Chapter XXX: Part IX: , p. 475, 1890), Dr. Johnstone Stoney, F. R. S., published an (20)

Mr. Peirce trusts that his favorite ideas will find support in his peculiar conception of the logic of relatives. Judging from the quiddities which he now so confidently propounds as weighty arguments, we cannot share his sanguine hopes. His arguments, to be derived from the logic of relatives, are like promises to pay out of the returns of a gold-mine, just discovered and boomed by the owners. There may be gold in the mine, but I do not as yet take any stock in it.

Mr. Peirce promises to prove by the logic of relatives what, if it were true, he should be able to demonstrate in plain language.

I have an idea that the logic of relatives can be worked out into as clear a science as is mathematics or algebra. But what shall we say when told that the logic of relatives is really abstruse, and that he who labors under the disadvantage of not understanding this abstruse science is not prepared to grasp Mr. Peirce’s philosophy? The abstrusity, in my mind, counts against Mr. Peirce’s philosophy, as much as against his logic of relatives.

In my childhood I was much plagued with Latin, but as soon as I had acquired a smattering of it, I began to talk Latin to the servants, and when they did not understand me I thought that they were “laboring under the great disadvantage” of not speaking Latin. Since then I have learned to translate my Latin into the language of the people with whom I have to deal.

Mr. Peirce seems to rely on his learning in proportion to its abstrusity; he likes to walk on stilts.

Mr. Peirce is scholarly to excess. He has a special talent of rendering issues involved. Not even his references to my articles in _The Monist_ are made directly by quoting the pages on which they appear. That method would be too common. He invents a ponderous system, necessitating the reader to look twice when he wishes to find a passage,—a scheme which is original and very dignified in appearance, but makes quotation unnecessarily complicated.

Learning is a virtue, but even virtues should be used with discretion.

6. THE PRINCIPLE OF POSITIVISM.

Says Mr. Peirce in confirmation of Whewell (p. 546):

“Progress in science depends upon the observation of the right
facts by minds _furnished with appropriate ideas_.”

To rely on the observation of facts is, in my opinion, a principle of positivism. That facts must be observed “by minds furnished with appropriate ideas” is undeniable, but ideas, in order to be appropriate, must be true; they must be representations of facts.

Because he relies on facts I have characterised Mr. Peirce’s method as positivistic. But he indignantly repudiates “the charge” as “totally unfounded.”

Positivism (which I have always carefully distinguished from Comtism, the latter being a special kind of positivism[128]) is not a peculiar philosophy, but a most important principle of science.

Mr. Peirce seems to use the term positivism in a different sense from that in which I use it. Be it so. I shall not nominalistically quarrel about words so long as there are more urgent subjects under discussion. Noticing that Mr. Peirce does not state that all ideas should be ultimately reducible to facts, he is to be acquitted.

7. LOPPING OFF THE ABSOLUTE.

Mr. Peirce thinks that an agreement between us could be arrived at. He says (p. 545):

“Dr. Carus’s philosophy would, in its general features, offer
no violent opposition to my opinions” (§ 16).

But the condition is (p. 545):

“To lop off the heads of all absolute propositions whose
subject is not the Absolute.”

As a matter of fact I have lopped off all absolutes. If Mr. Peirce were more familiar with my views he would have known that. Thus, on my part, I had done all I could to come to an agreement with him long before he asked me to do it. But I fear that having also lopped off the Absolute itself, I did too much of a good thing, for Mr. Peirce carefully records his opposition to all philosophies which deny the reality of the Absolute. (See § 18.)

I wish to improve this occasion for conciliation, by turning the tables. Mr. Peirce’s views would, upon the whole, offer no violent opposition to my opinions if he would only consent to lop off the absolute-property of his absolute chance. I would even swallow his Absolute if he would promise to designate by that name some real quality of the world, or the world itself as a whole, or something that is thinkable without making one’s head swim.[129]

Every predication of absolute, changes a real and useful idea into its caricature. To, say that a complicated calculation is “absolutely true,” that is, true without stipulating the condition that the methods are right, and that the execution is made without any mistake, is ridiculous; and thus the phrase “in a Pickwickian sense” (which we gratefully borrow from Mr. Peirce) would always form a drastic but adequate substitute for the term absolute. “Absolutely true” is “true in a Pickwickian sense” only. There are no absolute truths which are in this sense unconditionally true. In the same way, “absolute chance” is different from that real chance known to us in experience and instanced by the throw of the dice. Absolute chance is “chance in a Pickwickian sense.”

Strange Mr. Peirce speaks of real chance when he means an imaginary absolute chance. He apparently uses the word “real” in this connection not to denote something that is a fact of experience but to express the idea of its being perfect or complete. Thus we may speak of a “real” perpetual motion, stating at the same time that it is neither real nor realisable.

