Charles Sanders Peirce's Harvard Lectures

§1. TWO STATEMENTS OF THE PRAGMATIC MAXIM
14. A certain maxim of Logic which I have called Pragmatism has recommended itself to me for divers reasons and on sundry considerations. Having taken it as my guide in most of my thought, I find that as the years of my knowledge of it lengthen, my sense of the importance of it presses upon me more and more. If it is only true, it is certainly a wonderfully efficient instrument. It is not to philosophy only that it is applicable. I have found it of signal service in every branch of science that I have studied. My want of skill in practical affairs does not prevent me from perceiving the advantage of being well imbued with pragmatism in the conduct of life.

15. ... I propose, then, to submit to your judgment in half a dozen lectures an examination of the pros and cons of pragmatism by means of which I hope to show you the result of allowing to both pros and cons their full legitimate values.

16. I suppose I may take it for granted that you all know what pragmatism is. I have met with a number of definitions of it lately, against none of which I am much disposed to raise any violent protest. Yet to say exactly what pragmatism is describes pretty well what you and I have to puzzle out together.

We must start with some rough approximation of it, and I am inclined to think that the shape in which I first stated [it] will be the most useful one to adopt as matter to work upon, chiefly because it is the form most personal to your lecturer, and [upon] which for that reason he can discourse most intelligently. Besides pragmatism and personality are more or less of the same kidney.

17. I sent forth my statement in January 1878; and for about twenty years never heard from it again. I let fly my dove; and that dove has never come back to me to this very day. But of late quite a brood of young ones have been fluttering about, from the feathers of which I might fancy that mine had found a brood. To speak plainly, a considerable number of philosophers have lately written as they might have written in case they had been reading either what I wrote but were ashamed to confess it, or had been reading something that some reader of mine had read. For they seem quite disposed to adopt my term pragmatism. I shouldn't wonder if they were ashamed of me. What could be more humiliating than to confess that one has learned anything of a logician? But for my part I am delighted to find myself sharing the opinions of so brilliant a company. The new pragmatists seem to be distinguished for their terse, vivid and concrete style of expression together with a certain buoyancy of tone as if they were conscious of carrying about them the master key to all the secrets of metaphysics.

Every metaphysician is supposed to have some radical fault to find with every other, and I cannot find any direr fault to find with the new pragmatists than that they are lively. In order to be deep it is requisite to be dull.

18. On their side, one of the faults that I think they might find with me is that I make pragmatism to be a mere maxim of logic instead of a sublime principle of speculative philosophy. In order to be admitted to better philosophical standing I have endeavored to put pragmatism as I understand it into the same form of a philosophical theorem. I have not succeeded any better than this:
Pragmatism is the principle that every theoretical judgment expressible in a sentence in the indicative mood is a confused form of thought whose only meaning, if it has any, lies in its tendency to enforce a corresponding practical maxim expressible as a conditional sentence having its apodosis in the imperative mood.

But the Maxim of Pragmatism, as I originally stated it, Revue philosophique VII, is as follows:
Considérer quels sont les effets pratiques que nous pensons pouvoir être produits par l'objet de notre conception. La conception de tous ces effets est la conception complète de l'objet. [p. 48.]
Pour développer le sens d'une pensée, il faut donc simplement déterminer quelles habitudes elle produit, car le sens d'une chose consiste simplement dans les habitudes qu'elle implique. Le caractère d'une habitude dépend de la façon dont elle peut nous faire agir non pas seulement dans telle circonstance probable, mais dans toute circonstance possible, si improbable qu'elle puisse être. Ce qu'est une habitude dépend de ces deux points: quand et comment elle fait agir. Pour le premier point: quand? tout stimulant à l'action dérive d'une perception; pour le second point: comment? le but de toute action est d'amener au résultat sensible. Nous atteignons ainsi le tangible et le pratique comme base de toute différence de pensée, si subtile qu'elle puisse être. [p. 47.]

§2. THE MEANING OF PROBABILITY
19. The utility of the maxim, provided it is only true, appears in a sufficient light in the original article. I will here add a few examples which were not given in that paper.

There are many problems connected with probabilities which are subject to doubt. One of them, for example, is this: Suppose an infinitely large company of infinitely rich men sit down to play against an infinitely rich bank at a game of chance, at which neither side has any advantage, each one betting a franc against a franc at each bet. Suppose that each player continues to play until he has netted a gain of one franc and then retires, surrendering his place to a new player.

The chance that a player will ultimately net a gain of a franc may be calculated as follows:

Let XL be a player's chance, if he were to continue playing indefinitely, of ever netting a gain of 1 franc.

But after he has netted a gain of 1 franc, his chance of doing which is X[1], he is no richer than before, since he is infinitely rich. Consequently his chance of winning the second franc, after he has won the first, is the same as his chance of winning the first franc. That is, it is X[1] and his chance of winning both is X[2] = (X[1])2. And so in general, X[L] = (X[1])L.

Now his chance of netting a gain of 1 franc, X[1], is the sum of the chances of the two ways in which it may come about; namely by first winning the first bet of which the chance is 1/2, and by first losing the first bet and then netting a gain of 2 francs of which the chance is 1/2 X[1]2. Therefore

X[1] = 1/2 + 1/2 X[1]2
or X[1]2 - 2X[1] + 1 = 0
or (X[1] - 1)2 = 0.

But if the square of a number is zero, the number itself is zero. Therefore

X[1] - 1 = 0
or X[1] = 1.

Consequently, the books would say it was dead certain that any player will ultimately net his winning of a franc and retire. If so it must be certain that every player would win his franc and would retire.

Consequently there would be a continual outflow of money from the bank. And yet, since the game is an even one, the banker would not net any loss. How is this paradox to be explained?

20. The theory of probabilities is full of paradoxes and puzzles. Let us, then, apply the maxim of pragmatism to the solution of them.

In order to do this, we must ask What is meant by saying that the probability of an event has a certain value, p? According to the maxim of pragmatism, then, we must ask what practical difference it can make whether the value is p or something else. Then we must ask how are probabilities applied to practical affairs. The answer is that the great business of insurance depends upon it. Probability is used in insurance to determine how much must be paid on a certain risk to make it safe to pay a certain sum if the event insured against should occur. Then, we must ask how can it be safe to engage to pay a large sum if an uncertain event occurs. The answer is that the insurance company does a very large business and is able to ascertain pretty closely out of a thousand risks of a given description how many in any one year will be losses. The business problem is this. The number of policies of a certain description that can be sold in a year will depend on the price set upon them. Let p be that price, and let n be the number that can be sold at that price, so that the larger p is, the smaller n will be. Now n being a large number a certain proportion q of these policies, qn in all, will be losses during the year; and if I be the loss on each, qnl will be the total loss. Then what the insurance company has to do is to set p at such a figure that pn-qln or (p-ql)n shall reach its maximum possible value.

The solution of this equation is:

21. This is the problem of insurance. Now in order that probability may have any bearing on this problem, it is obvious that it must be of the nature of a real fact and not a mere state of mind. For facts only enter into the solution of the problem of insurance. And this fact must evidently be a fact of statistics.

Without now going into certain reasons of detail that I should enter into if I were lecturing on probabilities, it must be that probability is a statistical ratio; and further, in order to satisfy still more special conditions, it is convenient, for the class of problems to which insurance belongs, to make it the statistical ratio of the number of experiential occurrences of a specific kind to the number of experiential occurrences of a generic kind, in the long run.

In order, then, that probability should mean anything, it will be requisite to specify to what species of event it refers and to what genus of event it refers.

It also refers to a long run, that is, to an indefinitely long series of occurrences taken together in the order of their occurrence in possible experience.

In this view of the matter, we note, to begin with, that a given species of event considered as belonging to a given genus of events does not necessarily have any definite probability. Because [it may be the case that] the probability is the ratio of one infinite multitude to another. Now infinity divided by infinity is altogether indeterminate, except in special cases.

22. It is very easy to give examples of events that have no definite probability. If a person agrees to toss up a cent again and again forever and beginning as soon as the first head turns up whenever two heads are separated by any odd number of tails in the succession of throws, to pay 2 to that power in cents, provided that whenever the two successive heads are separated by any even number of throws he receives 2 to that power in cents, it is impossible to say what the probability will be that he comes out a winner. In half of the cases after the first head the next throw will be a head and he will receive (-2)0 = 1 cent. Which since it happens half the time will be in the long run a winning of 1/2 a cent per head thrown.

But in half of the other half the cases, that is in 1/4 of all the cases, one tail will intervene and he will have to receive (-2)1 = -2 cents, i.e., he will have to pay 2 cents, which happening 1/4 of the time will make an average loss of 1/2 a cent per head thrown.

But in half the remaining quarter of the cases, i.e., of all the cases, two tails will intervene and he will receive (-2)2 = 4 cents which happening one every eight times will be worth 1/2 a cent per head thrown and so on; so that his account in the long run will be 1/2-1/2+1/2-1/2+1/2-1/2+1/2-1/2 ad infinitum, the sum of which may be 1/2 or may be zero. Or rather it is quite indeterminate.

If instead of being paid (-2)n when n is the number of intervening tails, he were paid (-2)n2 the result would be he would probably either win or lose enormously without there being any definite probability that it would be winning rather than losing.

I think I may recommend this game with confidence to gamblers as being the most frightful ruin yet invented; and a little cheating would do everything in it.

23. Now let us revert to our original problem and consider the state of things after every other bet. After the second, 1/4 of the players will have gained, gone out, and been replaced by players who have gained and gone out, so that a number of francs equal to half the number of seats will have been paid out by the bank, 1/4 of the players will have gained and gone out and been replaced by players who have lost, making the bank even; 1/4 of the players will have lost and then gained, making the bank and them even; 1/4 of the players will have lost twice, making a gain to the bank of half as many francs as there are seats at the table. The bank then will be where it was. Players to the number of three-quarters of the seats will have netted their franc each; but players to the number of a quarter of the seats will have lost two francs each and another equal number one franc each, just paying for the gains of those who have retired. That is the way it will happen every time.

Just before the fifth bet of the players at the table, 3/8 will have lost nothing, 1/4 will have lost one franc, 1/4 two francs, 1/16 three francs and 1/16 four francs. Thus some will always have lost a good deal. Those who sit at the table will among them always have paid just what those who have gone out have carried away.

24. But it will be asked: How then can it happen that all gain? I reply that I never said that all would gain, I only said that the probability was 1 that anyone would ultimately gain his franc. But does not probability 1 mean certainty? Not at all, it only means that the ratio of the number of those who ultimately gain to the total number is 1. Since the number of seats at the table is infinite the ratio of the number of those who never gain to the number of seats may be zero and yet they may be infinitely numerous. So that probabilities 1 and 0 are very far from corresponding to certainty pro and con.

§3. THE MEANING OF "PRACTICAL" CONSEQUENCES
25. If I were to go into practical matters, the advantage of pragmatism, of looking at the substantial practical issue, would be still more apparent. But here pragmatism is generally practised by successful men. In fact, the genus of efficient men [is] mainly distinguished from inefficient precisely by this.

26. There is no doubt, then, that pragmatism opens a very easy road to the solution of an immense variety of questions. But it does not at all follow from that, that it is true. On the contrary, one may very properly entertain a suspicion of any method which so resolves the most difficult questions into easy problems. No doubt Ockham's razor is logically sound. A hypothesis should be stripped of every feature which is in no wise called for to furnish an explanation of observed facts. Entia non sunt multiplicanda praeter necessitatem; only we may very well doubt whether a very simple hypothesis can contain every factor that is necessary. Certain it is that most hypotheses which at first seemed to unite great simplicity with entire sufficiency have had to be greatly complicated in the further progress of science.

27. What is the proof that the possible practical consequences of a concept constitute the sum total of the concept? The argument upon which I rested the maxim in my original paper was that belief consists mainly in being deliberately prepared to adopt the formula believed in as the guide to action. If this be in truth the nature of belief, then undoubtedly the proposition believed in can itself be nothing but a maxim of conduct. That I believe is quite evident.

28. But how do we know that belief is nothing but the deliberate preparedness to act according to the formula believed?

My original article carried this back to a psychological principle. The conception of truth, according to me, was developed out of an original impulse to act consistently, to have a definite intention. But in the first place, this was not very clearly made out, and in the second place, I do not think it satisfactory to reduce such fundamental things to facts of psychology. For man could alter his nature, or his environment would alter it if he did not voluntarily do so, if the impulse were not what was advantageous or fitting. Why has evolution made man's mind to be so constructed? That is the question we must nowadays ask, and all attempts to ground the fundamentals of logic on psychology are seen to be essentially shallow.

29. The question of the nature of belief, or in other words the question of what the true logical analysis of the act of judgment is, is the question upon which logicians of late years have chiefly concentrated their energies. Is the pragmatistic answer satisfactory?

Do we not all perceive that judgment is something closely allied to assertion? That is the view that ordinary speech entertains. A man or woman will be heard to use the phrase, "I says to myself." That is, judgment is held to be either no more than an assertion to oneself or at any rate something very like that.

30. Now it is a fairly easy problem to analyze the nature of assertion. To find an easily dissected example, we shall naturally take a case where the assertive element is magnified -- a very formal assertion, such as an affidavit. Here a man goes before a notary or magistrate and takes such action that if what he says is not true, evil consequences will be visited upon him, and this he does with a view to thus causing other men to be affected just as they would be if the proposition sworn to had presented itself to them as a perceptual fact.

We thus see that the act of assertion is an act of a totally different nature from the act of apprehending the meaning of the proposition and we cannot expect that any analysis of what assertion is (or any analysis of what judgment or belief is, if that act is at all allied to assertion), should throw any light at all on the widely different question of what the apprehension of the meaning of a proposition is.

31. What is the difference between making an assertion and laying a wager? Both are acts whereby the agent deliberately subjects himself to evil consequences if a certain proposition is not true. Only when he offers to bet he hopes the other man will make himself responsible in the same way for the truth of the contrary proposition; while when he makes an assertion he always (or almost always) wishes the man to whom he makes it to be led to do what he does. Accordingly in our vernacular "I will bet" so and so, is the phrase expressive of a private opinion which one does not expect others to share, while "You bet" is a form of assertion intended to cause another to follow suit.

32. Such then seems at least in a preliminary glance at the matter to be a satisfactory account of assertion. Now let us pass to judgment and belief. There can, of course, be no question that a man will act in accordance with his belief so far as his belief has any practical consequences. The only doubt is whether this is all that belief is, whether belief is a mere nullity so far as it does not influence conduct. What possible effect upon conduct can it have, for example, to believe that the diagonal of a square is incommensurable with the side? Name a discrepancy e no matter how small, and the diagonal differs from a rational quantity by much less than that. Professor Newcomb in his calculus and all mathematicians of his rather antiquated fashion think that they have proved two quantities to be equal when they have proved that they differ by less than any assignable quantity. I once tried hard to make Newcomb say whether the diagonal of the square differed from a rational fraction of the side or not; but he saw what I was driving at and would not answer. The proposition that the diagonal is incommensurable has stood in the textbooks from time immemorial without ever being assailed and I am sure that the most modern type of mathematician holds to it most decidedly. Yet it seems quite absurd to say that there is any objective practical difference between commensurable and incommensurable.

33. Of course you can say if you like that the act of expressing a quantity as a rational fraction is a piece of conduct and that it is in itself a practical difference that one kind of quantity can be so expressed and the other not. But a thinker must be shallow indeed if he does not see that to admit a species of practicality that consists in one's conduct about words and modes of expression is at once to break down all the bars against the nonsense that pragmatism is designed to exclude.

What the pragmatist has his pragmatism for is to be able to say: here is a definition and it does not differ at all from your confusedly apprehended conception because there is no practical difference. But what is to prevent his opponent from replying that there is a practical difference which consists in his recognizing one as his conception and not the other? That is, one is expressible in a way in which the other is not expressible.

Pragmatism is completely volatilized if you admit that sort of practicality.

§4. THE RELATIONS OF THE NORMATIVE SCIENCES
34. It must be understood that all I am now attempting to show is that Pragmatism is apparently a matter of such great probable concern, and at the same time so much doubt hangs over its legitimacy, that it will be well worth our while to make a methodical, scientific, and thorough examination of the whole question, so as to make sure of our ground, and obtain some secure method for such a preliminary filtration of questions as pragmatism professes to furnish.

Let us, then, enter upon this inquiry. But before doing so let us mark out the proposed course of it. That should always be done in such cases, even if circumstances subsequently require the plan to be modified, as they usually will.

