Part 61

The most brilliant disciple of Duns Scotus was William of Occam, whose fame almost rivalled that of his master. Occam became an adversary of realism; he became a nominalist, and after him was named a method known as Occam’s razor, especially useful to nominalists in their warfare against realists.

Occam’s razor is expressed in the sentence: “_Entia non sunt multiplicanda præter necessitatem_,” which means: Only in cases of extremest necessity are we allowed to assume the existence of hypothetical facts. If assumed facts are not absolutely indispensable, cut them off!

Occam’s razor was invented for a special purpose, that of cutting off the realistic hypostatisation of abstract ideas.

I do not know which is more startling, that a realist in name, such as Mr. Peirce, should use a weapon forged by nominalists against realism, or that he whom in other respects we found in such a close contact with nominalistic methods, should not understand how to handle a nominalistic weapon.

Mr. Peirce censures me for making the statement that the formal is subjective as well as objective. This, he says, is cut off by Occam’s razor.

The formal is subjective, for our sensation is possessed of form and our mind is in possession of formal thought. It is objective, for reality is not void of form and the things are such as they are by virtue of their peculiar shape.

The proposition that the formal is objective and subjective at the same time is as little cut off by Occam’s razor as, for instance, the proposition that there is air inside and outside of us, viz. in our lungs and in the surrounding atmosphere.

Mr. Peirce’s usage of the beds of Procrustes is cruel, but his usage of Occam’s razor is inconsiderate. He should be careful in handling such a sharp knife, lest he do himself harm.

Mr. Peirce uses Occam’s razor to cut off statements and facts which make his pet theories dispensable; but he forgets that Occam’s razor cuts off ideas only, and when it comes in contact with facts its edge is turned.

Occam’s razor is an excellent instrument to dispose of such hypotheses as absolute chance, for it declares that if their assumption is not quite indispensable, we must cut them off.

Now it either is or is not a fact that the formal is objective and subjective at once. It cannot be untrue in my philosophy while it is true in Mr. Peirce’s system. My proposition of the formal being at once objective and subjective is, according to Mr. Peirce, “cut off by Occam’s razor.” “But,” adds he, “when synechism has united the two worlds this view gains new life.” So long as I say so, it is wrong; but should I adopt Mr. Peirce’s system, it will pass as right.

5. THE APPLICATION OF LEARNING.

Philosophers should make it a rule not to encumber their thoughts unnecessarily with learning. The great problems of philosophy are, in my opinion, much simpler than they are generally supposed to be. The art mainly consists in stating them in the simplest possible manner.

It is indispensable for a philosopher to be familiar, at least in a general way, with all the most important sciences, especially with psychology, physiology, logic, physics, mathematics, and mechanics. But he should not for that reason introduce any more than he can help their complicated details into his expositions.

Every specialist is inclined to look at things through the spectacles of his own speciality. But the philosopher who takes a higher standpoint should be on his guard. He should always endeavor to simplify matters and avoid introducing into philosophy issues which belong to a special field, and derive their peculiarities from special conditions. To confound the methods of the various sciences, or to generalise without sufficient discrimination, will throw everything into confusion.

Mr. Peirce, as we well know, has greatly distinguished himself in logic by valuable discoveries and independent investigations. We have repeatedly taken occasion to pronounce unreservedly our admiration of his achievements in this field. But we cannot approve of his application of certain methods of his speciality to philosophy in general. Mr. Peirce is inclined to look at the world through the spectacles of that new and extremely specialised branch of logic which he is at present about to invent.

One hindrance to properly appreciating his doctrines, says Mr. Peirce, lies in my “laboring under the great disadvantage of not understanding the logic of relatives,” which, he adds (p. 533):

“Is a subject I have been studying for a great many years, and I feel and know that I have an important report that I ought to make upon it. This branch of logic is, however, so abstruse that I have never been able to find the leisure to translate my conclusions into a form in which their significance would be manifest even to powerful thinkers, whose thoughts had not long been turned in that direction.”

I shall be glad to sit at Mr. Peirce’s feet as an attentive student, as soon as he has worked out his logic of relatives, or any other subject. But I cannot now accept any of his theories on the credit of some half-developed science, be it ever so profound or intricate, until I see plainly its connection with the present issues.

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.