8. THE THEORY OF PROBABLE INFERENCE.

Mr. Peirce applies his theory of probable inference to everything; also to those cases which are unequivocally determined. He granted in a private conversation that 2 × 2 = 4 admits of no exception. But of other purely formal statements which are in the same predicament, for instance, that the sum of the angles of a triangle in a plane measures 180°, he states as probable that they are either somewhat less or somewhat more than 180°, adding, “that they are exactly that amount is what nobody can ever be justified in concluding.” To determine the sum of the angles of a plane triangle by measuring the parallaxes of stars rests upon a fundamental misconception of the principles of formal sciences. It would be consistent for Mr. Peirce to say, that 2 × 2 = 4 is true only according to the definitions or axioms of arithmetic. But in order to know whether 2 × 2 = 4 in reality, we ought to apply the theory of probable inference. Until we had verified the statement 2 × 2 = 4 by applying this formula to the farthest solar systems, we should not be justified in concluding that it is exactly true. The theory of probable inferences is supposed to help us out of this perplexity, “and within another century our grandchildren will surely know whether the three angles of a triangle are greater or less than 180°.”[130]

There is always danger in the application of abstract ratiocination; and the theory of probable inference forms no exception to the rule. On the contrary, it is especially liable to lead one astray. There is the case of the doctor who said to his patient: “I am sure you will be cured, for I had ninety-nine patients who died during the operation, and statistics prove beyond doubt that one among a hundred will survive it. You are the hundredth.”

The theory of probable inferences is often misapplied, but can it be worse misapplied than by introducing it into the province of that which is certain? There is no sense in applying the theory of probabilities to what is certain. We may doubt whether the rays of light travel in exactly straight lines, but we cannot doubt the straightness of lines in plane geometry. We cannot doubt that all the radii in a circle are equal, or that the sum of the angles of a Euclidean triangle are 180°.

9. ZWEIDEUTIG BESTIMMT.

Mr. Peirce very kindly informs me that the term _eindeutig bestimmt_ is a translation of a French phrase. Very well, I do not deny it. I know very well that the phrase has a long history, but I do not consider myself bound to present the whole pedigree of every term I use.

Does Mr. Peirce perhaps suppose that the French phrase is the original? If we have to go back to the original beginning at all, why does he not tell us that the French _univoque_ is a translation from the mediæval Latin _univoce_, which was coined and used by the schoolmen in opposition to _æquivoce_. Neither the term _eindeutig_, as Mr. Peirce asserts, nor its scholastic original _univoce_, is an exclusively mathematical expression.

Although the term _eindeutig_ is a translation of the French _univoque_, there is after all a great difference between the French term and the German term, and I have a good reason to prefer the German expression. The French term is nominalistic or even vocalistic, the German one is realistic. _Univoque_ and _univocal_ mean that there is only one name or one _vox_, while _eindeutig_ lays no stress on the name but on the meaning of the name, denoting that which admits of but one interpretation. This is a sufficient reason for me to prefer it, and it ought to appeal to Mr. Peirce’s realistic mind.[131]

Mr. Peirce, maintaining that _eindeutig bestimmt_ is only a mathematical term, adduces two equations, each one of which, taken singly, admits, he says, of two possible determinations.[132] Mr. Peirce uses these equations as an argument against my application of the term, adding, sarcastically: “This shows how much that argument amounts to.” But his example proves at best only that there are incomplete determinations; some problems allow of several solutions. In a German township in which blue hussars are garrisoned, children used to propose to another this profound problem: “It lies under a plum-tree and is blue; what is it?” If the child questioned argues, “It is a plum,” he is corrected “No, it is a hussar.” But if he argues, “It is a hussar,” he is corrected, “No, it is a plum.” So he has no chance of guessing right. The result of Mr. Peirce’s first equation, which may be either 11·477 or 11·523, is like the conundrum of the plum-tree: it amounts to the same, viz. to nothing, and proves only that there are determinations which are _zweideutig bestimmt_.

10. EXPLANATION.

The differences of method become very serious when we disagree on the very meaning of “explanation” itself. How can two debaters accept or reject one another’s arguments, if their ideas of explanation are radically different?

Mr. Peirce’s definition of the term “explanation” appears to me very unsatisfactory. He says (p. 57):

“I cannot admit that explanation is description of the fact
explained. It is true that in the setting forth of some
explanations it is convenient to restate the fact explained so
as to set it under another aspect, but even in these cases the
statement of other facts is essential. (!) In all cases it is
_other facts_, (!) usually hypothetical, which constitute the
explanation; (!) and the process of explaining is a process by
which from those other facts the fact to be explained is shown
to follow as a consequence by virtue of a general principle or
otherwise.”

“To explain a fact is to show that it is a necessary or
at least a probable result from another fact (!) known or
supposed.”

My definition of “explanation,” as a description in which the process described is recognised as a transformation is sneered at. Says Mr. Peirce (p. 558):

“A magician transforms a watch into a dove. Recognise it as
a transformation and the trick is explained, is it? This is
delightfully facile.”

Indeed, the magician’s trick is explained as soon as we know all the changes that have taken place. Take the whole number of objects handled by the magician, those which he shows and those which he conceals. Let us observe how he hides the watch and how he produces the dove, and the trick is explained. Is it not?

Explanation is, as the word suggests, a making plain, so that we can look over the whole field before us, and leave nothing hidden from sight. This whole field, the survey of which is needed for the recognition of the transformation, is called the system of the explanation. After we have seen how the changes take place, and after we have described in exact formulas their modes of action, our desire for explanation is completely satisfied.

The instances adduced by Mr. Peirce prove plainly that his objections cannot be maintained. Every one of them is an instance of transformation (with the exception of the emerald vest, which, however, is not stated with sufficient completeness). Take, for instance, the following example adduced by Mr. Peirce (p. 557):

“A ‘special process of nature,’ calling for explanation, is the
circumstance that the planet Mars, while moving in a general
way from west to east among the fixed stars, yet retrogrades a
part of the time, so as to describe loops in the heavens. The
explanation is, that Mars revolves in one approximate circle
and we in another.”