Although our inquiry is to be an inquiry into truth, whatever the truth may turn out to be, and therefore, of course, is not to be influenced by any liking for pragmatism or any pride in it as an American doctrine, yet still we do not come to this inquiry, any more than anybody comes to any inquiry, in that blank state that the lawyers pretend to insist upon as desirable, though I give them credit for enough common-sense to know better.

35. We have some reason already to think there is some truth in pragmatism although we also have some reason to think that there is something wrong with it. For unless both branches of this statement were true we should do wrong to waste time and energy upon the inquiry we are undertaking.

I will, therefore, presume that there is enough truth in it to render a preliminary glance at ethics desirable. For if, as pragmatism teaches us, what we think is to be interpreted in terms of what we are prepared to do, then surely logic, or the doctrine of what we ought to think, must be an application of the doctrine of what we deliberately choose to do, which is Ethics.

36. But we cannot get any clue to the secret of Ethics -- a most entrancing field of thought but soon broadcast with pitfalls -- until we have first made up our formula for what it is that we are prepared to admire. I do not care what doctrine of ethics be embraced, it will always be so. Suppose, for example, our maxim of ethics to be Pearson's that all our action ought to be directed toward the perpetuation of the biological stock to which we belong. Then the question will arise, On what principle should it be deemed such a fine thing for this stock to survive -- or a fine thing at all? Is there nothing in the world or in posse that would be admirable per se except copulation and swarming? Is swarming a fine thing at all, apart from any results that it may lead to? The course of thought will follow a parallel line if we consider Marshall's ethical maxim: Act to restrain the impulses which demand immediate reaction, in order that the impulse-order determined by the existence of impulses of less strength, but of wider significance, may have full weight in the guidance of your life. Although I have not as clear an apprehension as I could wish of the philosophy of this very close, but too technical, thinker, yet I presume that he would not be among those who would object to making Ethics dependent upon Esthetics. Certainly, the maxim which I have just read to you from his latest book supposes that it is a fine thing for an impulse to have its way, but yet not an equally fine thing for one impulse to have its way and for another impulse to have its way. There is a preference which depends upon the significance of impulses, whatever that may mean. It supposes that there is some ideal state of things which, regardless of how it should be brought about and independently of any ulterior reason whatsoever, is held to be good or fine. In short, ethics must rest upon a doctrine which, without at all considering what our conduct is to be, divides ideally possible states of things into two classes, those that would be admirable and those that would be unadmirable, and undertakes to define precisely what it is that constitutes the admirableness of an ideal. Its problem is to determine by analysis what it is that one ought deliberately to admire per se in itself regardless of what it may lead to and regardless of its bearings upon human conduct. I call that inquiry Esthetics, because it is generally said that the three normative sciences are logic, ethics, and esthetics, being the three doctrines that distinguish good and bad; Logic in regard to representations of truth, Ethics in regard to efforts of will, and Esthetics in objects considered simply in their presentation. Now that third Normative science can, I think, be no other than that which I have described. It is evidently the basic normative science upon which as a foundation, the doctrine of ethics must be reared to be surmounted in its turn by the doctrine of logic.

37. But before we can attack any normative science, any science which proposes to separate the sheep from the goats, it is plain that there must be a preliminary inquiry which shall justify the attempt to establish such dualism. This must be a science that does not draw any distinction of good and bad in any sense whatever, but just contemplates phenomena as they are, simply opens its eyes and describes what it sees; not what it sees in the real as distinguished from figment -- not regarding any such dichotomy -- but simply describing the object, as a phenomenon, and stating what it finds in all phenomena alike. This is the science which Hegel made his starting-point, under the name of the Phänomenologie des Geistes -- although he considered it in a fatally narrow spirit, since he restricted himself to what actually forces itself on the mind and so colored his whole philosophy with the ignoration of the distinction of essence and existence and so gave it the nominalistic and I might say in a certain sense the pragmatoidal character in which the worst of the Hegelian errors have their origin. I will so far follow Hegel as to call this science Phenomenology although I will not restrict it to the observation and analysis of experience but extend it to describing all the features that are common to whatever is experienced or might conceivably be experienced or become an object of study in any way direct or indirect.

38. Hegel was quite right in holding that it was the business of this science to bring out and make clear the Categories or fundamental modes. He was also right in holding that these Categories are of two kinds; the Universal Categories all of which apply to everything, and the series of categories consisting of phases of evolution.

As to these latter, I am satisfied that Hegel has not approximated to any correct catalogue of them. It may be that here and there, in the long wanderings of his Encyclopædia he has been a little warmed by the truth. But in all its main features his catalogue is utterly wrong, according to me. I have made long and arduous studies of this matter, but I have not been able to draw up any catalogue that satisfies me. My studies, if they are ever published, will I believe be found helpful to future students of this most difficult problem, but in these lectures I shall have little to say on that subject. The case is quite different with the three Universal Categories, which Hegel, by the way, does not look upon as Categories at all, or at least he does not call them so, but as three stages of thinking. In regard to these, it appears to me that Hegel is so nearly right that my own doctrine might very well be taken for a variety of Hegelianism, although in point of fact it was determined in my mind by considerations entirely foreign to Hegel, at a time when my attitude toward Hegelianism was one of contempt. There was no influence upon me from Hegel unless it was of so occult a kind as to entirely escape my ken; and if there was such an occult influence, it strikes me as about as good an argument for the essential truth of the doctrine, as is the coincidence that Hegel and I arrived in quite independent ways substantially to the same result.

39. This science of Phenomenology, then, must be taken as the basis upon which normative science is to be erected, and accordingly must claim our first attention.

This science of Phenomenology is in my view the most primal of all the positive sciences. That is, it is not based, as to its principles, upon any other positive science. By a positive science I mean an inquiry which seeks for positive knowledge; that is, for such knowledge as may conveniently be expressed in a categorical proposition. Logic and the other normative sciences, although they ask, not what is but what ought to be, nevertheless are positive sciences since it is by asserting positive, categorical truth that they are able to show that what they call good really is so; and the right reason, right effort, and right being, of which they treat, derive that character from positive categorical fact.

40. Perhaps you will ask me whether it is possible to conceive of a science which should not aim to declare that something is positively or categorically true. I reply that it is not only possible to conceive of such a science, but that such science exists and flourishes, and Phenomenology, which does not depend upon any other positive science, nevertheless must, if it is to be properly grounded, be made to depend upon the Conditional or Hypothetical Science of Pure Mathematics, whose only aim is to discover not how things actually are, but how they might be supposed to be, if not in our universe, then in some other.†1 A Phenomenology which does not reckon with pure mathematics, a science hardly come to years of discretion when Hegel wrote, will be the same pitiful club-footed affair that Hegel produced.

§1. PRESENTNESS
Be it understood that what we have to do, as students of phenomenology, is simply to open our mental eyes and look well at the phenomenon and say what are the characteristics that are never wanting in it, whether that phenomenon be something that outward experience forces upon our attention, or whether it be the wildest of dreams, or whether it be the most abstract and general of the conclusions of science. (CP5-41)

The faculties which we must endeavor to gather for this work are three.
The first and foremost is that rare faculty, the faculty of seeing what stares one in the face, just as it presents itself, unreplaced by any interpretation, unsophisticated by any allowance for this or for that supposed modifying circumstance. This is the faculty of the artist who sees for example the apparent colors of nature as they appear. When the ground is covered by snow on which the sun shines brightly except where shadows fall, if you ask any ordinary man what its color appears to be, he will tell you white, pure white, whiter in the sunlight, a little greyish in the shadow. But that is not what is before his eyes that he is describing; it is his theory of what ought to be seen. The artist will tell him that the shadows are not grey but a dull blue and that the snow in the sunshine is of a rich yellow. That artist's observational power is what is most wanted in the study of phenomenology.
The second faculty we must strive to arm ourselves with is a resolute discrimination which fastens itself like a bulldog upon the particular feature that we are studying, follows it wherever it may lurk, and detects it beneath all its disguises.
The third faculty we shall need is the generalizing power of the mathematician who produces the abstract formula that comprehends the very essence of the feature under examination purified from all admixture of extraneous and irrelevant accompaniments. (CP5-42)

A very moderate exercise of this third faculty suffices to show us that the word Category bears substantially the same meaning with all philosophers. For Aristotle, for Kant, and for Hegel, a category is an element of phenomena of the first rank of generality. It naturally follows that the categories are few in number, just as the chemical elements are. The business of phenomenology is to draw up a catalogue of categories and prove its sufficiency and freedom from redundancies, to make out the characteristics of each category, and to show the relations of each to the others. I find that there are at least two distinct orders of categories, which I call the particular and the universal. The particular categories form a series, or set of series, only one of each series being present, or at least predominant, in any one phenomenon. The universal categories, on the other hand, belong to every phenomenon, one being perhaps more prominent in one aspect of that phenomenon than another but all of them belonging to every phenomenon. I am not very well satisfied with this description of the two orders of categories, but I am pretty well satisfied that there are two orders. I do not recognize them in Aristotle, unless the predicaments and the predicables are the two orders. But in Kant we have Unity, Plurality, and Totality not all present at once; Reality, Negation, and Limitation not all present at once; Inherence, Causation, and Reaction not all present at once; Possibility, Necessity, and Actuality not all present at once. On the other hand Kant's four greater categories, Quantity, Quality, Relation, and Modality, form what I should recognize as Kant's Universal Categories. In Hegel his long list which gives the divisions of his Encyclopædia are his Particular Categories. His three stages of thought, although he does not apply the word Category to them, are what I should call Hegel's Universal Categories. My intention this evening is to limit myself to the Universal, or Short List of Categories, and I may say, at once, that I consider Hegel's three stages as being, roughly speaking, the correct list of Universal Categories. . . . (CP5-43)

When anything is present to the mind, what is the very first and simplest character to be noted in it, in every case, no matter how little elevated the object may be? Certainly, it is its presentness. So far Hegel is quite right. Immediacy is his word. To say, however, that presentness, presentness as it is present, present presentness, is abstract, is Pure Being, is a falsity so glaring, that one can only say that Hegel's theory that the abstract is more primitive than the concrete blinded his eyes to what stood before them. Go out under the blue dome of heaven and look at what is present as it appears to the artist's eye. The poetic mood approaches the state in which the present appears as it is present. Is poetry so abstract and colorless? The present is just what it is regardless of the absent, regardless of past and future. It is such as it is, utterly ignoring anything else. Consequently, it cannot be abstracted (which is what Hegel means by the abstract) for the abstracted is what the concrete, which gives it whatever being it has, makes it to be. The present, being such as it is while utterly ignoring everything else, is positively such as it is. Imagine, if you please, a consciousness in which there is no comparison, no relation, no recognized multiplicity (since parts would be other than the whole), no change, no imagination of any modification of what is positively there, no reflexion -- nothing but a simple positive character. Such a consciousness might be just an odour, say a smell of attar; or it might be one infinite dead ache; it might be the hearing of a piercing eternal whistle. In short, any simple and positive quality of feeling would be something which our description fits that it is such as it is quite regardless of anything else. The quality of feeling is the true psychical representative of the first category of the immediate as it is in its immediacy, of the present in its direct positive presentness. Qualities of feeling show myriad-fold variety, far beyond what the psychologists admit. This variety however is in them only insofar as they are compared and gathered into collections. But as they are in their presentness, each is sole and unique; and all the others are absolute nothingness to it -- or rather much less than nothingness, for not even a recognition as absent things or as fictions is accorded to them. The first category, then, is Quality of Feeling, or whatever is such as it is positively and regardless of aught else. (CP5-44)

§2. STRUGGLE
The next simplest feature that is common to all that comes before the mind, and consequently, the second category, is the element of Struggle. It is convenient enough, although by no means necessary, to study this, at first, in a psychological instance. Imagine yourself making a strong muscular effort, say that of pressing with all your might against a half-open door. Obviously, there is a sense of resistance. There could not be effort without an equal resistance any more than there could be a resistance without an equal effort that it resists. Action and reaction are equal. If you find that the door is pushed open in spite of you, you will say that it was the person on the other side that acted and you that resisted, while if you succeed in pushing the door to, you will say that it was you who acted and the other person that resisted. In general, we call the one that succeeds by means of his effort the agent and the one that fails the patient. But as far as the element of Struggle is concerned, there is no difference between being an agent and being a patient. It is the result that decides; but what it is that is deemed to be the result for the purpose of this distinction is a detail into which we need not enter.
If while you are walking quietly along the sidewalk a man carrying a ladder suddenly pokes you violently with it in the back of the head and walks on without noticing what he has done, your impression probably will be that he struck you with great violence and that you made not the slightest resistance; although in fact you must have resisted with a force equal to that of the blow. Of course, it will be understood that I am not using force in the modern sense of a moving force but in the sense of Newton's actio; but I must warn you that I have not time to notice such trifles.
In like manner, if in pitch darkness a tremendous flash of lightning suddenly comes, you are ready to admit having received a shock and being acted upon, but that you reacted you may be inclined to deny. You certainly did so, however, and are conscious of having done so. The sense of shock is as much a sense of resisting as of being acted upon.
So it is when anything strikes the senses. The outward excitation succeeds in producing its effect on you, while you in turn produce no discernible effect on it; and therefore you call it the agent, and overlook your own part in the reaction. On the other hand, in reading a geometrical demonstration, if you draw the figure in your imagination instead of on paper, it is so easy to add to your image whatever subsidiary line is wanted, that it seems to you that you have acted on the image without the image having offered any resistance. That it is not so, however, is easily shown. For unless that image had a certain power of persisting such as it is and resisting metamorphosis, and if you were not sensible of its strength of persistence, you never could be sure that the construction you are dealing with at one stage of the demonstration was the same that you had before your mind at an earlier stage. The main distinction between the Inner and the Outer Worlds is that inner objects promptly take any modifications we wish, while outer objects are hard facts that no man can make to be other than they are. Yet tremendous as this distinction is, it is after all only relative. Inner objects do offer a certain degree of resistance and outer objects are susceptible of being modified in some measure by sufficient exertion intelligently directed. (CP5-45)

Experience is our only teacher. Far be it from me to enunciate any doctrine of a tabula rasa. There manifestly is not one drop of principle in the whole vast reservoir of established scientific theory that has sprung from any other source than the power of the human mind to originate ideas that are true. But this power, for all it has accomplished, is so feeble that as ideas flow from their springs in the soul, the truths are almost drowned in a flood of false notions; and that which experience does is gradually, and by a sort of fractionation, to precipitate and filter off the false ideas, eliminating them and letting the truth pour on in its mighty current. (CP5-50)
[Note: Peirce asserted quite emphatically that "experience is our only teacher," and thus embraced a fundamental tenet of classical empiricism. Yet he rejected the doctrine of a tabula rasa, claiming that there "is not one drop of principle in the whole vast reservoir of established scientific theory that has sprung from any other source than the power of the human mind to originate ideas that are true." But this power to originate ideas is feeble, Peirce said, and "the truths are almost drowned in a flood of false notions." Experience enables us to "filter off" the false ideas, "letting the truth pour on in its mighty current". ] (the Essential Peirce - Introduction to EP Volume 1 )

But precisely how does this action of experience take place? It takes place by a series of surprises. There is no need of going into details. At one time a ship is sailing along in the trades over a smooth sea, the navigator having no more positive expectation than that of the usual monotony of such a voyage, when suddenly she strikes upon a rock. The majority of discoveries, however, have been the result of experimentation. Now no man makes an experiment without being more or less inclined to think that an interesting result will ensue; for experiments are much too costly of physical and psychical energy to be undertaken at random and aimlessly. And naturally nothing can possibly be learned from an experiment that turns out just as was anticipated. It is by surprises that experience teaches all she deigns to teach us. (CP5-51)

The phenomenon of surprise in itself is highly instructive in reference to this category because of the emphasis it puts upon a mode of consciousness which can be detected in all perception, namely, a double consciousness at once of an ego and a non-ego, directly acting upon each other. Understand me well. My appeal is to observation -- observation that each of you must make for himself. (CP5-52)

The question is what the phenomenon is. We make no vain pretense of going beneath phenomena. We merely ask, what is the content of the Percept? Everybody should be competent to answer that of himself. Examine the Percept in the particularly marked case in which it comes as a surprise. Your mind was filled [with] an imaginary object that was expected. At the moment when it was expected the vividness of the representation is exalted, and suddenly, when it should come, something quite different comes instead. I ask you whether at that instant of surprise there is not a double consciousness, on the one hand of an Ego, which is simply the expected idea suddenly broken off, on the other hand of the Non-Ego, which is the strange intruder, in his abrupt entrance. (CP5-53)

