptions belong to the class of “indirect concepts” which represent objects not through marks belonging to the object itself, but originating through its relation to other objects. The basis of such indirect concepts had been called by Ehrenfels _Gestaltsqualitäten_, i. e. figure qualities, and by Meinong _fundierte Inhalte_ or founded contents. Thus indirect conceptions are parts contingent upon some such basis.

Number-conceptions are not always clearly thought out and there are some helps to represent higher or more complex numbers. Thus we can think of ten as represented by the outside and inside corners of a pentagram, twelve as the edges of a cube, etc., and common among all nations is the usage of the fingers to represent numbers up to ten. Such helps are quite different from indirect number-conceptions and may be called figurative number-conceptions.

That there are mathematical conceptions of magnitudes which have no objective analogon is quite natural, for there is even in an indirect conception no warrant for its objective reality; and we ought to consider how many word- and idea-combinations are possible without their possessing some analogous reality. Yet the so-called irrational cannot properly be called a number, it is the demand of a number which in fractions can sufficiently for certain purposes but never fully be realised.

Negative numbers always presuppose a contrast and such conditions arise naturally wherever the fundamental ideas imply two opposite directions, for instance past and future in time, credit and debit in business, etc. It is a matter of course that there are in reality as little either positive or negative numbers, as there are positive or negative colors or sounds.

Concerning the necessity idea, Ehrenfels says: “Nobody will consider it as possible that five plus seven will in some cases make any other number than twelve. We are confident that the same addition will under all circumstances yield the same sum.” Ehrenfels grants the psychical certitude of this but not the mathematical, and thinks that on this point there is a difference of opinion allowable. Here we disagree from Ehrenfels and refer the reader to former articles on kindred subjects in _The Monist_, especially the article on “The Origin of Thought-forms,” Vol. II, p. 111. We must bear in mind that in mathematics we are moving in a realm of pure forms and the statement 7 + 5 = 12 is, as the Germans express it, _eindeutig bestimmt_, i. e. it is determined exhaustively in one and the only one possible way. The numbers 7 and 5 being rigid, their sum and their product will also be rigid.

This difference of opinion may be contingent upon a difference of the conception of the _a priori_. Ehrenfels defines as “a priori” such judgments which having come into our possession, are readily accepted without proof. We follow Grassmann in rejecting the acceptance of anything without proof, including the idea of mathematical axioms. The _a priori_ in our terminology becomes identical with that which pertains to formal thought: and it would make no difference whether the instance presented is as simple as 1 + 1 = 2 or extremely complex as are the differential calculus and logarithms. Accordingly we disagree also from Ehrenfels when he finds even in such additions as for instance 825 + 217 = 1042 vestiges of an _a posteriori_ character. The employment of the logarithms accordingly appears to Ehrenfels also _aposterioristic_ because the fruits of other peoples’ labors are utilised!

Concerning John Stuart Mill’s view of the subject, Ehrenfels says that “it is still deeply entangled in the errors of that conception which it so bitterly opposes, viz. in the formalism of the old purely _a priori_ conception. For only he who adheres to the view that all mathematics are deduced from a few axioms can think of attributing to those axioms the highest degree of plausibility which is assumed for them on the ground of comprehensive deduction.” We agree with Ehrenfels’s objection to Mill, but we cannot agree with his view that mathematics derives any elements from _a posteriori_ elements, although we grant that quite new departments are created simply by a different employment of certain functions. Accordingly mathematics cannot be derived from a few axioms only but is the products of certain functions.

Ehrenfels calls attention to the fact that the mathematician operating with symbols often forgets entirely what he has to think of in connection with these symbols. “This is not strange,” he adds, “for thoughtless word-combinations present analogous instances, yet it is strange that the result almost without exception comes out right; _es stimmt!_” We object here; operations with mathematical symbols are not thoughtless combinations, at least, they are not meaningless. They are operations not with things, but with symbols representing certain relations among things. When gamblers play with chips representing real money, they need not think during the game of the value represented by a chip, and yet when the account is made, the result attained with the assistance of the chips will come out right. There is no reason to wonder at it. Chips like mathematical symbols might in a certain sense be called thoughtless, for certainly they do not think; but they are not thoughtless in the sense that they are meaningless, that nothing is thought by them.