Can any one deny that this explanation is a description? We draw the two orbits as correctly as possible for the required demonstration and combine the points representing the earth with those representing Mars at their successive positions. Considering the fact that we do not perceive the motion of the earth, we have to construct a diagram in which the directions of these lines are described as viewed from a stationary point. This is a description of changes that take place. It is a portrayal of the transpositions of two bodies, and the appearance which the change of this relation presents to one of them.

Mr. Peirce has neither the grace nor good-will to, understand my proposition, that _explanation is always a tracing of form_. He says (p. 558):

“Forms may indulge in whatever eccentricities they please, in
the world of dreams, without responsibility.”

In the world of dreams, yes! But not in the world of reality. And even the irresponsible eccentricities of dreams take place according to law.

Feeling that he mistakes my position, Mr. Peirce adds:

“Should Dr. Carus reply that I mistake his meaning, that it is
only ‘being in general’ (§ 66), that he holds unaccountable,
I reply that this is simply expressing scepticism as to the
possibility and need of philosophy.” (P. 558.)

Of course, I mean “being in general.” As to the scepticism imputed to me, I answer, that any attempt at explaining how matter and energy, which I take to be eternal, came into being, is a wrongly formulated problem. Mr. Peirce might as well call me a sceptic, because I recognise that we cannot square the circle. (Compare “Fundamental Problems,” 2d ed., pp. 283-285 and 291.)

Mr. Peirce’s gravest mistake is his belief that

“In all cases it is _other facts_ which constitute the
explanation.” (P. 557.)

The practical application of this mistake becomes fatal to his philosophy.

It is by no means necessary to pass beyond that system of facts which contains the phenomenon to be explained. We must, as a matter of course, keep completing the facts of a phenomenon until we have acquired a survey of what we call the whole system of the facts, but we have never to resort to other facts.

We are confronted every day with hundreds of facts of which we never see the whole system to which they belong, but we readily supply these deficiencies from the stock of our experience. We refer the unknown to the known. The single case under observation is referred to something with which we are familiar. Those systems of explanation which are known to us serve as patterns for others that are only partially known, and we fill out, with their assistance, the gaps of our observation.

The readiness and reliability of our explanation thus depends upon the stock of knowledge we have. The more we know, the easier shall we conquer the unknown; the more incomplete our knowledge is, the greater the number of hypothetical facts that will have to be introduced; and this always weakens the reliability of our explanations. Hypothetical facts should be introduced only in cases of urgent necessity. However, if they are admitted at all, they have to be thought of as parts of the system under investigation, for they have been invented only because we are compelled to assume that without them it would be incomplete.

Mr. Peirce adduces the following example to prove that “other facts” are required in an explanation:

“It has been stated that a warm spring in Europe is usually
followed by a cool autumn, and the explanation has been offered
that so many more icebergs than usual are liberated during
a warm spring, that they subsequently lower sensibly the
temperature of Europe. I care little whether the fact and the
explanation are correct or no. The case illustrates, at any
rate, my point that an explanation is a special fact, supposed
or known, from which the fact to be explained follows as a
consequence.” (P. 557.)

When, as in this instance, we recognise that one fact is the necessary result of another fact, we view them both as parts of one set or system of facts in which a transformation is taking place, and, unless we see the connection of the two facts as constituting one process of transformation, we cannot say that the problem is explained. When we observe changes which are the results of transformations taking place beyond the horizon of our knowledge, we are, as a matter of course, unable to give an explanation.

Mr. Peirce had perhaps in mind a special and more complex kind of explanation, which we define as “comprehension.” He says (p. 557):

“The fact to be explained is shown to follow as a consequence,
by virtue of a general principle or otherwise.”

Take as an instance the law of gravitation. There are the facts of falling stones and the motions of celestial bodies. Both sets of facts are explained, according to Mr. Peirce, “by virtue of a general principle,” i. e. gravitation, while we say, both sets of facts are comprehended under a common formula. Mr. Peirce’s conception of “explanation” rests on the antiquated view that gravitation is a principle behind the gravitating masses which compels the stone to fall. Gravitation, however, is not “another fact” foreign to the facts under consideration. It is not a principle called in from the outside. On the contrary, it is the essence and extract of the very facts that are to be explained.

Principles which have not been derived either from the facts to be explained, or from the additional facts which belong to their system, do not and cannot explain the phenomena.

* * * * *

Comprehension is, as it were, an explanation of a higher degree. The term means a grasping together, and it actually consists in viewing two or several facts in such a way as to recognise their common features. Comprehension is a reduction of our patterns of explanation; it unites two or several of them in one formula.

For instance, it has been observed that certain objects float in water while others sink to the bottom. The observations do not seem to agree, they present two incoherent facts. When we find out that the weight of a floating body is equal to the weight of water which it displaces, we understand at once why bodies whose specific gravity is greater than water sink while those of a lighter specific gravity float. Comprehension, in this as in every other case, is the description of a process which comprises all the facts that belong to a special class in a common formula. The description must be applicable to all single cases however different they may be.