The whole question is what the perceptual facts are, as given in direct perceptual judgments. By a perceptual judgment, I mean a judgment asserting in propositional form what a character of a percept directly present to the mind is. The percept of course is not itself a judgment, nor can a judgment in any degree resemble a percept. It is as unlike it as the printed letters in a book, where a Madonna of Murillo is described, are unlike the picture itself. (CP5-54)

If, therefore, our careful direct interpretation of perception, and more emphatically of such perception as involves surprise, is that the perception represents two objects reacting upon one another, that is not only a decision from which there is no appeal, but it is downright nonsense to dispute the fact that in perception two objects really do so react upon one another. (CP5-55)

That, of course, is the doctrine of Immediate Perception which is upheld by Reid, Kant, and all dualists who understand the true nature of dualism, and the denial of which led Cartesians to the utterly absurd theory of divine assistance upon which the preestablished harmony of Leibniz is but a slight improvement. Every philosopher who denies the doctrine of Immediate Perception -- including idealists of every stripe -- by that denial cuts off all possibility of ever cognizing a relation. Nor will he better his position by declaring that all relations are illusive appearances, since it is not merely true knowledge of them that he has cut off, but every mode of cognitive representation of them. (CP5-55)

When a man is surprised he knows that he is surprised. Now comes a dilemma. Does he know he is surprised by direct perception or by inference?
First try the hypothesis that it is by inference. This theory would be that a person (who must be supposed old enough to have acquired self-consciousness) on becoming conscious of that peculiar quality of feeling which unquestionably belongs to all surprise, is induced by some reason to attribute this feeling to himself. It is, however, a patent fact that we never, in the first instance, attribute a Quality of Feeling to ourselves. We first attribute it to a Non-Ego and only come to attribute it to ourselves when irrefragable reasons compel us to do so. Therefore, the theory would have to be that the man first pronounces the surprising object a wonder, and upon reflection convinces himself that it is only a wonder in the sense that he is surprised. That would have to be the theory. But it is in conflict with the facts which are that a man is more or less placidly expecting one result, and suddenly finds something in contrast to that forcing itself upon his recognition. A duality is thus forced upon him: on the one hand, his expectation which he had been attributing to Nature, but which he is now compelled to attribute to some mere inner world, and on the other hand, a strong new phenomenon which shoves that expectation into the background and occupies its place. The old expectation, which is what he was familiar with, is his inner world, or Ego. The new phenomenon, the stranger, is from the exterior world or Non- Ego. He does not conclude that he must be surprised because the object is so marvellous. But on the contrary, it is because of the duality presenting itself as such that he [is] led by generalization to a conception of a quality of marvellousness. (CP5-57)

Try, then, the other alternative that it is by direct perception, that is, in a direct perceptual judgment, that a man knows that he is surprised. The perceptual judgment, however, certainly does not represent that it is he himself who has played a little trick upon himself. A man cannot startle himself by jumping up with an exclamation of Boo! Nor could the perceptual judgment have represented anything so out of nature. The perceptual judgment, then, can only be that it is the Non-Ego, something over against the Ego and bearing it down, is what has surprised him. But if that be so, this direct perception presents an Ego to which the smashed expectation belonged, and the Non-Ego, the sadder and wiser man, to which the new phenomenon belongs. . . . (CP5-58)

§3. LAWS: NOMINALISM
There never was a sounder logical maxim of scientific procedure than Ockham's razor: Entia non sunt multiplicanda praeter necessitatem. That is to say; before you try a complicated hypothesis, you should make quite sure that no simplification of it will explain the facts equally well. No matter if it takes fifty generations of arduous experimentation to explode the simpler hypothesis, and no matter how incredible it may seem that that simpler hypothesis should suffice, still fifty generations are nothing in the life of science, which has all time before it; and in the long run, say in some thousands of generations, time will be economized by proceeding in an orderly manner, and by making it an invariable rule to try the simpler hypothesis first. Indeed, one can never be sure that the simpler hypothesis is not the true one, after all, until its cause has been fought out to the bitter end. But you will mark the limitation of my approval of Ockham's razor. It is a sound maxim of scientific procedure. If the question be what one ought to believe, the logic of the situation must take other factors into account. Speaking strictly, belief is out of place in pure theoretical science, which has nothing nearer to it than the establishment of doctrines, and only the provisional establishment of them, at that. Compared with living belief it is nothing but a ghost. If the captain of a vessel on a lee shore in a terrific storm finds himself in a critical position in which he must instantly either put his wheel to port acting on one hypothesis, or put his wheel to starboard acting on the contrary hypothesis, and his vessel will infallibly be dashed to pieces if he decides the question wrongly, Ockham's razor is not worth the stout belief of any common seaman. For stout belief may happen to save the ship, while Entia non sunt multiplicanda praeter necessitatem would be only a stupid way of spelling Shipwreck. Now in matters of real practical concern we are all in something like the situation of that sea-captain. (CP5-60)

Philosophy, as I understand the word, is a positive theoretical science, and a science in an early stage of development. As such it has no more to do with belief than any other science. Indeed, I am bound to confess that it is at present in so unsettled a condition, that if the ordinary theorems of molecular physics and of archaeology are but the ghosts of beliefs, then to my mind, the doctrines of the philosophers are little better than the ghosts of ghosts. I know this is an extremely heretical opinion. The followers of Haeckel are completely in accord with the followers of Hegel in holding that what they call philosophy is a practical science and the best of guides in the formation of what they take to be Religious Beliefs. I simply note the divergence, and pass on to an unquestionable fact; namely, the fact that all modern philosophy is built upon Ockhamism; by which I mean that it is all nominalistic and that it adopts nominalism because of Ockham's razor. And there is no form of modern philosophy of which this is more essentially true than the philosophy of Hegel. But it is not modern philosophers only who are nominalists. The nominalistic Weltanschauung has become incorporated into what I will venture to call the very flesh and blood of the average modern mind. (CP5-61)

The third category of which I come now to speak is precisely that whose reality is denied by nominalism. For although nominalism is not credited with any extraordinarily lofty appreciation of the powers of the human soul, yet it attributes to it a power of originating a kind of ideas the like of which Omnipotence has failed to create as real objects, and those general conceptions which men will never cease to consider the glory of the human intellect must, according to any consistent nominalism, be entirely wanting in the mind of Deity. Leibniz, the modern nominalist par excellence, will not admit that God has the faculty of Reason; and it seems impossible to avoid that conclusion upon nominalistic principles. (CP5-62)

But it is not in Nominalism alone that modern thought has attributed to the human mind the miraculous power of originating a category of thought that has no counterpart at all in Heaven or Earth. Already in that strangely influential hodge-podge, the salad of Cartesianism, the doctrine stands out very emphatically that the only force is the force of impact, which clearly belongs to the category of Reaction; and ever since Newton's Principia began to affect the general thought of Europe through the sympathetic spirit of Voltaire, there has been a disposition to deny any kind of action except purely mechanical action. The Corpuscular Philosophy of Boyle -- although the pious Boyle did not himself recognize its character -- was bound to come to that in the last resort; and the idea constantly gained strength throughout the eighteenth century and the nineteenth until the doctrine of the Conservation of Energy, generalized rather loosely by philosophers, led to the theory of psycho-physical parallelism, against which there has, only of recent years, been any very sensible and widespread revolt. Psychophysical parallelism is merely the doctrine that mechanical action explains all the real facts, except that these facts have an internal aspect which is a little obscure and a little shadowy. (CP5-63)

To my way of regarding philosophy, all this movement was perfectly good scientific procedure. For the simpler hypothesis which excluded the influence of ideas upon matter had to be tried and persevered in until it was thoroughly exploded. But I believe that now at last, at any time for the last thirty years, it has been apparent, to every man who sufficiently considered the subject, that there is a mode of influence upon external facts which cannot be resolved into mere mechanical action, so that henceforward it will be a grave error of scientific philosophy to overlook the universal presence in the phenomenon of this third category. Indeed, from the moment that the Idea of Evolution took possession of the minds of men the pure Corpuscular Philosophy together with nominalism had had their doom pronounced. I grew up in Cambridge, [Massachusetts] and was about 21 when the Origin of Species appeared. There was then living here a thinker who left no remains from which one could now gather what an educative influence his was upon the minds of all of us who enjoyed his intimacy, Mr. Chauncey Wright. He had at first been a Hamiltonian but had early passed over into the warmest advocacy of the nominalism of John Stuart Mill; and being a mathematician at a time when dynamics was regarded as the loftiest branch of mathematics, he was also inclined to regard nature from a strictly mechanical point of view. But his interests were wide and he was also a student of Gray. I was away surveying in the wilds of Louisiana when Darwin's great work appeared, and though I learned by letters of the immense sensation it had created, I did not return until early in the following summer when I found Wright all enthusiasm for Darwin, whose doctrines appeared to him as a sort of supplement to those of Mill. I remember well that I then made a remark to him which although he did not assent to it, evidently impressed him enough to perplex him. The remark was that these ideas of development had more vitality by far than any of his other favorite conceptions and that though they might at that moment be in his mind like a little vine clinging to the tree of Associationalism, yet after a time that vine would inevitably kill the tree. He asked me why I said that and I replied that the reason was that Mill's doctrine was nothing but a metaphysical point of view to which Darwin's, which was nourished by positive observation, must be deadly. Ten or fifteen years later, when Agnosticism was all the go, I prognosticated a short life for it, as philosophies run, for a similar reason. What the true definition of Pragmatism may be, I find it very hard to say; but in my nature it is a sort of instinctive attraction for living facts. (CP5-64)

All nature abounds in proofs of other influences than merely mechanical action, even in the physical world. They crowd in upon us at the rate of several every minute. And my observation of men has led me to this little generalization. Speaking only of men who really think for themselves and not of mere reporters, I have not found that it is the men whose lives are mostly passed within the four walls of a physical laboratory who are most inclined to be satisfied with a purely mechanical metaphysics. On the contrary, the more clearly they understand how physical forces work the more incredible it seems to them that such action should explain what happens out of doors. A larger proportion of materialists and agnostics is to be found among the thinking physiologists and other naturalists, and the largest proportion of all among those who derive their ideas of physical science from reading popular books. These last, the Spencers, the Youmanses, and the like, seem to be possessed with the idea that science has got the universe pretty well ciphered down to a fine point; while the Faradays and Newtons seem to themselves like children who have picked up a few pretty pebbles upon the ocean beach. But most of us seem to find it difficult to recognize the greatness and wonder of things familiar to us. As the prophet is not without honor save [in his own country] so it is also with phenomena. Point out to the ordinary man evidence, however conclusive, of other influence than physical action in things he sees every day, and he will say: "Well, I don't see as that frog has got any points about him that's any different from any other frog." For that reason we welcome instances perhaps of less real cogency but which have the merit of being rare and strange. Such, for example, are the right-handed and lefthanded screw-structures of the molecules of those bodies which are said to be "optically active." Of every such substance there are two varieties, or as the chemists call them, two modifications, one of which twists a ray of light that passes through it to the right, and the other, by an exactly equal amount, to the left. All the ordinary physical properties of the right-handed and left-handed modifications are identical. Only certain faces of their crystals, often very minute, are differently placed. No chemical process can ever transmute the one modification into the other. And their ordinary chemical behaviour is absolutely the same, so that no strictly chemical process can separate them if they are once mixed. Only the chemical action of one optically active substance upon another is different if they both twist the ray the same way from what it is if they twist the ray different ways. There are certain living organisms which feed on one modification and destroy it while leaving the other one untouched. This is presumably due to such organisms containing in their substance, possibly in very minute proportion, some optically active body. Now I maintain that the original segregation of levo-molecules, or molecules with a left-handed twist, from dextromolecules, or molecules with a right-handed twist, is absolutely incapable of mechanical explanation. Of course you may suppose that in the original nebula at the very formation of the world right-handed quartz was collected into one place, while left-handed quartz was collected into another place. But to suppose that, is ipso facto to suppose that that segregation was a phenomenon without any mechanical explanation. The three laws of motion draw no dynamical distinction between right-handed and left-handed screws, and a mechanical explanation is an explanation founded on the three laws of motion. There, then, is a physical phenomenon absolutely inexplicable by mechanical action. This single instance suffices to overthrow the Corpuscular Philosophy. (CP5-65)

§1. DEGENERATE THIRDNESS
66. Category the First is the Idea of that which is such as it is regardless of anything else. That is to say, it is a Quality of Feeling.

Category the Second is the Idea of that which is such as it is as being Second to some First, regardless of anything else, and in particular regardless of any Law, although it may conform to a law. That is to say, it is Reaction as an element of the Phenomenon.

Category the Third is the Idea of that which is such as it is as being a Third, or Medium, between a Second and its First. That is to say, it is Representation as an element of the Phenomenon.

67. A mere complication of Category the Third, involving no idea essentially different, will give the idea of something which is such as it is by virtue of its relations to any multitude, enumerable, denumeral, or abnumerable or even to any supermultitude of correlates; so that this Category suffices of itself to give the conception of True Continuity, than which no conception yet discovered is higher.

68. Category the First owing to its Extremely Rudimentary character is not susceptible of any degenerate or weakened modification.

69. Category the Second has a Degenerate Form, in which there is Secondness indeed, but a weak or secondary Secondness that is not in the pair in its own quality, but belongs to it only in a certain respect. Moreover, this degeneracy need not be absolute but may be only approximative. Thus a genus characterized by Reaction will by the determination of its essential character split into two species, one a species where the secondness is strong, the other a species where the secondness is weak, and the strong species will subdivide into two that will be similarly related, without any corresponding subdivision of the weak species. For example, Psychological Reaction splits into Willing, where the Secondness is strong, and Sensation, where it is weak; and Willing again subdivides into Active Willing and Inhibitive Willing, to which last dichotomy nothing in Sensation corresponds. But it must be confessed that subdivision, as such, involves something more than the second category.

70. Category the Third exhibits two different ways of Degeneracy, where the irreducible idea of Plurality, as distinguished from Duality, is present indeed but in maimed conditions. The First degree of Degeneracy is found in an Irrational Plurality which, as it exists, in contradistinction [to] the form of its representation, is a mere complication of duality. We have just had an example of this in the idea of Subdivision. In pure Secondness, the reacting correlates are Singulars, and as such are Individuals, not capable of further division. Consequently, the conception of Subdivision, say by repeated dichotomy, certainly involves a sort of Thirdness, but it is a thirdness that is conceived to consist in a second secondness.

71. The most degenerate Thirdness is where we conceive a mere Quality of Feeling, or Firstness, to represent itself to itself as Representation. Such, for example, would be Pure Self-Consciousness, which might be roughly described as a mere feeling that has a dark instinct of being a germ of thought. This sounds nonsensical, I grant. Yet something can be done toward rendering it comprehensible.

I remember a lady's averring that her father had heard a minister, of what complexion she did not say, open a prayer as follows: "O Thou, All-Sufficient, Self-Sufficient, Insufficient God." Now pure Self-consciousness is Self-sufficient, and if it is also regarded as All-sufficient, it would seem to follow that it must be Insufficient. I ought to apologize for introducing such Buffoonery into serious lectures. I do so because I seriously believe that a bit of fun helps thought and tends to keep it pragmatical.

Imagine that upon the soil of a country, that has a single boundary line thus , there lies a map of that same country. This map may distort the different provinces of the country to any extent. But I shall suppose that it represents every part of the country that has a single boundary, by a part of the map that has a single boundary, that every part is represented as bounded by such parts as it really is bounded by, that every point of the country is represented by a single point of the map, and that every point of the map represents a single point in the country. Let us further suppose that this map is infinitely minute in its representation so that there is no speck on any grain of sand in the country that could not be seen represented upon the map if we were to examine it under a sufficiently high magnifying power. Since, then, everything on the soil of the country is shown on the map, and since the map lies on the soil of the country, the map itself will be portrayed in the map, and in this map of the map everything on the soil of the country can be discerned, including the map itself with the map of the map within its boundary. Thus there will be within the map, a map of the map, and within that, a map of the map of the map, and so on ad infinitum. These maps being each within the preceding ones of the series, there will be a point contained in all of them, and this will be the map of itself. Each map which directly or indirectly represents the country is itself mapped in the next; i.e., in the next [it] is represented to be a map of the country. In other words each map is interpreted as such in the next. We may therefore say that each is a representation of the country to the next map; and that point that is in all the maps is in itself the representation of nothing but itself and to nothing but itself. It is therefore the precise analogue of pure self-consciousness. As such it is self-sufficient. It is saved from being insufficient, that is as no representation at all, by the circumstance that it is not all-sufficient, that is, is not a complete representation but is only a point upon a continuous map. I dare say you may have heard something like this before from Professor Royce, but if so, you will remark an important divergency. The idea itself belongs neither to him nor to me, and was used by me in this connection thirty years ago.