Ehrenfels apparently sees a problem where there is none and this is closely connected with another point. He looks upon the mathematician’s inability of thinking out in every respect the objective meaning of mathematical symbols as a shortcoming of man’s intellect. While it appears that we cannot think anything by many mathematical symbols (for instance by _a⁰ = 1_) except the symbol itself, the enormous success of mathematical thought is evidence that they must have some definite meaning although it is to be excogitated only by those beings who will transgress the average intelligence of to-day, the first germs of whose existence are the mathematical geniuses of the present generation. It appears to us that undoubtedly every mathematical symbol has a definite meaning, representing the result of some function. That the result will sometimes be unattainable or unrealisable, that especially all operations with zero make the whole calculation indefinite (which naturally arises from the nature of zero) does not alter the truth of this proposition in the least.

We have to make one additional remark. The peculiarity of mathematics that we do not throughout our operations think out the meaning of the symbols is not a shortcoming of our intelligence, but the strength of mathematical science. The advantage of all the formal sciences and especially of mathematics consists in this that we _need not_ think out every detail, but that we can, through the assistance of mathematical symbols, perform the most intricate operations with machine-like exactness. The economy of thought produced in this way is not a deficiency of man’s mind, but a virtue.

Prof. H. Höffding (in No. 4) insists upon the causal law as being indispensable in psychology. There are some people and among others his colleague Professor Kroman who regard moral motives as an exception. “Yet,” says Professor Höffding, “should the decisive moment of a decision not be determined by the causal law, the will could never be determined through a reflection on the possible effects of the action and thus every reason would be missing to attribute to man any responsibility.”

E. Grosse expatiates on the proposition to apply the comparative method of ethnology to æsthetics. Ferd. Rosenberger proposes the following programme: “Knowledge is power; activity based upon such power is the cause of happiness. Therefore with the increase of knowledge, there is an increase of happiness, successful activity however is impossible without virtue. Therefore we conclude that an increase of happiness will be accompanied with an increase of virtue.” A. Marty in this his ninth article blames Steinthal for having misrepresented the eighteenth century theories of the origin of language.

M. Offner reviews Dr. Charles Richet’s reports of his telepathic experiments, but the reviewer cannot assent to Richet’s opinion “that these facts possess a strange coincidence and that they are, probably, the result of a relation and not of pure chance.” (Leipsic: O. R. Reisland.)

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PHILOSOPHISCHE MONATSHEFTE. Vol. XXVIII. Nos. 1 and 2.

CONTENTS:

ZUM BEGRIFF DER UNBEWUSSTEN VORSTELLUNG. By _E. v. Hartmann_.

UEBER DAS GEBET. EIN RELIGIONSPHILOSOPHISCHES FRAGMENT.
Sendschreiben an Herrn E. Renan in Paris. By _M. J. Monrad_.

WERKE ZUR PHILOSOPHIE DES SOCIALEN LEBENS UND DER GESCHICHTE.
Erster Artikel (H. Spencer, Sociologie, Bd. III). By _F.
Tönnies_.

RECENSIONEN: H. Münsterberg, Beiträge zur experimentellen
Psychologie No. 3. Neue Grundlegung der Psychophysik. By _Th.
Ziehen_. W. Enoch Der Begriff der Wahrnehmung. By _P. Natorp_.
Ch. Bénard. L’esthétique d’Aristote et de ses successeurs. By
_A. Döring_.

LITTERATURBERICHT.

The well-known philosopher Edward von Hartmann defines his position with reference to the idea of an unconscious representation. Granting that there are no unconscious sensations, perceptions, conceptions or memories, because feeling either is conscious or not at all, he introduces the idea of unconscious representations again as the most adequate determination. He says, “Either we must renounce all speaking and thinking of non-sensual objects or we must be satisfied with using figurative expressions.”