This conception of comprehension has a great advantage over Mr. Peirce’s view. While he has to bring in some “other fact” from the outside, we need not introduce any foreign element. Comprehension, as we understand it, can rise from the statement of particular facts to more and more general formulations, until finally we arrive at universal laws. All the laws thus formulated to satisfy our cravings for comprehension, are found to belong to one great system of laws, and our scientists are constantly engaged not only in widening the range of our experience by new discoveries, but also in revising our statements of the uniformities of nature and, where they appear to be in collision, in bringing them into harmony.

This conception of comprehension is monistic, Mr. Peirce’s is dualistic. We need not, in order to explain the facts of existence, go beyond them into a supernatural realm. Mr. Peirce must go outside of the world into non-existence when he attempts to understand the world by the principles of his philosophy. It is very doubtful whether explanations, the “essential” nature of which is to consist of “other facts usually hypothetical,” will be satisfactory to anybody except himself.

Otherness makes any fact unfit to serve as a factor of an explanation and indeed I cannot think of any instance, real or imaginary, in which the explanatory facts, be they real or hypothetical, do not form parts of the system under consideration.

There is only one instance to which Mr. Peirce’s method of explanation has been applied, and I am under the impression that it has been invented solely for this purpose. Mr. Peirce’s philosophy is too original to be explained by the usual methods; it must have an original method of its own. In order to explain “law” Mr. Peirce calls in “chance.” His explanation must be an “other fact” and the only fact different from law is not-law, lawlessness, or absolute chance. According to my idea of explanation, law can never be explained by chance. According to Mr. Peirce, it is the only possible thing that can be called in as that “_other_ fact” which is supposed to be the essential constituent of an explanation.

If Mr. Peirce’s method of explanation were sound, we should have to explain order from chaos, possibility from impossibility, and sense from nonsense.

II. MR. PEIRCE’S PHILOSOPHY.

Mr. Peirce’s constant references to scholastic philosophy remind me of happy years long past when I was extremely interested in the theories of such men as Thomas Aquinas, Duns Scotus, Occam, Abelard, Tauler, and others. Together with my chum, now a sober Professor of physics at a German University, I freely indulged in the construction of various world-theories, which, alas! were quickly overthrown one after another by the slightest puff of wind. I have not lost my interest in the schoolmen, but it is considerably weakened.

Mr. Peirce’s repeated praise of scholastic realism and his condemnation of any theory that he brands as nominalistic, seems to me like the method of some of our politicians who, eager to revive toryism, should censure all evils of the politics of to-day as whiggish. This comparison is not exaggerated, for there are a few Hamiltonians who miss the refining influence of an aristocratic class and regret that the historical tradition of toryism has been so completely broken. I would not deny that there is some truth in it, and there is some truth, too, in mediæval realism, which has been neglected by the, first violently suppressed and then triumphant, nominalism. But in reviving realism the Scotists should be very careful to avoid a resurrection of its errors.

1. DUNS SCOTUS AS A PHILOSOPHICAL PATRON SAINT.

Johannes Duns Scotus, a Franciscan, honored since his successful defense of the Blessed Virgin’s Immaculate Conception by the title Doctor Subtilis, and the very same man after whom, on account of the narrowness of his later disciples during the time of the Reformation, a blockhead is to-day called a dunce, was one of the most characteristic figures of scholastic philosophy. He lived at the end of the thirteenth Century when the authority of the philosophy of Thomas Aquinas who had died March 7th, 1274, was all but universally recognised. Scotus appeared as the most powerful opponent of Thomas. Ingenious, original, bold, and buoyant in his attacks he had a short but brilliant career and died comparatively young at Cologne, in November, 1308.

While Thomas, surnamed Dr. Universalis, or Dr. Angelicus, is regarded by his order, the Dominicans, as the greatest authority in philosophical matters, Scotus succeeded in impressing his mode of thought upon the Franciscans; yet Thomas is universally regarded in the Roman church and also among Protestant theologians as the more orthodox Christian.

Almost all the ideas of Scotus were set forth in opposition to the views of others and mainly of Thomas. Thomas was a determinist, Scotus an outspoken indeterminist. Thomas says that man’s action is necessarily determined by what he thinks is best. Scotus avers that man thinks in a certain way because he wills in a certain way. Man’s ideas are fashioned to suit his character. His motto is, “_voluntas superior est intellectu_” and his idea of will is identified with the indetermined arbitrariness of a perfect _liberum arbitrium_. According to Thomas, God commands us to do the good because it is good. Scotus calls good that which God commands simply because God commands it. The will of God, like the will of man is, in Scotus’s opinion, undetermined, it is arbitrary. Thus God created the world not because his will was determined by some motive, but because it so pleased him; and Christ’s passion and death were not really an atonement; they simply were accepted as such by God.

Without entering into this controversy of _anno olim_ we might say that we side neither with Thomas nor with Scotus, but would modify the statement of the former by the criticism of the latter. Thomas goes too far when he says that whatever is recognised as the best will of necessity be done. He overlooks the power of passions. Thomas’s statement would be right, if every passion were regarded as a will which has its own and independent but mistaken ideas about good. A soul whose passions are more powerful than rational considerations will necessarily be inclined to obey its irrational impulses. There is something in Scotus’s criticism, but his view is no improvement. In speaking of will as superior to the intellect, did he ever ask himself the question, What his own will would be independent of his intellect? Further, when God is said to command the good because it is good, Thomas separates in a logical consideration two ideas which are identical. Scotus is right in defining good as the will of God. From our standpoint we should say, the will of God, viz., the moral order of the universe, is of a definite kind which can be ascertained by experience. To speak of the will of God as good is an anthropomorphic expression. Good is that which agrees with the will of God; bad, that which opposes it. Suppose the moral order of the universe were different, goodness and badness would change with it.