72. The relatively degenerate forms of the Third category do not fall into a catena, like those of the Second. What we find is this. Taking any class in whose essential idea the predominant element is Thirdness, or Representation, the selfdevelopment of that essential idea -- which development, let me say, is not to be compassed by any amount of mere "hard thinking," but only by an elaborate process founded upon experience and reason combined -- results in a trichotomy giving rise to three sub-classes, or genera, involving respectively a relatively genuine thirdness, a relatively reactional thirdness or thirdness of the lesser degree of degeneracy, and a relatively qualitative thirdness or thirdness of the last degeneracy. This last may subdivide, and its species may even be governed by the three categories, but it will not subdivide, in the manner which we are considering, by the essential determinations of its conception. The genus corresponding to the lesser degree of degeneracy, the reactionally degenerate genus, will subdivide after the manner of the Second category, forming a catena; while the genus of relatively genuine Thirdness will subdivide by Trichotomy just like that from which it resulted. Only as the division proceeds, the subdivisions become harder and harder to discern.

73. The representamen, for example, divides by trichotomy into the general sign or symbol, the index, and the icon. An icon is a representamen which fulfills the function of a representamen by virtue of a character which it possesses in itself, and would possess just the same though its object did not exist. Thus, the statue of a centaur is not, it is true, a representamen if there be no such thing as a centaur. Still, if it represents a centaur, it is by virtue of its shape; and this shape it will have, just as much, whether there be a centaur or not. An index is a representamen which fulfills the function of a representamen by virtue of a character which it could not have if its object did not exist, but which it will continue to have just the same whether it be interpreted as a representamen or not. For instance, an old-fashioned hygrometer is an index. For it is so contrived as to have a physical reaction with dryness and moisture in the air, so that the little man will come out if it is wet, and this would happen just the same if the use of the instrument should be entirely forgotten, so that it ceased actually to convey any information. A symbol is a representamen which fulfills its function regardless of any similarity or analogy with its object and equally regardless of any factual connection therewith, but solely and simply because it will be interpreted to be a representamen. Such for example is any general word, sentence, or book.

Of these three genera of representamens, the Icon is the Qualitatively degenerate, the Index the Reactionally degenerate, while the Symbol is the relatively genuine genus.

74. Now the Icon may undoubtedly be divided according to the categories; but the mere completeness of the notion of the icon does not imperatively call for any such division. For a pure icon does not draw any distinction between itself and its object. It represents whatever it may represent, and whatever it is like, it in so far is. It is an affair of suchness only.

75. It is quite otherwise with the Index. Here is a reactional sign, which is such by virtue of a real connection with its object. Then the question arises is this dual character in the Index, so that it has two elements, by virtue of the one serving as a substitute for the particular object it does, while the other is an involved icon that represents the representamen itself regarded as a quality of the object -- or is there really no such dual character in the index, so that it merely denotes whatever object it happens to be really connected with just as the icon represents whatever object it happens really to resemble? Of the former, the relatively genuine form of Index, the hygrometer, is an example. Its connection with the weather is dualistic, so that by an involved icon, it actually conveys information. On the other hand any mere land-mark by which a particular thing may be recognized because it is as a matter of fact associated with that thing, a proper name without signification, a pointing finger, is a degenerate index. Horatio Greenough, who designed Bunker Hill Monument, tells us in his book that he meant it to say simply "Here!" It just stands on that ground and plainly is not movable. So if we are looking for the battle-field, it will tell us whither to direct our steps.

76. The Symbol, or relatively genuine form of Representamen, divides by Trichotomy into the Term, the Proposition, and the Argument. The Term corresponds to the Icon and to the degenerate Index. It does excite an icon in the imagination. The proposition conveys definite information like the genuine index, by having two parts of which the function of the one is to indicate the object meant, while that of the other is to represent the representamen by exciting an icon of its quality. The argument is a representamen which does not leave the interpretant to be determined as it may by the person to whom the symbol is addressed, but separately represents what is the interpreting representation that it is intended to determine. This interpreting representation is, of course, the conclusion. It would be interesting to push these illustrations further; but I can linger nowhere. As soon as a subject begins to be interesting I am obliged to pass on to another.

§2. THE SEVEN SYSTEMS OF METAPHYSICS
77. The three categories furnish an artificial classification of all possible systems of metaphysics which is certainly not without its utility. The scheme is shown in this figure. It depends upon what ones of the three categories each system admits as important metaphysico-cosmical elements.

78. One very naturally and properly endeavors to give an account of the universe with the fewest and simplest possible categories. Praedicamenta non sunt multiplicanda praeter necessitatem.

79. We ought therefore to admire and extol the efforts of Condillac and the Associationalists to explain everything by means of qualities of feeling [i]. If, however, this turns out to be a failure, the next most admirable hypothesis is that of the corpuscularians, Helmholtz and the like, who would like to explain everything by means of mechanical force, which they do not distinguish from individual reaction [ii]. That again failing, the doctrine of Hegel is to be commended who regards Category the Third as the only true one [iii]. For in the Hegelian system the other two are only introduced in order to be aufgehoben. All the categories of Hegel's list, from Pure Being up, appear to me very manifestly to involve Thirdness, although he does not appear to recognize it, so immersed is he in this category.

80. All three of these simplest systems having worked themselves out into absurdity, it is natural next in accordance with the maxim of Parsimony to try explanations of the Universe based on the recognition of two only of the Categories.

81. The more moderate nominalists who nevertheless apply the epithet mere to thought and to representamens may be said to admit Categories First and Second and to deny the third [i ii]. The Berkeleyans, for whom there are but two kinds of entities, souls, or centres of determinable thought, and ideas in the souls, these ideas being regarded as pure statical entities, little or nothing else than Qualities of Feeling, seem to admit Categories First and Third and to deny Secondness, which they wish to replace by Divine Creative Influence, which certainly has all the flavor of Thirdness [i iii]. So far as one can make out any intelligible aim in that singular hodge-podge, the Cartesian metaphysics, it seems to have been to admit Categories Second and Third as fundamental and to deny the First [ii iii]. Otherwise, I do not know to whom we can attribute this opinion which certainly does not seem to be less acceptable and attractive than several others. But there are other philosophies which seem to do full justice to Categories Second and Third and to minimize the first, and among these perhaps Spinoza and Kant are to be included.

§3. THE IRREDUCIBILITY OF THE CATEGORIES
82. We must begin by asking whether the three categories can be admitted as simple and irreducible conceptions; and afterward go on to ask whether they cannot all be supposed to be real constituents of the universe. For when I say that certain metaphysical schools do not admit them, I do not mean to say that they do not admit them as mere conceptions but that they do not admit them as real constituents of the universe.

I do not know that I could add anything material to what I said in my last lecture to show that Category the First must be admitted as an irreducible constituent of the phenomenon.

83. There would be no question that Category the Second is an irreducible conception were it not for the deplorable condition of the science of logic. This is illustrated by the fact that so flippant and wildly theorizing work as Prantl's Geschichte der Logik should be accepted, as it generally is, even among learned men, as a marvel of patient research. It is true that one or two chapters of it are relatively well done. The account of Aristotle's logic, though not good upon any high standard of completeness or of thorough comprehension, is nevertheless the best account of its subject that we have. But Prantl, to begin with, does not himself understand logic, meaning by logic the science of which those works treated, of which he gives or he professes to give an account; and yet with the shallowest ideas, he is so puffed up with his own views that he disdains to take the trouble to penetrate their meaning. The crude expressions of contempt in which he continually indulges toward great thinkers ought to put readers on their guard against him. In the next place he belongs to that too well-known class of German critics who get bitten with theories deduced from general conceptions, and who fall in love with these theories because they are their own offspring and treat them as absolute certainties although the complete refutation of them is near at hand. You will understand, of course, that I do not say these things without having read all the chief contributions to the questions on both sides and without having subjected them to careful study and criticism. Prantl's opinions about the Megarian philosophers, about what he calls the Byzantine logic, about the Latin medieval logic, about the Parva Logicalia, are wild theories, utterly untenable, and in several cases easily refuted by an easy examination of the MSS. Moreover, it is not a history of logic but mostly of the most trivial parts of logic. But I shall be asked whether I do not think his reading marvellously extensive. No, I do not. He had the Munich library at his hand. He had only to look into the books, and for the most part he has done little more than merely to look into them. He really often has no idea of what the real substance of the books is; and nothing is more common than to find in his notes passages copied out of one book which are nothing but textual copies of celebrated passages in much older works. I do not deny that the book is useful, because the rest of us haven't access to such a library; but I do not consider it a work of respectable erudition. There is no need of mincing words because he himself not only refers most disrespectfully to such solid students of medieval writings as Charles Thurot, Haureau and others, but frequently descends to what in English we should call the language of Billingsgate in characterising ancient opinions which he may or may not be aware are identical with those held today by analysts of logical forms whose studies are so much more exact than his that they are not to be named in the same day.

84. Nevertheless, bad as Prantl's history is, it is the best we have, and any person who reads it critically, as every book ought to be read, will easily be able to see that the ancient students of logic, Democritus, Plato, Aristotle, Epicurus, Philoponus, even Chrysippus, were thinkers of the highest order, and that St. Augustine, Abelard, Aquinas, Duns Scotus, Ockham, Paulus Venetus, even Laurentius Valla, were logicians of the most painstaking and subtle types. But when the revival of learning came, the finest minds had their attention turned in quite another direction, and modern mathematics and modern physics drew away still more. The result of all this has been that during the centuries that have elapsed since the appearance of the De Revolutionibus [1543] -- and remember, if you please, that the work of Copernicus was the fruit of the scientific nourishment that he had imbibed in Italy in his youth -- throughout these ages, the chairs of Logic in the Universities have been turned over to a class of men, of whom we should be speaking far too euphemistically if we were to say that they have in no wise represented the Intellectual Level of their age. No, no; let us speak the plain truth -- modern logicians as a class have been distinctly puerile minds, the kind of minds that never mature, and yet never have the élan and originality of youth. First cast your eyes over the pages of a dozen average treatises, dismissing all preconceived estimates of their authors, and see if that is not the impression you derive from them. Why, in the majority of them, the greatest contribution to reasoning that has been generally applied during these centuries -- the Calculus of Probabilities -- is almost entirely ignored. If it were only the common run of logics that were affected by this state of things, it would not much matter; for if only one per cent of works on the subject were what they should be, we should still be in possession of a splendid and extensive literature. But unfortunately the general standard has been so terribly lowered that even the treatises written by men of real ability have been but half thought out things. Arnauld, for example, was a thinker of considerable force, and yet L'Art de penser, or the Port Royal Logic, is a shameful exhibit of what the two and a half centuries of man's greatest achievements could consider as a good account of how to think. You may retort that the past three centuries seem to have got on nicely without the aid of logic. Yes, I reply, they have, because there is one thing even more vital to science than intelligent methods; and that is, the sincere desire to find out the truth, whatever it may be; and that those centuries have been blessed with. But according to such estimate -- not exactly mere guess-work, although rough enough, no doubt -- as I have been able to form, if logic during those centuries had been studied with half the zeal and genius that has been bestowed upon mathematics, the twentieth century might have opened with the special sciences generally -- particularly such vitally important sciences as molecular physics, chemistry, physiology, psychology, linguistics, and ancient historical criticism -- in a decidedly more advanced condition than there is much promise that they will have reached at the end of 1950. I shouldn't say that human lives were the most precious things in the world; but after all they have their value; and only think how many lives might thus have been saved. We can mention individuals who might probably have done more work; say Abel, Steiner, Gaulois, Sadi Carnot. Think of the labor of a generation of Germany being allowed to flow off into Hegelianism! Think of the extravagant admiration that half a generation of English -- decidedly the best average reasoners of any modern people, bestowed on that silly thing, Hamilton's New Analytic. Look through Vaihinger's commentary to see what an army of students have been entrapped by Kant's view of the relation between his Analytic and Synthetic Judgments -- a view that a study of the logic of relatives would at once have exploded.

85. Had logic not been sunk since the time of Copernicus into a condition of semi-idiocy, the Logic of Relatives would by this time have been pursued for three centuries by hundreds of students, among whom there would have been no small number who in this direction or in that would have surpassed in ability any of the poor handful of students who have been at work upon it for the last generation or so. And let me tell you that this study would have completely revolutionized men's most general notions about logic -- the very ideas that are today current in the market-place and on the boulevards. One of the early results of such wide study of the logic of relatives must have been to cause the idea of reaction to be solidly fixed in the minds of all men as an irreducible category of Thought -- whatever place might have been accorded to it in metaphysics as a cosmical category. This I venture to say, notwithstanding that the lamented Schröder did not seem to see it so. Schröder followed Sigwart in his most fundamental ideas of logic. Now I entertain a high respect for Sigwart -- the kind of respect that I feel for Rollin as a historian, for Buffon as a zoölogist, for Priestley as a chemist, for Biot as a physicist -- a class of men whom {ohi polloi} always place too high, and scientific specialists too low. He is one of the most critical and least inexact of the inexact logicians. Sigwart, like almost all the stronger logicians of today, present company excepted, makes the fundamental mistake of confounding the logical question with the psychological question.†3 The psychological question is what processes the mind goes through. But the logical question is whether the conclusion that will be reached, by applying this or that maxim, will or will not accord with the fact. It may be that the mind is so constituted that that which our intellectual instinct approves will be true to the extent to which that instinct approves of it. If so, that is an interesting fact about the human mind; but it has no relevancy for logic whatsoever. Sigwart says that the question of what is good logic and what bad must in the last resort come down to a question of how we feel; it is a matter of Gefühl, that is, a Quality of Feeling. And this he undertakes to demonstrate. For he says if any other criterion be employed, the correctness of this criterion has to be established by reasoning, and in this reasoning antecedent to the establishment of any rational criterion we must rely upon Gefühl; so that Gefühl is that to which any other criterion must ultimately be referred. Good! This is good intelligent work, such as advances philosophy -- a good, square, explicit fallacy that can be squarely met and definitively refuted. It is the more valuable because it is a form of argument of very wide applicability. It is precisely analogous to the reasoning by which the hedonist in ethics, the subjectivist in esthetics, the idealist in metaphysics, attacks the category of reaction. You perceive the analogy between their arguments. The hedonist says that the question of what is good morals and what bad must ultimately come down to a question of pleasure. For, he says, suppose we desire anything but our own pleasure. Then whatever it may be that we desire, we take satisfaction in; and if we did not take satisfaction in it we should not desire it. But this satisfaction is that very Quality of Feeling that we call pleasure; and thus the only thing we ever can desire is pleasure, and all deliberate action must be performed for the sake of our own pleasure.

Every idealist, too, begins with an analogous argument, though he very likely may not remain consistently on the ground it leads to, so far as it leads anywhere. He says: When I perceive anything I am conscious; and when I am conscious of anything, I am immediately conscious and aught else I may be conscious of, I am conscious of through that immediate consciousness. Consequently whatever I learn from perception is merely that I have a feeling together with whatever I infer from that immediate consciousness.

86. The answer to all such arguments is that no desire can possibly desire its own satisfaction, no judgment can judge itself to be true, and no reasoning can conclude that it is itself sound. For all these propositions stand on the same footing and must stand or fall together. If any judgment judges itself to be true, all judgments -- or at least all assertory judgments -- do so likewise; for there is no ground of discrimination between assertory judgments in this respect. Either therefore the judgment, J, and the judgment "I say that J is true" are the same for all judgments or for none. But if they are identical, their denials are identical. But their denials are respectively "J is not true" and "I do not say that J is true," which are very different. Consequently no judgment judges itself to be true. All that J does is to furnish a premiss which is complete evidence warranting my assertion in another judgment that J is true. It is important to draw this distinction. The judgment J may, for example, be that "Sirius is white." That is a judgment about Sirius. To myself who perceive myself making this judgment, or to another who hears me assert it and admits my veracity, the evidence is complete that I believe Sirius to be white. But the two propositions "Sirius is white" "I judge that Sirius is white" are two distinct propositions.