M. J. Monrad, a Norwegian, argues, in the second article against M. E. Renan’s theory of prayer, whom he had visited some years ago in Paris, that prayer has after all an effect upon the objective world and it is not limited to a merely subjective and psychological influence. Monrad presupposes a belief in God, prayer bringing the individual in unison with God, changes the will of the individual into a co-ordinate willing of God and thus renders the individual a co-worker of God. This, however, should not be conceived to take place by magic and in contradiction to nature, but through nature, man using the laws of nature.

F. Tönnies of Kiel gives an exposition of Mr. Spencer’s social views which are, briefly expressed, “the final victory of society over the state.” Professor Tönnies answers that “we all want a higher civilisation, but the development of a higher civilisation is not conditioned by the final victory of society over the state. On the contrary, it may be said that it depends upon a victory of the state over society in so far as public rights will supersede private rights.... The truth is that state and society are contingent, the one upon the other and also limiting each other.” (Berlin: Dr. R. Salinger.)

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FOOTNOTES:

[52] _Questions of Philosophy and Psychology._ In the Russian language.

VOL. II. APRIL, 1892. NO. 3.

THE MONIST.

THE DOCTRINE OF NECESSITY EXAMINED.

In _The Monist_ 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.

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 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 _reductio ad absurdum_, very naturally became the one school of ancient philosophy to stand by a strict necessitarianism, thus returning to the 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 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.

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 _future_ 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.

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 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.

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 compromised 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 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.

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 in 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, centre, 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 _A_. 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 _experimentally_ and _provisionally_. By saying that we infer it _experientially_, I mean that our conclusion makes no pretension to knowledge of wheat-in-itself, our ἀλήθεια, as the derivation of that word implies, has nothing to do with _latent_ 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 _A_, to which our inference seeks to approximate. By saying that we draw the inference _provisionally_, 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 _to come_ (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 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.

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 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 _bevue_, 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 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 _latent_ individuals of which our conclusion does not pretend to speak.

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 _A_ 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 _A_. 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 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.

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.

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 _nil_? 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 recognised 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; 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.

Still, I am obliged to admit that this rule is subject to a certain qualification. Namely, it only applies to continuous[53] 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 _no_ indigo in a given ear of wheat, and absolutely _no_ 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 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 _better_ position than this in regard to the presence of the element of chance or spontaneous departures from law in nature.

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 _exactitude_, all observation is directly _opposed_ 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.

But it may be asked whether if there were an element 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.

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 _a priori_ reasons to support his thesis. These received such a sockdologer 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.

To say that we cannot help believing a given proposition is no argument, but it is a conclusive fact if it be 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.

Some seek to back up the _a priori_ 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 recognisable utilities or ends. Now, the adaptations of nature, beautiful and often marvellous as they verily are, are never found to be quite perfect; so that the argument is quite _against_ the absolute exactitude of any natural belief, including that of the principle of causation.

Another argument, or convenient commonplace, is that absolute chance is _inconceivable_. This word has eight current significations. The Century Dictionary enumerates 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.

Another _a priori_ 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 _never_ 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 _vera causa_, and ought not unnecessarily to be introduced into a hypothesis.

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.

“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.]

Clearly one throw is as much chance as another.

“Do you think throws of dice are of a different nature from other events?”

I see that I must say that _all_ the diversity and specificalness of events is attributable to chance.

“Would you, then, deny that there is any regularity in the world?”

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.

“If you reflect more deeply, you will come to see that _chance_ is only a name for a cause that is unknown to us.”

Do you mean that we have no idea whatever what kind of causes could bring about a throw of sixes?

“On the contrary, each die moves under the influence of precise mechanical laws.”

But it appears to me that it is not these _laws_ 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.

“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.”

Does the operation of mechanical law not increase the diversity?

“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.”

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:

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 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.

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 _sui generis_ 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.

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 _general_ 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 philosophising which does not thus barricade the road of discovery.