We have sketched the views of Scotus only to show the points of contact between him and Mr. Peirce. Mr. Peirce is also an outspoken indeterminist. He identifies feeling with chance, and his free will is a _liberum arbitrium_. Mr. Peirce, like Scotus, also separates theology, and, with it, religion, from philosophy.[133] Scotus ridicules those who confound both, clearly indicating that he is aiming at Thomas, to whose fervent faith their conciliation was a matter of momentous and all important consequence. Scotus goes so far as to aver that something might be true in philosophy which is wrong in theology (see Ed. “Wadding” Fol. 4, p. 848)—a statement that to an honest searcher for truth must almost appear as frivolous.[134]

How much more imbued with true religiosity was his great namesake John Scotus Erigena the venerable founder of scholasticism when saying: “_Non est alia philosophia, i. e. sapientiae stadium, et alia religio_.”

2. MR. PEIRCE’S ORIGINAL THEORIES.

Mr. Peirce as a controversalist and critic is like Scotus, brilliant, versatile, and powerful. But he is more; he is also constructive.

Mr. Peirce’s style of architecture reminds us of neo-Platonism, and this is quite in harmony with Scotism, for Scotus, through Avicebron, derived many of his ideas from the Neo-Platonists. Mr. Peirce proposes a modern view of emanation, which starts the world from that βῦθος of nothingness which at the same time is the womb of all existence. The primeval state of being, says Mr. Peirce, “Was mere nothing from a physical aspect,” but, if it was not really nothing, what, then, was it?

It was chance.

Here lies the essential difference between Mr. Peirce and the neo-Platonists. The neo-Platonists (whose speculations, if they are treated not as philosophy, but as poetical effusions, are very profound and thoughtful) look to the Logos, or world-reason, as the beginning of the world emanation, while Mr. Peirce shows a certain contempt for reason. To the neo-Platonist, reasons _are_ explanations, while to our modern Scotist, reasons explain nothing. He says:

“Reasons explain nothing, except upon some theistic hypothesis
which may be pardoned to the yearning heart of man, but must be
doubtful in the eyes of philosophy....” (P. 567.)

Mr. Peirce goes so far as to speak of “the dullness of ratiocination’s self.”

Mr. Peirce’s gospel would deviate in the very first verse from that of St. John, for it would read

Ἐν ἀρχῇ ἦν ἡ τυχή.—In the Beginning was Chance!

And this chance which was in the beginning actually is, to Mr. Peirce, God, a personal God, an anthropomorphic deity endowed with consciousness. He says:

“That primeval chaos in which there was no regularity was
mere nothing from a physical aspect. Yet it was not a blank
zero; for there was an intensity of consciousness there, in
comparison with which all that we ever feel is but as the
struggling of a molecule or two to throw off a little of the
force of law to an endless and innumerable diversity of chance
utterly unlimited.” (_The Monist_, Vol. III, No. 1, p. 19.)

And in another passage he says of chance:

“That it is a being living and conscious is what all the
dullness that belongs to ratiocination’s self can scarce muster
hardihood to deny.” (P. 560.)

Mr. Peirce’s argument that all the dullness that belongs to ratiocination’s self can scarcely muster hardihood to deny his proposition, sounds strange in the mouth of a scientist. But it is not strange; for I have found that enthusiastic defenders of improbable theories always fill the holes of their argumentation with abuse of those who dare to discover these holes. Call a person who doubts the truth of your statements dull, and you will frighten many a weak mind into a patient acceptance of your view.

We may rest assured that whenever a philosopher scolds he is at his wit’s end. For why should he lose patience if he can prove his proposition? Thus diatribes are always symptoms that there is some flaw in one’s logic and the louder one chides the sorer is the spot.

Mr. Peirce is serious in the statement that chance is a conscious being. He actually identifies chance and feeling. He says:

“Chance is but the outward aspect of that which within itself
is feeling.”

The primordial chance, the existence of which, according to Mr. Peirce, “calls for no explanation,” has “a primordial habit-taking tendency.” Whence this tendency gets into the universe of absolute chance, Mr. Peirce is unable to disclose. The deviations from the mechanical order in the present course of things, which, by the by, are by no means proved, suggest to him and justify, in his opinion, this assumption. Thus, assumes he, primordial chance ceased to be chance; it changed by a gradual habit-taking into regularities. Consciousness ceased to be consciousness and became crystallised into natural laws. Mind ceased to be an arbitrary sporting, and by becoming effete it begot, through a summation of minute effects, this material universe of ours. Accordingly, real existence or thing-ness consists merely in the regularities thus produced, and “physical events are but the degraded ... forms of psychical events.”

This is in brief Mr. Peirce’s cosmogony, which, as the prophet of Tychism, he reveals to us in axiomatic aphorisms.

By gradual habit-taking, Mr. Peirce declares (_The Monist_, Vol. I, No. 2, p. 176), mind will at last be “crystallised in the infinitely distant future.” This rather sad outlook is, in another passage, modified by a counter-oracle, which announces that “an element of pure chance survives.” Why, he does not say. Irregularities, not being entirely suppressed, can increase again, and as such they are “undeveloped forms of psychical events.” Says Mr. Peirce (_The Monist_, Vol. III, No. 1, p. 18):

“There are almost insensible fortuitous departures from
regularity; these will produce, in general, equally minute
effects.... Protoplasm is in an excessively unstable
condition.... In the protoplasm these habits are to some slight
extent broken up, so that, according to the law of mind, ...
feeling becomes intensified.