There are precisely analogous distinctions in the other cases. I may desire that my sick child should recover, and afterwards reflecting upon the intensity of that desire, I probably shall be unable to refrain from desiring that that desire should be gratified. But I cannot desire that a desire of mine should be gratified unless I already have such a desire; and I have no such desire as long as I am yet in the act of forming the desire, so that the desire is not yet complete. I dare say that some people's psychical disposition is such that they have no sooner formed a strong desire than their thoughts take a subjective turn and they forthwith begin to think what satisfaction it would give them if that desire were gratified, and such people find it difficult to conceive that there are other people whose thoughts follow a train of objective suggestions and who think very little about themselves and their gratifications. That is just one of those respects in which different people may be expected to differ widely. But in no case is the desire absolutely the same as the desire of the satisfaction of that desire.

87. To return, then, to Sigwart's argument, I not only deny what he asserts that when I make an inference I can only do so because of a certain feeling of logical satisfaction that is connected with doing so, but I maintain that I never can draw an inference because of such a feeling. On the contrary, I never know the inference will afford me any such satisfaction except by a subsequent reflexion after I have already drawn it. It may be that on recognizing the satisfaction the inference gives me I shall consider that as an additional reason for believing in it. But this is another inference which in its turn will afford a new gratification if I stop to reflect about it.

In point of fact it is a serious error of reasoning to regard the sense of logicality as anything more than a tolerably strong argument in favor of the soundness of an inference. For although no doubt the sense of logicality carries men right in the main, yet it very frequently deceives them.

But Sigwart's argument is plainly either wholly fallacious or else what it proves is that which he himself distinctly maintains that it proves, namely, that the soundness of an argument consists in nothing but the Gefühl of logicality. Yet this is a downright absurd position for a logician to take; since, if it were true, there could be no such thing as sincere reasoning that was illogical, and logic, as the criticism of arguments and discrimination of the good from the bad, would have no existence at all; and my sincere argument that Sigwart is wholly in the wrong would be a decision from which there would be no appeal.

If the Holy Father by virtue of his infallibility were to command the faithful to believe that everything that any protestant had ever said was ipso facto necessarily true, it could hardly strain one's assent more.

88. It is certainly hard to believe, until one is forced to the belief, that a conception, so obtrusively complex as Thirdness is, should be an irreducible unanalyzable conception. What, one naturally exclaims, does this man think to convince us that a conception is complex and simple, at the same time! I might answer this by drawing a distinction. It is complex in the sense that different features may be discriminated in it, but the peculiar idea of complexity that it contains, although it has complexity as its object, is an unanalyzable idea. Of what is the conception of complexity built up? Produce it by construction without using any idea which involves it if you can.

89. The best way of satisfying oneself whether Thirdness is elementary or not -- at least, it would be the best way for me, who had in the first place a natural aptitude for logical analysis which has been in constant training all my life long (and I rather think it would be the best way for anybody provided he ruminates over his analysis, returns to it again and again, and criticizes it severely and sincerely, until he reaches a complete insight into the analysis) -- the best way, I say, is to take the idea of representation, say the idea of the fact that the object, A, is represented in the representation, B, so as to determine the interpretation, C: to take this idea and endeavor to state what it consists in without introducing the idea of Thirdness at all if possible, or, if you find that impossible, to see what is the minimum or most degenerate form of Thirdness which will answer the purpose.

Then, having exercised yourself on that problem, take another idea in which, according to my views, Thirdness takes a more degenerate form. Try your hand at a logical analysis of the Fact that A gives B to C.

Then pass to a case in which Thirdness takes a still more degenerate form, as for example the idea of "A and B." What is at once A and B involves the idea of three variables. Putting it mathematically, it is Z = XY, which is the equation of the simpler of the two hyperboloids, the two-sheeted one, as it is called.

Whoever wishes to train his logical powers will find those problems furnish capital exercise; and whoever wishes to get a just conception of the universe will find that the solutions of those problems have a more intimate connection with that conception than he could suspect in advance.

90. I have thus far been intent on repelling attacks upon the categories which should consist in maintaining that the idea of Reaction can be reduced to that of Quality of Feeling, and the idea of Representation to those of Reaction and Quality of Feeling taken together. But meantime may not the enemy have stolen upon my rear, and shall I not suddenly find myself exposed to an attack which shall run as follows:

We fully admit that you have proved, until we begin to doubt it, that Secondness is not involved in Firstness nor Thirdness in Secondness and Firstness. But you have entirely failed to prove that Firstness, Secondness, and Thirdness are independent ideas for the obvious reason that it is as plain as the nose on your face that the idea of a triplet involves the idea of pairs, and the idea of a pair the idea of units. Consequently, Thirdness is the one and sole category. This is substantially the idea of Hegel; and unquestionably it contains a truth.

Not only does Thirdness suppose and involve the ideas of Secondness and Firstness, but never will it be possible to find any Secondness or Firstness in the phenomenon that is not accompanied by Thirdness.

91. If the Hegelians confined themselves to that position they would find a hearty friend in my doctrine.

But they do not. Hegel is possessed with the idea that the Absolute is One. Three absolutes he would regard as a ludicrous contradiction in adjecto Consequently, he wishes to make out that the three categories have not their several independent and irrefutable standings in thought. Firstness and Secondness must somehow be aufgehoben. But it is not true. They are in no way refuted nor refutable. Thirdness it is true involves Secondness and Firstness, in a sense. That is to say, if you have the idea of Thirdness you must have had the ideas of Secondness and Firstness to build upon. But what is required for the idea of a genuine Thirdness is an independent solid Secondness and not a Secondness that is a mere corollary of an unfounded and inconceivable Thirdness; and a similar remark may be made in reference to Firstness.

92. Let the Universe be an evolution of Pure Reason if you will. Yet if, while you are walking in the street reflecting upon how everything is the pure distillate of Reason, a man carrying a heavy pole suddenly pokes you in the small of the back, you may think there is something in the Universe that Pure Reason fails to account for; and when you look at the color red and ask yourself how Pure Reason could make red to have that utterly inexpressible and irrational positive quality it has, you will be perhaps disposed to think that Quality and Reaction have their independent standing in the Universe.

§1. SCHOLASTIC REALISM
93. I proceed to argue that Thirdness is operative in Nature. Suppose we attack the question experimentally. Here is a stone. Now I place that stone where there will be no obstacle between it and the floor, and I will predict with confidence that as soon as I let go my hold upon the stone it will fall to the floor. I will prove that I can make a correct prediction by actual trial if you like. But I see by your faces that you all think it will be a very silly experiment. Why so? Because you all know very well that I can predict what will happen, and that the fact will verify my prediction.

94. But how can I know what is going to happen? You certainly do not think that it is by clairvoyance, as if the future event by its existential reactiveness could affect me directly, as in an experience of it, as an event scarcely past might affect me. You know very well that there is nothing of the sort in this case. Still, it remains true that I do know that that stone will drop, as a fact, as soon as I let go my hold. If I truly know anything, that which I know must be real. It would be quite absurd to say that I could be enabled to know how events are going to be determined over which I can exercise no more control than I shall be able to exercise over this stone after it shall have left my hand, that I can so peer in the future merely on the strength of any acquaintance with any pure fiction.

95. I know that this stone will fall if it is let go, because experience has convinced me that objects of this kind always do fall; and if anyone present has any doubt on the subject, I should be happy to try the experiment, and I will bet him a hundred to one on the result.

96. But the general proposition that all solid bodies fall in the absence of any upward forces or pressure, this formula I say, is of the nature of a representation. Our nominalistic friends would be the last to dispute that. They will go so far as to say that it is a mere representation -- the word mere meaning that to be represented and really to be are two very different things; and that this formula has no being except a being represented. It certainly is of the nature of a representation. That is undeniable, I grant. And it is equally undeniable that that which is of the nature of a representation is not ipso facto real. In that respect there is a great contrast between an object of reaction and an object of representation. Whatever reacts is ipso facto real. But an object of representation is not ipso facto real. If I were to predict that on my letting go of the stone it would fly up in the air, that would be mere fiction; and the proof that it was so would be obtained by simply trying the experiment. That is clear. On the other hand, and by the same token, the fact that I know that this stone will fall to the floor when I let it go, as you all must confess, if you are not blinded by theory, that I do know -- and you none of you care to take up my bet, I notice -- is the proof that the formula, or uniformity, as furnishing a safe basis for prediction, is, or if you like it better, corresponds to, a reality.

97. Possibly at this point somebody may raise an objection and say: You admit, that is one thing really to be and another to be represented; and you further admit that it is of the nature of the law of nature to be represented. Then it follows that it has not the mode of being of a reality. My answer to this would be that it rests upon an ambiguity. When I say that the general proposition as to what will happen, whenever a certain condition may be fulfilled, is of the nature of a representation, I mean that it refers to experiences in futuro, which I do not know are all of them experienced and never can know have been all experienced. But when I say that really to be is different from being represented, I mean that what really is, ultimately consists in what shall be forced upon us in experience, that there is an element of brute compulsion in fact and that fact is not a mere question of reasonableness. Thus, if I say, "I shall wind up my watch every day as long as I live," I never can have a positive experience which certainly covers all that is here promised, because I never shall know for certain that my last day has come. But what the real fact will be does not depend upon what I represent, but upon what the experiential reactions shall be. My assertion that I shall wind up my watch every day of my life may turn out to accord with facts, even though I be the most irregular of persons, by my dying before nightfall.

If we call that being true by chance, here is a case of a general proposition being entirely true in all its generality by chance.

98. Every general proposition is limited to a finite number of occasions in which it might conceivably be falsified, supposing that it is an assertion confined to what human beings may experience; and consequently it is conceivable that, although it should be true without exception, it should still only be by chance that it turns out true.

99. But if I see a man who is very regular in his habits and am led to offer to wager that that man will not miss winding his watch for the next month, you have your choice between two alternative hypotheses only:

1. You may suppose that some principle or cause is really operative to make him wind his watch daily, which active principle may have more or less strength; or

2. You may suppose that it is mere chance that his actions have hitherto been regular; and in that case, that regularity in the past affords you not the slightest reason for expecting its continuance in the future, any more than, if he had thrown sixes three times running, that event would render it either more or less likely that his next throw would show sixes.

100. It is the same with the operations of nature. With overwhelming uniformity, in our past experience, direct and indirect, stones left free to fall have fallen. Thereupon two hypotheses only are open to us. Either

1. the uniformity with which those stones have fallen has been due to mere chance and affords no ground whatever, not the slightest for any expectation that the next stone that shall be let go will fall; or

2. the uniformity with which stones have fallen has been due to some active general principle, in which case it would be a strange coincidence that it should cease to act at the moment my prediction was based upon it.

That position, gentlemen, will sustain criticism. It is irrefragable.

101. Of course, every sane man will adopt the latter hypothesis. If he could doubt it in the case of the stone -- which he can't -- and I may as well drop the stone once for all -- I told you so! -- if anybody doubts this still, a thousand other such inductive predictions are getting verified every day, and he will have to suppose every one of them to be merely fortuitous in order reasonably to escape the conclusion that general principles are really operative in nature. That is the doctrine of scholastic realism.

§2. THIRDNESS AND GENERALITY
102. You may, perhaps, ask me how I connect generality with Thirdness. Various different replies, each fully satisfactory, may be made to that inquiry. The old definition of a general is Generale est quod natum aptum est dici de multis. This recognizes that the general is essentially predicative and therefore of the nature of a representamen. And by following out that path of suggestion we should obtain a good reply to the inquiry.

103. In another respect, however, the definition represents a very degenerate sort of generality. None of the scholastic logics fails to explain that sol is a general term; because although there happens to be but one sun yet the term sol aptum natum est dici de multis. But that is most inadequately expressed. If sol is apt to be predicated of many, it is apt to be predicated of any multitude however great, and since there is no maximum multitude, those objects, of which it is fit to be predicated, form an aggregate that exceeds all multitude. Take any two possible objects that might be called suns and, however much alike they may be, any multitude whatsoever of intermediate suns are alternatively possible, and therefore as before these intermediate possible suns transcend all multitude. In short, the idea of a general involves the idea of possible variations which no multitude of existent things could exhaust but would leave between any two not merely many possibilities, but possibilities absolutely beyond all multitude.

104. Now Thirdness is nothing but the character of an object which embodies Betweenness or Mediation in its simplest and most rudimentary form; and I use it as the name of that element of the phenomenon which is predominant wherever Mediation is predominant, and which reaches its fullness in Representation.

105. Thirdness, as I use the term, is only a synonym for Representation, to which I prefer the less colored term because its suggestions are not so narrow and special as those of the word Representation. Now it is proper to say that a general principle that is operative in the real world is of the essential nature of a Representation and of a Symbol because its modus operandi is the same as that by which words produce physical effects. Nobody can deny that words do produce such effects. Take, for example, that sentence of Patrick Henry which, at the time of our Revolution, was repeated by every man to his neighbor:

"Three millions of people, armed in the holy cause of Liberty, and in such a country as we possess, are invincible against any force that the enemy can bring against us."

Those words present this character of the general law of nature. They might have produced effects indefinitely transcending any that circumstances allowed them to produce. It might, for example, have happened that some American schoolboy, sailing as a passenger in the Pacific Ocean, should have idly written down those words on a slip of paper. The paper might have been tossed overboard and might have been picked up by some Jagala on a beach of the island of Luzon; and if he had had them translated to him, they might easily have passed from mouth to mouth there as they did in this country, and with similar effect.

106. Words then do produce physical effects. It is madness to deny it. The very denial of it involves a belief in it; and nobody can consistently fail to acknowledge it until he sinks to a complete mental paresis.

But how do they produce their effect? They certainly do not, in their character as symbols, directly react upon matter. Such action as they have is merely logical. It is not even psychological. It is merely that one symbol would justify another. However, suppose that first difficulty to have been surmounted, and that they do act upon actual thoughts. That thoughts act on the physical world and conversely, is one of the most familiar of facts. Those who deny it are persons with whom theories are stronger than facts. But how thoughts act on things it is impossible for us, in the present state of our knowledge, so much as to make any very promising guess; although, as I will show you presently, a guess can be made which suffices to show that the problem is not beyond all hope of ultimate solution.

107. All this is equally true of the manner in which the laws of nature influence matter. A law is in itself nothing but a general formula or symbol. An existing thing is simply a blind reacting thing, to which not merely all generality, but even all representation, is utterly foreign. The general formula may logically determine another, less broadly general. But it will be of its essential nature general, and its being narrower does not in the least constitute any participation in the reacting character of the thing. Here we have that great problem of the principle of individuation which the scholastic doctors after a century of the closest possible analysis were obliged to confess was quite incomprehensible to them. Analogy suggests that the laws of nature are ideas or resolutions in the mind of some vast consciousness, who, whether supreme or subordinate, is a Deity relatively to us. I do not approve of mixing up Religion and Philosophy; but as a purely philosophical hypothesis, that has the advantage of being supported by analogy. Yet I cannot clearly see that beyond that support to the imagination it is of any particular scientific service. . . .

§3. NORMATIVE JUDGMENTS
108. Reasoning cannot possibly be divorced from logic; because, whenever a man reasons, he thinks that he is drawing a conclusion such as would be justified in every analogous case. He therefore cannot really infer without having a notion of a class of possible inferences, all of which are logically good. That distinction of good and bad he always has in mind when he infers. Logic proper is the critic of arguments, the pronouncing them to be good or bad. There are, as I am prepared to maintain, operations of the mind which are logically exactly analogous to inferences excepting only that they are unconscious and therefore uncontrollable and therefore not subject to criticism. But that makes all the difference in the world; for inference is essentially deliberate, and selfcontrolled. Any operation which cannot be controlled, any conclusion which is not abandoned, not merely as soon as criticism has pronounced against it, but in the very act of pronouncing that decree, is not of the nature of rational inference -- is not reasoning. Reasoning as deliberate is essentially critical, and it is idle to criticize as good or bad that which cannot be controlled. Reasoning essentially involves self-control; so that the logica utens is a particular species of morality. Logical goodness and badness, which we shall find is simply the distinction of Truth and Falsity in general, amounts, in the last analysis, to nothing but a particular application of the more general distinction of Moral Goodness and Badness, or Righteousness and Wickedness.

109. To criticize as logically sound or unsound an operation of thought that cannot be controlled is not less ridiculous than it would be to pronounce the growth of your hair to be morally good or bad. The ridiculousness in both cases consists in the fact that such a critical judgment may be pretended but cannot really be performed in clear thought, for on analysis it will be found absurd.

110. I am quite aware that this position is open to two serious objections, which I have not time to discuss, but which I have carefully considered and refuted. The first is that this is making logic a question of psychology. But this I deny. Logic does rest on certain facts of experience among which are facts about men, but not upon any theory about the human mind or any theory to explain facts. The other objection is that if the distinction [between] Good and Bad Logic is a special case [of the distinction between] Good and Bad Morals, by the same token the distinction of Good and Bad Morals is a special case of the distinction [between] esthetic Goodness and Badness. Now to admit this is not only to admit hedonism, which no man in his senses, and not blinded by theory or something worse, can admit, but also, having to do with the essentially Dualistic distinction of Good and Bad -- which is manifestly an affair of Category the Second -- it seeks the origin of this distinction in Esthetic Feeling, which belongs to Category the First.

111. This last objection deceived me for many years. The reply to it involves a very important point which I shall have to postpone to the next lecture. When it first presented itself to me, all I knew of ethics was derived from the study of Jouffroy †1 under Dr. Walker, of Kant, and of a wooden treatise by Whewell;†3 and I was led by this objection to a line of thought which brought me to regard ethics as a mere art, or applied science, and not a pure normative science at all. But when, beginning in 1883, I came to read the works of the great moralists, whose great fertility of thought I found in wonderful contrast to the sterility of the logicians -- I was forced to recognize the dependence of Logic upon Ethics; and then took refuge in the idea that there was no science of esthetics, that, because de gustibus non est disputandum, therefore there is no esthetic truth and falsity or generally valid goodness and badness. But I did not remain of this opinion long. I soon came to see that this whole objection rests upon a fundamental misconception. To say that morality, in the last resort, comes to an esthetic judgment is not hedonism -- but is directly opposed to hedonism. In the next place, every pronouncement between Good and Bad certainly comes under Category the Second; and for that reason such pronouncement comes out in the voice of conscience with an absoluteness of duality which we do not find even in logic; and although I am still a perfect ignoramus in esthetics, I venture to think that the esthetic state of mind is purest when perfectly naive without any critical pronouncement, and that the esthetic critic founds his judgments upon the result of throwing himself back into such a pure naive state -- and the best critic is the man who has trained himself to do this the most perfectly.

112. It is a great mistake to suppose that the phenomena of pleasure and pain are mainly phenomena of feeling. Examine pain, which would seem to be a good deal more positive than pleasure. I am unable to recognize with confidence any quality of feeling common to all pains; and if I cannot I am sure it cannot be an easy thing for anybody. For I have gone through a systematic course of training in recognizing my feelings. I have worked with intensity for so many hours a day every day for long years to train myself to this; and it is a training which I would recommend to all of you. The artist has such a training; but most of his effort goes to reproducing in one form or another what he sees or hears, which is in every art a very complicated trade; while I have striven simply to see what it is that I see. That this limitation of the task is a great advantage is proved to me by finding that the great majority of artists are extremely narrow. Their esthetic appreciations are narrow; and this comes from their only having the power of recognizing the qualities of their percepts in certain directions.

But the majority of those who opine that pain is a quality of feeling are not even artists; and even among those who are artists there are extremely few who are artists in pain. But the truth is that there are certain states of mind, especially among states of mind in which Feeling has a large share, which we have an impulse to get rid of. That is the obvious phenomenon; and the ordinary theory is that this impulse is excited by a quality of feeling common to all these states -- a theory which is supported by the fact that this impulse is particularly energetic in regard to states in which Feeling is the predominant element. Now whether this be true or false, it is a theory. It is not the fact that any such common quality in all pains is readily to be recognized.

113. At any rate, while the whole phenomenon of pain and the whole phenomenon of pleasure are phenomena that arise within the universe of states of mind and attain no great prominence except when they concern states of mind in which Feeling is predominant, yet these phenomena themselves do not mainly consist in any common Feeling-quality of Pleasure and any common Feelingquality of Pain, even if there are such Qualities of Feeling; but they mainly consist [in a] Pain [which lies] in a Struggle to give a state of mind its quietus, and [in a] Pleasure in a peculiar mode of consciousness allied to the consciousness of making a generalization, in which not Feeling, but rather Cognition is the principal constituent. This may be hard to make out as regards the lower pleasures, but they do not concern the argument we are considering. It is esthetic enjoyment which concerns us; and ignorant as I am of Art, I have a fair share of capacity for esthetic enjoyment; and it seems to me that while in esthetic enjoyment we attend to the totality of Feeling -- and especially to the total resultant Quality of Feeling presented in the work of art we are contemplating -- yet it is a sort of intellectual sympathy, a sense that here is a Feeling that one can comprehend, a reasonable Feeling. I do not succeed in saying exactly what it is, but it is a consciousness belonging to the category of Representation, though representing something in the Category of Quality of Feeling.

In that view of the matter, the objection to the doctrine that the distinction Moral approval and disapproval is ultimately only a species of the distinction Esthetic approval and disapproval seems to be answered.

114. It appears, then, that Logica utens consisting in self-control, the distinction of logical goodness and badness must begin where control of the processes of cognition begins; and any object that antecedes the distinction, if it has to be named either good or bad, must be named good. For since no fault can be found with it, it must be taken at its own valuation.

§4. PERCEPTUAL JUDGMENTS
115. Where then in the process of cognition does the possibility of controlling it begin? Certainly not before the percept is formed.

Even after the percept is formed there is an operation which seems to me to be quite uncontrollable. It is that of judging what it is that the person perceives. A judgment is an act of formation of a mental proposition combined with an adoption of it or act of assent to it. A percept on the other hand is an image or moving picture or other exhibition. The perceptual judgment, that is, the first judgment of a person as to what is before his senses, bears no more resemblance to the percept than the figure I am going to draw is like a man.

I do not see that it is possible to exercize any control over that operation or to subject it to criticism. If we can criticize it at all, as far as I can see, that criticism would be limited to performing it again and seeing whether, with closer attention, we get the same result. But when we so perform it again, paying now closer attention, the percept is presumably not such as it was before. I do not see what other means we have of knowing whether it is the same as it was before or not, except by comparing the former perceptual judgment and the later one. I should utterly distrust any other method of ascertaining what the character of the percept was. Consequently, until I am better advised, I shall consider the perceptual judgment to be utterly beyond control. Should I be wrong in this, the Percept, at all events, would seem to be so.

116. It follows, then, that our perceptual judgments are the first premisses of all our reasonings and that they cannot be called in question. All our other judgments are so many theories whose only justification is that they have been and will be borne out by perceptual judgments. But the perceptual judgments declare one thing to be blue, another yellow -- one sound to be that of A, another that of U, another that of I. These are the Qualities of Feeling which the physicists say are mere illusions because there is no room for them in their theories. If the facts won't agree with the Theory, so much the worse for them. They are bad facts. This sounds to me childish, I confess. It is like an infant that beats an inanimate object that hurts it. Indeed this is true of all fault-finding with others than oneself, and those for whose conduct one is responsible. Reprobation is a silly [business].

117. But peradventure I shall be asked whether I do not admit that there is any such thing as an illusion or hallucination. Oh, yes; among artists I have known more than one case of downright hallucinatory imaginations at the beck and call of these {poietai}. Of course, the man knows that such obedient spectres are not real experiences, because experience is that which forces itself upon him, will-he nill-he.

Hallucinations proper -- obsessional hallucinations -- will not down at one's bidding, and people who are subject to them are accustomed to sound the people who are with them in order to ascertain whether the object before them has a being independent of their disease or not. There are also social hallucinations.

In such a case, a photographic camera or other instrument might be of service.

118. Of course, everybody admits and must admit that these apparitions are entities -- entia; the question is whether these entia belong to the class of realities or not, that is, whether they are such as they are independently of any collection of singular representations that they are so, or whether their mode of being depends upon abnormal conditions. But as for the entire universe of Qualities which the physicist would pronounce Illusory, there is not the smallest shade of just suspicion resting upon their normality. On the contrary, there is considerable evidence that colors, for example, and sounds have the same character for all mankind.

Well, I will skip this. Suffice it to say that there is no reason for suspecting the veracity of the senses, and the presumption is that the physics of the future will find out that they are more real than the present state of scientific theory admits of their being represented as being.

119. Therefore, if you ask me what part Qualities can play in the economy of the universe, I shall reply that the universe is a vast representamen, a great symbol of God's purpose, working out its conclusions in living realities. Now every symbol must have, organically attached to it, its Indices of Reactions and its Icons of Qualities; and such part as these reactions and these qualities play in an argument that, they of course, play in the universe -- that Universe being precisely an argument. In the little bit that you or I can make out of this huge demonstration, our perceptual judgments are the premisses for us and these perceptual judgments have icons as their predicates, in which icons Qualities are immediately presented. But what is first for us is not first in nature. The premisses of Nature's own process are all the independent uncaused elements of facts that go to make up the variety of nature which the necessitarian supposes to have been all in existence from the foundation of the world, but which the Tychist supposes are continually receiving new accretions. These premisses of nature, however, though they are not the perceptual facts that are premisses to us, nevertheless must resemble them in being premisses. We can only imagine what they are by comparing them with the premisses for us. As premisses they must involve Qualities.

Now as to their function in the economy of the Universe. The Universe as an argument is necessarily a great work of art, a great poem -- for every fine argument is a poem and a symphony -- just as every true poem is a sound argument. But let us compare it rather with a painting -- with an impressionist seashore piece -- then every Quality in a Premiss is one of the elementary colored particles of the Painting; they are all meant to go together to make up the intended Quality that belongs to the whole as whole. That total effect is beyond our ken; but we can appreciate in some measure the resultant Quality of parts of the whole -- which Qualities result from the combinations of elementary Qualities that belong to the premisses.

But I shall endeavor to make this clearer in the next lecture.

§1. THE DIVISIONS OF PHILOSOPHY
I have already explained that by Philosophy I mean that department of Positive Science, or Science of Fact, which does not busy itself with gathering facts, but merely with learning what can be learned from that experience which presses in upon every one of us daily and hourly. It does not gather new facts, because it does not need them, and also because new general facts cannot be firmly established without the assumption of a metaphysical doctrine; and this, in turn, requires the coöperation of every department of philosophy; so that such new facts, however striking they may be, afford weaker support to philosophy by far than that common experience which nobody doubts or can doubt, and which nobody ever even pretended to doubt except as a consequence of belief in that experience so entire and perfect that it failed to be conscious of itself; just as an American who has never been abroad fails to perceive the characteristics of Americans; just as a writer is unaware of the peculiarities of his own style; just as none of us can see himself as others see him. (CP 5-120)

Philosophy has three grand divisions.
The first is Phenomenology, which simply contemplates the Universal Phenomenon and discerns its ubiquitous elements, Firstness, Secondness, and Thirdness, together perhaps with other series of categories.
The second grand division is Normative Science, which investigates the universal and necessary laws of the relation of Phenomena to Ends, that is, perhaps, to Truth, Right, and Beauty.
The third grand division is Metaphysics, which endeavors to comprehend the Reality of Phenomena.

Now Reality is an affair of Thirdness as Thirdness, that is, in its mediation between Secondness and Firstness. Most, if not all of you, are, I doubt not, Nominalists; and I beg you will not take offence at a truth which is just as plain and undeniable to me as is the truth that children do not understand human life. To be a nominalist consists in the undeveloped state in one's mind of the apprehension of Thirdness as Thirdness. The remedy for it consists in allowing ideas of human life to play a greater part in one's philosophy. Metaphysics is the science of Reality. Reality consists in regularity. Real regularity is active law. Active law is efficient reasonableness, or in other words is truly reasonable reasonableness. Reasonable reasonableness is Thirdness as Thirdness.

So then the division of Philosophy into these three grand departments, whose distinctness can be established without stopping to consider the contents of Phenomenology (that is, without asking what the true categories may be), turns out to be a division according to Firstness, Secondness, and Thirdness, and is thus one of the very numerous phenomena I have met with which confirm this list of categories. (CP 5-121)

Phenomenology treats of the universal Qualities of Phenomena in their immediate phenomenal character, in themselves as phenomena. It, thus, treats of Phenomena in their Firstness. (CP 5-122)

Normative Science treats of the laws of the relation of phenomena to ends; that is, it treats of Phenomena in their Secondness. (CP 5-123)

Metaphysics treats of Phenomena in their Thirdness. (CP 5-124)

Normative Science is not a skill, nor is it an investigation conducted with a view to the production of skill. … It is purely theoretical. Of course there are practical sciences of reasoning and investigation, of the conduct of life, and of the production of works of art. They correspond to the Normative Sciences, and may be probably expected to receive aid from them. But they are not integrant parts of these sciences. … Nor again is Normative Science a special science, that is, one of those sciences that discover new phenomena. It is not even aided in any appreciable degree by any such science. … The fact that men for the most part show a natural disposition to approve nearly the same arguments that logic approves, nearly the same acts that ethics approves, and nearly the same works of art that esthetics approves, may be regarded as tending to support the conclusions of logic, ethics, and esthetics. But such support is perfectly insignificant; and when it comes to a particular case, to urge that anything is sound and good logically, morally, or esthetically, for no better reason than that men have a natural tendency to think so, I care not how strong and imperious that tendency may be, is as pernicious a fallacy as ever was. (CP 5-125)

In one of the ways I have indicated, Normative Science is by the majority of writers of the present day ranked too low in the scale of the sciences. On the other hand, some students of exact logic rank that normative science, at least, too high, by virtually treating it as on a par with pure mathematics. There are three excellent reasons any one of which ought to rescue them from the error of this opinion. In the first place, the hypotheses from which the deductions of normative science proceed are intended to conform to positive truth of fact and those deductions derive their interest from that circumstance almost exclusively; while the hypotheses of pure mathematics are purely ideal in intention, and their interest is purely intellectual. But in the second place, the procedure of the normative sciences is not purely deductive, as that of mathematics is, nor even principally so. Their peculiar analyses of familiar phenomena, analyses which ought to be guided by the facts of phenomenology in a manner in which mathematics is not at all guided, separate Normative Science from mathematics quite radically. In the third place, there is a most intimate and essential element of Normative Science which is still more proper to it, and that is its peculiar appreciations, to which nothing at all in the phenomena, in themselves, corresponds. These appreciations relate to the conformity of phenomena to ends which are not immanent within those phenomena. (CP 5-126)

There are sundry other widely spread misconceptions of the nature of Normative Science. One of these is that the chief, if not the only, problem of Normative Science is to say what is good and what bad, logically, ethically, and esthetically; or what degree of goodness a given description of phenomenon attains. Were this the case, normative science would be, in a certain sense, mathematical, since it would deal entirely with a question of quantity. But I am strongly inclined to think that this view will not sustain critical examination. Logic classifies arguments, and in doing so recognizes different kinds of truth. In ethics, too, qualities of good are admitted by the great majority of moralists. As for esthetics, in that field qualitative differences appear to be so prominent that, abstracted from them, it is impossible to say that there is any appearance which is not esthetically good. Vulgarity and pretension, themselves, may appear quite delicious in their perfection, if we can once conquer our squeamishness about them, a squeamishness which results from a contemplation of them as possible qualities of our own handiwork --but that is a moral and not an esthetic way of considering them. I hardly need remind you that goodness, whether esthetic, moral, or logical, may either be negative --consisting in freedom from fault --or quantitative --consisting in the degree to which it attains. But in an inquiry, such as we are now engaged upon, negative goodness is the important thing. (CP 5-127)

A subtle and almost ineradicable narrowness in the conception of Normative Science runs through almost all modern philosophy in making it relate exclusively to the human mind. The beautiful is conceived to be relative to human taste, right and wrong concern human conduct alone, logic deals with human reasoning. Now in the truest sense these sciences certainly are indeed sciences of mind. Only, modern philosophy has never been able quite to shake off the Cartesian idea of the mind, as something that "resides" in the pineal gland. (CP 5-128)

§2. ETHICAL AND ESTHETICAL GOODNESS
I cannot linger more upon the general conception of Normative Science. I must come down to the particular Normative Sciences. These are now commonly said to be logic, ethics, and esthetics. Formerly only logic and ethics were reckoned as such. A few logicians refuse to recognize any other normative science than their own. My own opinions of ethics and esthetics are far less matured than my logical opinions. It is only since 1883 that I have numbered ethics among my special studies; and until about four years ago, I was not prepared to affirm that ethics was a normative science. As for esthetics, although the first year of my study of philosophy was devoted to this branch exclusively, yet I have since then so completely neglected it that I do not feel entitled to have any confident opinions about it. I am inclined to think that there is such a Normative Science; but I feel by no means sure even of that.