“This breaking up of habit and renewed fortuitous spontaneity
will, according to the law of mind, be accompanied by an
intensification of feeling.”

This is the gist of Mr. Peirce’s mental philosophy, which proclaims that “consciousness is not to be reinstated without tychism.” The reappearance of chance is said to explain the origin of mind!

Our conception of mind is different. We see mind develop out of sentiency by the recognition of the regularities of the surrounding world. Reason is almost a synonym of man’s ability to form generalisations, of his having and operating with concepts, of his thinking ideas. Not the arbitrariness of a wilful mind is the properly mental of man’s soul, but his reason; and man’s reason originates under the influence of the uniformities of the surrounding world, which impress themselves, in what we call experience, upon his existence. The more a creature recognises the regularities of existence, and the more its soul becomes an image of this world-order, which is the prototype of his reason, of the divine Logos, the higher it rises in the scale of evolution.

If chance, as Mr. Peirce declares, is but the outward aspect of that which within is feeling, we should henceforth have to look upon the roulette and dice as sentient beings.

3. THE FOUR POSITIVE ARGUMENTS OF TYCHISM INSUFFICIENT.

Mr. Peirce adduces four positive arguments for believing in absolute chance. They are: (1) the prevalence of growth; (2) the variety of the universe; (3) the necessity of explaining law; and (4) the existence of feeling.

By growth, Mr. Peirce does not understand the growth of crystals, or trees, or organisms. That kind of growth is a mere transformation. Mr. Peirce’s idea of “real” growth is “opposed to the conservation of energy.” It is not an increase of the thing growing through the assimilation of substances taken from the surrounding world; it is an actual increase of energy, not a mere change; it is a growth of the universe itself. Granted the possibility of this so-called “real” growth, and we can easily explain the evolution of the world out of the tiniest beginning. But, of course, one thing has to go: either the conservation of energy or “real growth.” Mr. Peirce lets go the former, I the latter.[135]

The variety of the universe is, in my world-conception, sufficiently explained by the variety of forms, for form is indeed the _principium individuationis_; a doctrine, which, but for Mr. Peirce’s philosophy, I should regard as almost universally accepted. Among its advocates we find also Mr. Peirce’s great master, Duns Scotus, and Scotus’s teacher, Avicebron. In so far as various formations are possible, (exactly as the die can show six different surfaces,) chance plays an important part in the diversification of nature, but this chance is not to be thought of as a violation of the law, but appears to be a special case only, and a true manifestation of the law under complicated conditions.

Chance and probability are not mere subjective ideas, creatures of our ignorance, playing a rôle simply in our limited knowledge of the world. The words signify a certain condition of objective existence.

For instance, the probability of throwing 1 with one die is 1/6. This means, the die is so constructed that it can show six different positions, one among them being 1; and these six possibilities are as real a quality of the die, as its weight or its color.

The die has six possible positions. Now I take a die and throw 3. Are we not entitled to believe that the throw was sufficiently determined by all the innumerable conditions which accompany the act? We confidently think so, and feel no need of assuming any absolute chance. Now I throw again. What is now the probability of throwing 1? We answer again, 1/6. And, lo! there it is! It came at the second throw, and we ask, was our statement of the probabilities wrong? We say, no! it was not wrong, for it remains true even now. The statement does not mean that we shall throw a 1 at each sixth throw, but that (supposing the die to be perfect) 1/6 among all the possible throws will be 1, so that supposing all the possible throws realised in an infinite series of throws, the average number of 1’s among them will be the one-sixth part of the whole.

The enormous importance of chance (viz., of that real chance which is no violation of the law) has been recognised since Democritus and has received a fresh illustration from the investigations of Darwin, which I need not here recapitulate.

The theory of probabilities teaches, that whatever can happen in the long course of an infinite number of events, actually will happen, and that whatever, according to the nature of things, has a greater probability, will in an infinite number of cases occur with proportionately greater frequency.

The lesson which we have to draw from this statement is, that that which we wish not to happen, should be made impossible. And this can be done, perhaps not perfectly, but approximately. According to Mr. Peirce, the evolution of mind is due to the reappearance of chance; we say that the evolution of mind is marked by man’s increasing power in the restriction of chance.

The identification of chance with feeling, or even with mind, is to me an idea so grotesque, that I am inclined to regard it as a relic of gnostic speculations.

Mr. Peirce, instead of attempting to comprehend laws, as we do, seeks to trace their origin. He tries to explain their existence by growth, as if they were beings that evolve like the forms of planetary systems or the organisms of living creatures. Considering the fact that Mr. Peirce is a realist only in name, and that his philosophy is soaked with nominalistic traditions, we should say (and Mr. Peirce will pardon me that I quote the expression from him) that:

“The puzzle for him is simply the usual difficulty that plagues
nominalism when it finds itself confronted with a reality which
has an element of generality.”