Supposing, however, that normative science divides into esthetics, ethics, and logic, then it is easily perceived, from my standpoint, that this division is governed by the three categories. For Normative Science in general being the science of the laws of conformity of things to ends, esthetics considers those things whose ends are to embody qualities of feeling, ethics those things whose ends lie in action, and logic those things whose end is to represent something. (CP 5-129)

The act of inference consists in the thought that the inferred conclusion is true because in any analogous case an analogous conclusion would be true. Thus, logic is coeval with reasoning. ... It essentially involves an approval of it --a qualitative approval. Now such self-approval supposes self-control. Not that we regard our approval as itself a voluntary act, but that we hold the act of inference, which we approve, to be voluntary. That is, if we did not approve, we should not infer.
There are mental operations which are as completely beyond our control as the growth of our hair. But when we institute an experiment to test a theory, or when we imagine an extra line to be inserted in a geometrical diagram in order to determine a question in geometry, these are voluntary acts which our logic, whether it be of the natural or the scientific sort, approves.
Now, the approval of a voluntary act is a moral approval.
Ethics is the study of what ends of action we are deliberately prepared to adopt. That is right action which is in conformity to ends which we are prepared deliberately to adopt. That is all there can be in the notion of righteousness, as it seems to me. The righteous man is the man who controls his passions, and makes them conform to such ends as he is prepared deliberately to adopt as ultimate. If it were in the nature of a man to be perfectly satisfied to make his personal comfort his ultimate aim, no more blame would attach to him for doing so than attaches to a hog for behaving in the same way.
A logical reasoner is a reasoner who exercises great self-control in his intellectual operations; and therefore the logically good is simply a particular species of the morally good.
Ethics --the genuine normative science of ethics, as contradistinguished from the branch of anthropology which in our day often passes under the name of ethics --this genuine ethics is the normative science par excellence, because an end --the essential object of normative science --is germane to a voluntary act in a primary way in which it is germane to nothing else.
For that reason I have some lingering doubt as to there being any true normative science of the beautiful. On the other hand, an ultimate end of action deliberately adopted --that is to say, reasonably adopted --must be a state of things that reasonably recommends itself in itself aside from any ulterior consideration. It must be an admirable ideal, having the only kind of goodness that such an ideal can have; namely, esthetic goodness. From this point of view the morally good appears as a particular species of the esthetically good. (CP 5-130)

If this line of thought be sound, the morally good will be the esthetically good specially determined by a peculiar superadded element; and the logically good will be the morally good specially determined by a special superadded element. (CP 5-131)

This suggestion must go for what it may be worth, which I dare say may be very little. If it be correct, it will follow that there is no such thing as positive esthetic badness; and since by goodness we chiefly in this discussion mean merely the absence of badness, or faultlessness, there will be no such thing as esthetic goodness. All there will be will be various esthetic qualities; that is, simple qualities of totalities not capable of full embodiment in the parts, which qualities may be more decided and strong in one case than in another. But the very reduction of the intensity may be an esthetic quality; nay, it will be so; and I am seriously inclined to doubt there being any distinction of pure esthetic betterness and worseness. My notion would be that there are innumerable varieties of esthetic quality, but no purely esthetic grade of excellence. (CP 5-132)

But the instant that an esthetic ideal is proposed as an ultimate end of action, at that instant a categorical imperative pronounces for or against it. Kant, as you know, proposes to allow that categorical imperative to stand unchallenged --an eternal pronouncement. His position is in extreme disfavor now, and not without reason. Yet I cannot think very highly of the logic of the ordinary attempts at refuting it. The whole question is whether or not this categorical imperative be beyond control. If this voice of conscience is unsupported by ulterior reasons, is it not simply an insistent irrational howl, the hooting of an owl which we may disregard if we can? Why should we pay any more attention to it than we would to the barking of a cur? If we cannot disregard conscience, all homilies and moral maxims are perfectly idle. But if it can be disregarded, it is, in one sense, not beyond control. It leaves us free to control ourselves. So then, it appears to me that any aim whatever which can be consistently pursued becomes, as soon as it is unfalteringly adopted, beyond all possible criticism, except the quite impertinent criticism of outsiders. An aim which cannot be adopted and consistently pursued is a bad aim. It cannot properly be called an ultimate aim at all. The only moral evil is not to have an ultimate aim. (CP 5-133)

Accordingly the problem of ethics is to ascertain what end is possible. It might be thoughtlessly supposed that special science could aid in this ascertainment. But that would rest on a misconception of the nature of an absolute aim, which is what would be pursued under all possible circumstances --that is, even though the contingent facts ascertained by special sciences were entirely different from what they are. Nor, on the other hand, must the definition of such aim be reduced to a mere formalism. (CP 5-134)

The importance of the matter for pragmatism is obvious. For if the meaning of a symbol consists in how it might cause us to act, it is plain that this "how" cannot refer to the description of mechanical motions that it might cause, but must intend to refer to a description of the action as having this or that aim. In order to understand pragmatism, therefore, well enough to subject it to intelligent criticism, it is incumbent upon us to inquire what an ultimate aim, capable of being pursued in an indefinitely prolonged course of action, can be. (CP 5-135)

The deduction of this is somewhat intricate, on account of the number of points which have to be taken into account; and of course I cannot go into details. In order that the aim should be immutable under all circumstances, without which it will not be an ultimate aim, it is requisite that it should accord with a free development of the agent's own esthetic quality. At the same time it is requisite that it should not ultimately tend to be disturbed by the reactions upon the agent of that outward world which is supposed in the very idea of action. It is plain that these two conditions can be fulfilled at once only if it happens that the esthetic quality toward which the agent's free development tends and that of the ultimate action of experience upon him are parts of one esthetic total. Whether or not this is really so, is a metaphysical question which it does not fall within the scope of Normative Science to answer. If it is not so, the aim is essentially unattainable. But just as in playing a hand of whist, when only three tricks remain to be played, the rule is to assume that the cards are so distributed that the odd trick can be made, so the rule of ethics will be to adhere to the only possible absolute aim, and to hope that it will prove attainable. Meantime, it is comforting to know that all experience is favorable to that assumption. (CP 5-136)

§3. LOGICAL GOODNESS
The ground is now cleared for the analysis of logical goodness, or the goodness of representation. There is a special variety of esthetic goodness that may belong to a representamen, namely, expressiveness. There is also a special moral goodness of representations, namely, veracity. But besides this there is a peculiar mode of goodness which is logical. What this consists in we have to inquire. (CP 5-137)

The mode of being of a representamen is such that it is capable of repetition. Take, for example, any proverb. "Evil communications corrupt good manners." Every time this is written or spoken in English, Greek, or any other language, and every time it is thought of it is one and the same representamen. Itis the same with a diagram or picture. It is the same with a physical sign or symptom. If two weathercocks are different signs, it is only in so far as they referto different parts of the air. A representamen which should have a unique embodiment, incapable of repetition, would not be a representamen, but a part of the very fact represented. This repetitory character of the representamen involves as a consequence that it is essential to a representamen that it should contribute to the determination of another representamen distinct from itself. ... I call a representamen which is determined by another representamen, an interpretant of the latter. Every representamen is related or is capable of being related to a reacting thing, its object, and every representamen embodies, in some sense, some quality, which may be called its signification. (CP 5-138)

A representamen [as symbol] is either a rhema, a proposition, or an argument. An argument is a representamen which separately shows what interpretant it is intended to determine. A proposition is a representamen which is not an argument, but which separately indicates what object it is intended to represent. A rhema is a simple representation without such separate parts. (CP 5-139)

Esthetic goodness, or expressiveness, may be possessed, and in some degree must be possessed, by any kind of representamen -- rhema, proposition, or argument. (CP 5-140)

Moral goodness, or veracity, may be possessed by a proposition or by an argument, but cannot be possessed by a rhema. A mental judgment or inference must possess some degree of veracity. (CP 5-141)

As to logical goodness, or truth, the statements in the books are faulty; and it is highly important for our inquiry that they should be corrected. The books distinguish between logical truth, which some of them rightly confine to arguments that do not promise more than they perform, and material truth which belongs to propositions, being that which veracity aims to be; and this is conceived to be a higher grade of truth than mere logical truth.
I would correct this conception as follows. In the first place, all our knowledge rests upon perceptual judgments. These are necessarily veracious in greater or less degree according to the effort made, but there is no meaning in saying that they have any other truth than veracity, since a perceptual judgment can never be repeated. At most we can say of a perceptual judgment that its relation to other perceptual judgments is such as to permit a simple theory of the facts. Thus I may judge that I see a clean white surface. But a moment later I may question whether the surface really was clean, and may look again more sharply. If this second more veracious judgment still asserts that I see a clean surface, the theory of the facts will be simpler than if, at my second look, I discern that the surface is soiled. Still, even in this last case, I have no right to say that my first percept was that of a soiled surface. I absolutely have no testimony concerning it, except my perceptual judgment, and although that was careless and had no high degree of veracity, still have to accept the only evidence in my possession.
Now consider any other judgment I may make. That is a conclusion of inferences ultimately based on perceptual judgments, and since these are indisputable, all the truth which my judgment can have must consist in the logical correctness of those inferences. Or I may argue the matter in another way. To say that a proposition is false is not veracious unless the speaker has found out that it is false. Confining ourselves, therefore, to veracious propositions, to say that a proposition is false and that it has been found to be false are equivalent, in the sense of being necessarily either both true or both false. Consequently, to say that a proposition is perhaps false is the same as to say that it will perhaps be found out to be false. Hence to deny one of these is to deny the other. To say that a proposition is certainly true means simply that it never can be found out to be false, or in other words, that it is derived by logically correct arguments from veracious perceptual judgments. Consequently, the only difference between material truth and the logical correctness of argumentation is that the latter refers to a single line of argument and the former to all the arguments which could have a given proposition or its denial as their conclusion.
Let me say to you that this reasoning needs to be scrutinized with the severest and minutest logical criticism, because pragmatism largely depends upon it. (CP 5-142)

It appears, then, that logical goodness is simply the excellence of argument -- its negative, and more fundamental, goodness being its soundness and weight, its really having the force that it pretends to have and that force being great, while its quantitative goodness consists in the degree in which it advances our knowledge. In what then does the soundness of argument consist? (CP 5-143)

In order to answer that question it is necessary to recognize three radically different kinds of arguments which I signalized in 1867 and which had been recognized by the logicians of the eighteenth century, although [those] logicians quite pardonably failed to recognize the inferential character of one of them. Indeed, I suppose that the three were given by Aristotle in the Prior Analytics, although the unfortunate illegibility of a single word in his MS. and its replacement by a wrong word by his first editor, the stupid [Apellicon], has completely altered the sense of the chapter on Abduction. At any rate, even if my conjecture is wrong, and the text must stand as it is, still Aristotle, in that chapter on Abduction, was even in that case evidently groping for that mode of inference which I call by the otherwise quite useless name of Abduction -- a word which is only employed in logic to translate the [{apagoge}] of that chapter. (CP 5-144)

These three kinds of reasoning are Abduction, Induction, and Deduction. Deduction is the only necessary reasoning. It is the reasoning of mathematics. It starts from a hypothesis, the truth or falsity of which has nothing to do with the reasoning; and of course its conclusions are equally ideal. The ordinary use of the doctrine of chances is necessary reasoning, although it is reasoning concerning probabilities. Induction is the experimental testing of a theory. The justification of it is that, although the conclusion at any stage of the investigation may be more or less erroneous, yet the further application of the same method must correct the error. The only thing that induction accomplishes is to determine the value of a quantity. It sets out with a theory and it measures the degree of concordance of that theory with fact. It never can originate any idea whatever. No more can deduction. All the ideas of science come to it by the way of Abduction. Abduction consists in studying facts and devising a theory to explain them. Its only justification is that if we are ever to understand things at all, it must be in that way. (CP 5-145)

Concerning the relations of these three modes of inference to the categories and concerning certain other details, my opinions, I confess, have wavered. ... This perhaps ought to give a slight additional weight to those opinions in which I have never wavered. Among these opinions which I have constantly maintained is this, that while Abductive and Inductive reasoning are utterly irreducible, either to the other or to Deduction, or Deduction to either of them, yet the only rationale of these methods is essentially Deductive or Necessary. If then we can state wherein the validity of Deductive reasoning lies, we shall have defined the foundation of logical goodness of whatever kind. (CP 5-146)

Now all necessary reasoning, whether it be good or bad, is of the nature of mathematical reasoning.
My analyses of reasoning surpass in thoroughness all that has ever been done in print, whether in words or in symbols. (CP 5-147)

It is on the basis of such analysis that I declare that all necessary reasoning, be it the merest verbiage of the theologians, so far as there is any semblance of necessity in it, is mathematical reasoning. Now mathematical reasoning is diagrammatic. This is as true of algebra as of geometry. But in order to discern the features of diagrammatic reasoning, it is requisite to begin with examples that are not too simple. In simple cases, the essential features are so nearly obliterated that they can only be discerned when one knows what to look for. But beginning with suitable examples and thence proceeding to others, one finds that the diagram itself, in its individuality, is not what the reasoning is concerned with. I will take an example which recommends itself only by its consideration requiring but a moment. A line abuts upon an ordinary point of another line forming two angles. The sum of these angles is proved by Legendre to be equal to the sum of two right angles by erecting a perpendicular to the second line in the plane of the two and through the point of abuttal. This perpendicular must lie in the one angle or the other. The pupil is supposed to see that. He sees it only in a special case, but he is supposed to perceive that it will be so in any case. The more careful logician may demonstrate that it must fall in one angle or the other; but this demonstration will only consist in substituting a different diagram in place of Legendre's figure. But in any case, either in the new diagram or else, and more usually, in passing from one diagram to the other, the interpreter of the argumentation will be supposed to see something, which will present this little difficulty for the theory of vision, that it is of a general nature. (CP 5-148)

Mr. Mill's disciples will say that this proves that geometrical reasoning is inductive. I do not wish to speak disparagingly of Mill's treatment of the Pons Asinorum because it penetrates further into the logic of the subject than anybody had penetrated before. Only it does not quite touch bottom. As for such general perceptions being inductive, I might treat the question from a technical standpoint and show that the essential characters of induction are wanting. But besides the interminable length, such a way of dealing with the matter would hardly meet the point. It is better to remark that the "uniformity of nature" is not in question, and that there is no way of applying that principle to supporting the mathematical reasoning that will not enable me to give a precisely analogous instance in every essential particular, except that it will be a fallacy that no good mathematician could overlook. If you admit the principle that logic stops where self-control stops, you will find yourself obliged to admit that a perceptual fact, a logical origin, may involve generality. This can be shown for ordinary generality. But if you have already convinced yourself that continuity is generality, it will be somewhat easier to show that a perceptual fact may involve continuity than that it can involve non-relative generality. (CP 5-149)

If you object that there can be no immediate consciousness of generality, I grant that. If you add that one can have no direct experience of the general, I grant that as well. Generality, Thirdness, pours in upon us in our very perceptual judgments, and all reasoning, so far as it depends on necessary reasoning, that is to say, mathematical reasoning, turns upon the perception of generality and continuity at every step. (CP 5-150)

§1. PERCEPTUAL JUDGMENTS AND GENERALITY
Perceptual judgments involve generality.
What is the general? The Aristotelian definition is good enough. It is quod aptum natum est praedicari de pluribus; {legö de katholou men ho epi pleionön pephyke katégoreisthai}. De Interp.
When logic was studied in a scientific spirit of exactitude it was recognized on all hands that all ordinary judgments contain a predicate and that this predicate is general. There seemed to be some exceptions, of which the only noticeable ones were expository judgments, such as "Tully is Cicero." But the Logic of Relations has now reduced logic to order, and it is seen that a proposition may have any number of subjects but can have but one predicate which is invariably general. Such a proposition as "Tully is Cicero" predicates the general relation of identity of Tully and Cicero.
Consequently, it is now clear that if there be any perceptual judgment, or proposition directly expressive of and resulting from the quality of a present percept, or sense-image, that judgment must involve generality in its predicate. (CP5-151)