The assumption of absolute chance might be used to account for any otherwise inexplicable event, but Mr. Peirce does not countenance this idea. He warns us to be cautious in its use, like the druggist who labels his poisons “handle with care”; “I only use chance,” he says, “to give room for the development of law.” Having used absolute chance to start the world with, he dismisses it. So Fiesco discharges his negro after he has done his work: “_Der Mohr hat seine Schuldigkeit gethan, der Mohr kann gehen_.”

In my criticism of Mr. Peirce’s theory I said (_The Monist_, II, p. 574):

“How little, after all, we can escape the determinism of law as
being a feature of the world, will be seen from the fact that
the explanation for the evolution of law is presented by Mr.
Peirce as being itself a law, i. e., a formula describing a
regularity supposed to obtain in facts.”

Mr. Peirce replies:

“Is there no difference between a law, the essence of which
is to be inviolable ... and _that mental law, the violation
of which is so included in the essence that unless it were
violated, it would cease to exist_?... Thus I clearly escape
the contradiction attributed to me.” (P. 561.)

Mr. Peirce’s escape is like the disappearance of a medium from a room without doors. He must have got out through the fourth dimension. The argument is so subtle that I cannot see it, and I feel tempted to retort in a sentence quoted from my profound adversary:

“I confess, I can find only words without ideas in the
objection.” (P. 561.)

Mr. Peirce speaks of law as having developed out of chance, but he himself, in fact, after a fashion, explains the origin of those laws of nature which represent its present uniformities by a law of habit-taking.

That the conservation of energy should leave no room for feeling is to me an obscure proposition. The law of the conservation of energy declares only that the sum of all energy in the world, potential as well as kinetic, remains constant. If a living and feeling being renews its waste and stores up new energy in its tissues, it must take it out of the general storehouse of nature; it must transform it, and cannot produce it out of nothing. Why should feeling become impossible, if the conservation of energy is true?

The identification of chance with feeling is, to my mind, a vagary. It is true that feeling develops mind; mind makes deliberation possible, and deliberation implies choice. But choice is not chance. The choice which a man makes is determined by his character. There is more resemblance between logical identity and a pun, than between feeling and chance.

4. THE NEGATIVE ARGUMENT A LOGICAL FALLACY.

The four positive arguments for believing in absolute chance are untenable. But Mr. Peirce, knowing that he had to weather a storm of criticisms, has taken along a sheet-anchor, consisting of a negative argument, which, if it were true, would make the four positive arguments redundant.

What shall we say to the statement, that chance need not be explained? Mr. Peirce says:

“Chance, according to me, or irregularity—that is, the absence
of any coincidence,—calls for no explanation. If _law_ calls
for explanation, as Dr. Carus admits it does, surely the
mere absence of law calls for no further explanation than is
afforded by the mere absence of any particular circumstance
necessitating the result.” (P. 559.)

Mr. Peirce is a great logician, but the logical arguments of his philosophy are not sound. If the absence of law, of coincidences, of regularities, did not require explanation, the scientist would (as is but right) still have to explain the uniformities of nature, but the miracle monger would have a good time; for he could tell us boldly that, according to the rules of modern logic he is not bound to give any explanation.

It is true that while everything must be explained, the absence of everything (i. e. nothing) need not be explained; but we cannot use this pattern as a schedule which can be filled out at our pleasure. The ideas “absence of,” “no,” “no one,” and “nothing” play a part in logic analogous to that of zero in mathematics. I need hardly remind the reader of the puzzling demonstration, that since one cat has one tail more than _no_ cat, and since no cat has eight tails, one cat must have nine tails. Operations with zero act like death in the realm of human conventionalities. Death makes the beggar equal to the king. Multiply any equation that is wrong with zero, and it will be correct. Operations with zero render the impossible possible.

But let us look closer at Mr. Peirce’s proposition. He avers that “the mere absence of any particular circumstance necessitating the result calls for no explanation.”

Should it ever happen that the absence of any particular circumstance necessitates the result, I do not see why this absence should remain unexplained. Say for instance, a certain stronghold is taken because the enemy discovers the absence of guards in a certain part of the walls. If this absence of guards be counted as an important circumstance helpful in the conquest of the citadel (and there is no reason why we should not count it as such) can we say that while the presence of guards on all other spots of the wall has to be and can be explained as an endeavor to secure the place against a _coup de main_, the mere absence of guards calls for no explanation? The absence of guards in a particular spot of the Capitol during the siege by the Gauls, was accounted for by the steepness of the place. This particular spot was regarded as safe on account of its inaccessibility. Similarly, the absence of guards in the citadel of the Messenians is explained by the idea that the Spartans would make no attack because in that particularly stormy night a cloudburst seemed to prevent all approach.

Obviously the necessity of explaining a rule, does not confer the privilege of neglecting to explain its exceptions.

It goes without saying that Mr. Peirce’s argument (even if it were formally faultless) can have no force with a necessitarian. Such a one, after having explained and proved to his satisfaction that _Gesetzmässigkeit_ (or regularity such as can be formulated in laws) is a characteristic feature of the universe, is not only asked to believe that there are after all exceptions to law, but is even told that according to some paragraph in Mr. Peirce’s unwritten logic of relatives no further argument is needed to prove the non-existence of law. Only Mr. Peirce’s extreme love of his pet theories can make him blind to such palpable fallacies. But such are the foundations of his philosophical architecture.

III. MR. PEIRCE AS A CRITIC.

A good general, who has to mask the weak points of his position, uses the strategem of making demonstrative sallies upon his enemy. Mr. Peirce, although apparently quite unconscious of the fact that his basic doctrines are untenable, instinctively imitates this maxim of warfare. His defence is mostly aggressive. Instead of replying to my arguments he endeavors to represent my views as incohesive and contradictory.

The present issue is not whether my views are tenable, but whether Mr. Peirce’s are. However, I am glad to have the benefit of the searching criticism of so subtle a thinker as Mr. Peirce. Therefore, I willingly appear before his tribunal to expurgate myself of his charges.

1. THE A PRIORI AND POSITIVISM.

Mr. Peirce is greatly puzzled with my position. He quotes several statements of mine which appear to him contradictory. I said: (1) that millions of _single_ experiences cannot establish a belief in necessity, (2) that necessitarianism must be founded upon the _a priori_, and (3) that the _a priori_ must be founded upon experience.[136] To him who overlooks the here italicised word “single” this may, indeed, seem to be a vicious circle.

All knowledge begins with experience. We define experience as the effects of events upon sentient beings, and these effects are sense-impressions of certain forms and interrelations. At an advanced stage of evolution, the formal and relational are first unconsciously, as, for instance, in counting, and then consciously, with scientific deliberation, abstracted from the sensory. Systems of pure forms are constructed out of the purely formal elements, thus gained from experience by abstraction, such as our system of numbers and the logical categories. Now the laws of these forms of thought are applicable to all formal and relational conditions of reality. The formal and relational of reality are known to us even in those regions of the universe and in those provinces of scientific investigation which have not as yet been explored. The scientist knows them _a priori_, even before he investigates objects which he never saw before. He is acquainted with certain of their qualities, viz., with the laws of their formal and relational conditions.

Thus the _a priori_, or, as I prefer to call it, formal thought, is a product of experience, and is again applicable to experience.

Single experiences, isolated observations, innumerable particular cases cannot directly yield or reveal the laws of formal thought. So long as they remain single and isolated they will never develop into mental factors; but such is the nature of reality that the single experiences will be built up and arranged in feeling substance as systematically as, for instance, the formation of crystals or the harmonious growth of cells in organisms? When sentient creatures become conscious not only of the sensory element of their experience, but also of this system of their soul, of the formal of their psychical existence, they become rational beings; and the formal which grows with their sentiency is not an exclusive and peculiar quality of theirs; it is not purely subjective, but it has been imparted to them, piecemeal, together with the single data of their experience. It constitutes a part of their _Anschauung_; it is found in the objective world and is a general feature of reality.

Out of the formal elements of our _Anschauungen_, of the facts of experience, that organ of cognition is developed which Kant calls “pure reason.”

Experience is often used to denote sense-experience only; thus Kant contrasts experience or sense-perception, which he calls _a posteriori_, with pure reason and formal thought, which he calls _a priori_. We use experience in the sense defined above, _so as to include the formal element_.

I am unable to form a clear conception of Mr. Peirce’s view of the _a priori_. Those systems of formal thought which I regard as constructions he regards as products of analysis. He says, “They are results dependent upon the action of reason in the depths of our own consciousness.” He only grants that “their abstract and distinct formulation comes very late.” He still holds that the _a priori_ is innate.

In my conception, mathematical ideas, like that of the contrivance of logarithms, are inventions; and they are constructions as much as the invention of the steam-engine by James Watt.

There is one peculiarity about the purely formal which is not found in the sensory elements of experience. Our knowledge of the various spheres of the purely formal is of a general nature; it applies to any form of the same kind. This gives system to our formal conceptions, and enables us to make statements which are rigidly and unequivocally determined. It is this quality which makes them available as an organ of cognition when dealing with facts of experience. They furnish us with methods, schedules of reference, and plans which like blanks have to be filled out.

Science begins with the application of formal thought, viz., with counting, measuring, and classifying. Only with the assistance of the formal sciences can we master the material of the sensory data of experience; and thus it happens that the formal is the condition, not of any kind of experience, but of every systematic experience.

The formal sciences are the tools of cognition. That to which they cannot be applied remains unexplained, and this is the ultimate reason why processes of nature can be regarded as explained only when recognised as processes of transformation. Cognition is the tracing of form. We can understand a change only if it is a change of form. We cannot understand how anything real can disappear into, or originate out of, nothing. We have no explanation for any actual increase or decrease either of matter or energy. Whenever we see something entirely new we regard it as a new combination, the elements of which existed before.

If there were processes in the universe which could positively be proved not to be transformations we should be confronted with an unfathomable mystery; and it is a matter of course that we must not be duped so easily by the appearance of problems which cannot be solved at first sight. The advance of science which has resolved so many mysterious phenomena into plain instances of transformation gives us confidence that this method is the only reliable maxim of inquiry. It has helped us so far, and it will help us in the future.

* * * * *

I call my views positivism, because like the French positivists and also like Locke and his school I maintain that all knowledge is to be derived from the positive facts of experience. But my positivism is not of the old kind; it is neither sensationalism nor materialism nor Comtism. It is a new positivism broadened by a study of Kantian philosophy and Kant’s problem of the _a priori_; and this new positivism, I hope, deserves the attention of the thinkers of mankind.

Mr. Peirce calls it a “straddling of the question,” by which he means that a man is “on both sides of the fence,” and has learned so to formulate the issues, “that both parties can readily subscribe to his propositions.”

2. DETERMINISM AND FATALISM.