In saying that perceptual judgments involve general elements I certainly never intended to be understood as enunciating any proposition in psychology. For my principles absolutely debar me from making the least use of psychology in logic. I am confined entirely to the unquestionable facts of everyday experience, together with what can be deduced from them. All that I can mean by a perceptual judgment is a judgment absolutely forced upon my acceptance, and that by a process which I am utterly unable to control and consequently am unable to criticize. Nor can I pretend to absolute certainty about any matter of fact.
Now consider the judgment that one event C appears to be subsequent to another event A. Certainly, I may have inferred this; because I may have remarked that C was subsequent to a third event B which was itself subsequent to A. But then these premisses are judgments of the same description. It does not seem possible that I can have performed an infinite series of acts of criticism each of which must require a distinct effort. The case is quite different from that of Achilles and the tortoise because Achilles does not require to make an infinite series of distinct efforts. It therefore appears that I must have made some judgment that one event appeared to be subsequent to another without that judgment having been inferred from any premiss [i.e.] without any controlled and criticized action of reasoning. If this be so, it is a perceptual judgment in the only sense that the logician can recognize. But from that proposition that one event, Z, is subsequent to another event, J, I can at once deduce by necessary reasoning a universal proposition. Namely, the definition of the relation of apparent subsequence is well known, or sufficiently so for our purpose. Z will appear to be subsequent to Y if and only if Z appears to stand in a peculiar relation, R, to Y such that nothing can stand in the relation R to itself, and if, furthermore, whatever event, X, there may be to which Y stands in the relation R, to that same X, Z also stands in the relation R. This being implied in the meaning of subsequence, concerning which there is no room for doubt, it easily follows that whatever is subsequent to C is subsequent to anything, A, to which C is subsequent --which is a universal proposition.
Thus my assertion at the end of the last lecture appears to be most amply justified. Thirdness pours in upon us through every avenue of sense. (CP5-157)

§2. THE PLAN AND STEPS OF REASONING
We may now profitably ask ourselves what logical goodness is. We have seen that any kind of goodness consists in the adaptation of its subject to its end. … If you call this utilitarianism, I shall not be ashamed of the title. For I do not know what other system of philosophy has wrought so much good in the world as that same utilitarianism. Bentham may be a shallow logician; but such truths as he saw, he saw most nobly. As for the vulgar utilitarian, his fault does not lie in his pressing too much the question of what would be the good of this or that. On the contrary his fault is that he never presses the question half far enough, or rather he never really raises the question at all. He simply rests in his present desires as if desire were beyond all dialectic. He wants, perhaps, to go to heaven. But he forgets to ask what would be the good of his going to heaven. He would be happy, there, he thinks. But that is a mere word. It is no real answer to the question. (CP5-158)

Our question is, What is the use of thinking? We have already remarked that it is the argument alone which is the primary and direct subject of logical goodness and badness. We have therefore to ask what the end of argumentation is, what it ultimately leads to. (CP5-159)

Reasoning is of three types, Deduction, Induction, and Abduction.
In deduction, or necessary reasoning, we set out from a hypothetical state of things which we define in certain abstracted respects. …. We consider this hypothetical state of things and are led to conclude that … something else not explicitly supposed in that hypothesis will be true invariably. Our inference is valid if and only if there really is such a relation between the state of things supposed in the premisses and the state of things stated in the conclusion. (CP5-161)

All necessary reasoning without exception is diagrammatic. That is, we construct an icon of our hypothetical state of things and proceed to observe it. This observation leads us to suspect that something is true, which we may or may not be able to formulate with precision, and we proceed to inquire whether it is true or not.
For this purpose it is necessary to form a plan of investigation and this is the most difficult part of the whole operation. We not only have to select the features of the diagram which it will be pertinent to pay attention to, but it is also of great importance to return again and again to certain features. Otherwise, although our conclusions may be correct, they will not be the particular conclusions at which we are aiming. (CP5-162)

Having thus determined the plan of the reasoning, we proceed to the reasoning itself, and this I have ascertained can be reduced to three kinds of steps. The first consists in copulating separate propositions into one compound proposition. The second consists in omitting something from a proposition without possibility of introducing error. The third consists in inserting something into a proposition without introducing error. (CP5-163)

Somebody may answer that the copulative proposition contains the conjunction "and" or something equivalent, and that the very meaning of this "and" is that the entire copulation is true if and only if each of the members is singly true; so that it is involved in the very meaning of the copulative proposition that any member may be dropped.
It is another way of saying that what we call the meaning of a proposition embraces every obvious necessary deduction from it.
But how it helps us to understand our passing from an accepted judgment A to another judgment C of which we not only feel equally confident but in point of fact are equally sure?
To this the advocate of the explanation by the conception of "meaning" may reply: that is meant which is intended or purposed; that a judgment is a voluntary act, and our intention is not to employ the form of the judgment A, except to the interpretation of images to which judgments, corresponding in form to C, can be applied. (CP5-165)

Perhaps it may reconcile the psychologist to the admission of perceptual judgments involving generality to be told that they are perceptual judgments concerning our own purposes. I certainly think that the certainty of pure mathematics and of all necessary reasoning is due to the circumstance that it relates to objects which are the creations of our own minds, and that mathematical knowledge is to be classed along with knowledge of our own purposes. When we meet with a surprising result in pure mathematics, as we so often do, because a loose reasoning had led us to suppose it impossible, this is essentially the same sort of phenomenon as when in pursuing a purpose we are led to do something that we are quite surprised to find ourselves doing, as being contrary, or apparently contrary, to some weaker purpose.(CP5-166)

§3. INDUCTIVE REASONING
Induction consists in starting from a theory, deducing from it predictions of phenomena, and observing those phenomena in order to see how nearly they agree with the theory. The justification for believing that an experiential theory which has been subjected to a number of experimental tests will be in the near future sustained about as well by further such tests as it has hitherto been, is that by steadily pursuing that method we must in the long run find out how the matter really stands. The reason that we must do so is that our theory, if it be admissible even as a theory, simply consists in supposing that such experiments will in the long run have results of a certain character. But I must not be understood as meaning that experience can be exhausted, or that any approach to exhaustion can be made. What I mean is that if there be a series of objects, say crosses and circles, this series having a beginning but no end, then whatever may be the arrangement or want of arrangement of these crosses and circles in the entire endless series must be discoverable to an indefinite degree of approximation by examining a sufficient finite number of successive ones beginning at the beginning of the series. This is a theorem capable of strict demonstration. The principle of the demonstration is that whatever has no end can have no mode of being other than that of a law, and therefore whatever general character it may have must be describable, but the only way of describing an endless series is by stating explicitly or implicitly the law of the succession of one term upon another. But every such term has a finite ordinal place from the beginning and therefore, if it presents any regularity for all finite successions from the beginning, it presents the same regularity throughout. Thus the validity of induction depends upon the necessary relation between the general and the singular. It is precisely this which is the support of Pragmatism.(CP5-170)

§4. INSTINCT AND ABDUCTION
Abduction is the process of forming an explanatory hypothesis. It is the only logical operation which introduces any new idea; for induction does nothing but determine a value, and deduction merely evolves the necessary consequences of a pure hypothesis.
Deduction proves that something must be; Induction shows that something actually is operative; Abduction merely suggests that something may be.
Its only justification is that from its suggestion deduction can draw a prediction which can be tested by induction, and that, if we are ever to learn anything or to understand phenomena at all, it must be by abduction that this is to be brought about.
No reason whatsoever can be given for it, as far as I can discover; and it needs no reason, since it merely offers suggestions. (CP5-171)

A man must be downright crazy to deny that science has made many true discoveries. But every single item of scientific theory which stands established today has been due to Abduction.
But how is it that all this truth has ever been lit up by a process in which there is no compulsiveness nor tendency toward compulsiveness? Is it by chance? Consider the multitude of theories that might have been suggested. A physicist comes across some new phenomenon in his laboratory. How does he know but the conjunctions of the planets have something to do with it or that it is not perhaps because the dowager empress of China has at that same time a year ago chanced to pronounce some word of mystical power or some invisible jinnee may be present. Think of what trillions of trillions of hypotheses might be made of which one only is true; and yet after two or three or at the very most a dozen guesses, the physicist hits pretty nearly on the correct hypothesis. By chance he would not have been likely to do so in the whole time that has elapsed since the earth was solidified. You may tell me that astrological and magical hypotheses were resorted to at first and that it is only by degrees that we have learned certain general laws of nature in consequence of which the physicist seeks for the explanation of his phenomenon within the four walls of his laboratory. But when you look at the matter more narrowly, the matter is not to be accounted for in any considerable measure in that way. Take a broad view of the matter. Man has not been engaged upon scientific problems for over twenty thousand years or so. But put it at ten times that if you like. But that is not a hundred thousandth part of the time that he might have been expected to have been searching for his first scientific theory. (CP5-172)

However man may have acquired his faculty of divining the ways of Nature, it has certainly not been by a self-controlled and critical logic. Even now he cannot give any exact reason for his best guesses. It appears to me that the clearest statement we can make of the logical situation --the freest from all questionable admixture --is to say that man has a certain Insight, not strong enough to be oftener right than wrong, but strong enough not to be overwhelmingly more often wrong than right, into the Thirdnesses, the general elements, of Nature. An Insight, I call it, because it is to be referred to the same general class of operations to which Perceptive Judgments belong. This Faculty is at the same time of the general nature of Instinct, resembling the instinct s of the animals in its so far surpassing the general powers of our reason and for its directing us as if we were in possession of facts that are entirely beyond the reach of our senses. It resembles instinct too in its small liability to error; for though it goes wrong oftener than right, yet the relative frequency with which it is right is on the whole the most wonderful thing in our constitution. (CP5-173)

If you ask an investigator why he does not try this or that wild theory, he will say, "It does not seem reasonable." It is curious that we seldom use this word where the strict logic of our procedure is clearly seen. We do [not] say that a mathematical error is not reasonable. We call that opinion reasonable whose only support is instinct. . . . (CP5-174)

§5. THE MEANING OF AN ARGUMENT
We have already seen some reason to hold that the idea of meaning is such as to involve some reference to a purpose. But Meaning is attributed to representamens alone, and the only kind of representamen which has a definite professed purpose is an "argument." The professed purpose of an argument is to determine an acceptance of its conclusion, and it quite accords with general usage to call the conclusion of an argument its meaning. But I may remark that the word meaning has not hitherto been recognized as a technical term of logic, and in proposing it as such (which I have a right to do since I have a new conception to express, that of the conclusion of an argument as its intended interpretant) I should have a recognized right slightly to warp the acceptation of the word "meaning," so as to fit it for the expression of a scientific conception. It seems natural to use the word meaning to denote the intended interpretant of a symbol. (CP5-175)

On the whole, then, if by the meaning of a term, proposition, or argument, we understand the entire general intended interpretant, then the meaning of an argument is explicit. It is its conclusion; while the meaning of a proposition or term is all that that proposition or term could contribute to the conclusion of a demonstrative argument. But while this analysis will be found useful, it is by no means sufficient to cut off all nonsense or to enable us to judge of the maxim of pragmatism. What we need is an account of the ultimate meaning of a term. To this problem we have to address ourselves. (CP5-179)

§1. THE THREE COTARY PROPOSITIONS
At the end of my last lecture I had just enunciated three propositions which seem to me to give to pragmatism its peculiar character. I will call them my cotary propositions. Cos, cotis, is a whetstone. They appear to me to put the edge on the maxim of pragmatism. (CP5-180)

These cotary propositions are as follows: .
(1) Everything in our minds is based on something generated by our senses.
Nihil est in intellectu quod non prius fuerit in sensu (Nothing is in the intellect that was not first in the senses). I take this in a sense somewhat different from that which Aristotle intended. By intellectus, I understand the meaning of any representation in any kind of cognition, virtual, symbolic, or whatever it may be. … As for the other term, in sensu, that I take in the sense of in a perceptual judgment, the starting point or first premiss of all critical and controlled thinking.
(2) The second is that perceptual judgments contain general elements, so that universal propositions are deducible from them in the manner in which the logic of relations shows that particular propositions usually, not to say invariably, allow universal propositions to be necessarily inferred from them. (This I sufficiently argued in my last lecture. I shall now take the truth of it for granted.)
(3) The third cotary proposition is that abductive inference shades into perceptual judgment without any sharp line of demarcation between them; or, in other words, our first premisses, the perceptual judgments, are to be regarded as an extreme case of abductive inferences, from which they differ in being absolutely beyond criticism. The abductive suggestion comes to us like a flash. It is an act of insight, although of extremely fallible insight. It is true that the different elements of the hypothesis were in our minds before; but it is the idea of putting together what we had never before dreamed of putting together which flashes the new suggestion before our contemplation.

On its side, the perceptive judgment is the result of a process, although of a process not sufficiently conscious to be controlled, or, to state it more truly, not controllable and therefore not fully conscious. If we were to subject this subconscious process to logical analysis, we should find that it terminated in what that analysis would represent as an abductive inference, resting on the result of a similar process which a similar logical analysis would represent to be terminated by a similar abductive inference, and so on ad infinitum. This analysis would be precisely analogous to that which the sophism of Achilles and the Tortoise applies to the chase of the Tortoise by Achilles, and it would fail to represent the real process for the same reason. Namely, just as Achilles does not have to make the series of distinct endeavors which he is represented as making, so this process of forming the perceptual judgment, because it is sub-conscious and so not amenable to logical criticism, does not have to make separate acts of inference, but performs its act in one continuous process. (CP5-181)

§2. ABDUCTION AND PERCEPTUAL JUDGMENTS
There are some phenomena which, I think, do aid us to see what is meant by asserting that perceptual judgments contain general elements, and which will also naturally lead up to a consideration of the third cossal proposition. (CP5-182)

I will show you a figure which I remember my father [Benjamin Peirce] drawing in one of his lectures. I do not remember what it was supposed to show; but I cannot imagine what else it could have been but my cotary proposition No. 2. If so, in maintaining that proposition I am substantially treading in his footprints, though he would doubtless have put the proposition into a shape very different from mine. Here is the figure (though I cannot draw it as skillfully as he did). It consists of a serpentine line. But when it is completely drawn, it appears to be a stone wall.

The point is that there are two ways of conceiving the matter. Both, I beg you to remark, are general ways of classing the line, general classes under which the line is subsumed. But the very decided preference of our perception for one mode of classing the percept shows that this classification is contained in the perceptual judgment. So it is with that well-known unshaded outline figure of a pair of steps seen in perspective.

We seem at first to be looking at the steps from above (B view); but some unconscious part of the mind seems to tire of putting that construction upon it and suddenly we seem to see the steps from below (A view), and so the perceptive judgment, and the percept itself, seems to keep shifting from one general aspect to the other and back again.
In all such visual illusions of which two or three dozen are well known, the most striking thing is that a certain theory of interpretation of the figure has all the appearance of being given in perception. The first time it is shown to us, it seems as completely beyond the control of rational criticism as any percept is; but after many repetitions of the now familiar experiment, the illusion wears off, becoming first less decided, and ultimately ceasing completely. This shows that these phenomena are true connecting links between abductions and perceptions. (CP5-183)

If the percept or perceptual judgment were of a nature entirely unrelated to abduction, one would expect that the percept would be entirely free from any characters that are proper to interpretations, while it can hardly fail to have such characters if it be merely a continuous series of what, discretely and consciously performed, would be abductions. We have here then almost a crucial test of my third cotary proposition. Now, then, how is the fact? The fact is that it is not necessary to go beyond ordinary observations of common life to find a variety of widely different ways in which perception is interpretative. (CP5-184)

The whole series of hypnotic phenomena, of which so many fall within the realm of ordinary everyday observation --such as our waking up at the hour we wish to wake much nearer than our waking selves could guess it -involve the fact that we perceive what we are adjusted for interpreting, though it be far less perceptible than any express effort could enable us to perceive; while that, to the interpretation of which our adjustments are not fitted, we fail to perceive although it exceed in intensity what we should perceive with the utmost ease, if we cared at all for its interpretation. It is a marvel to me that the clock in my study strikes every half hour in the most audible manner, and yet I never hear it. I should not know at all whether the striking part were going, unless it is out of order and strikes the wrong hour. If it does that, I am pretty sure to hear it. Another familiar fact is that we perceive, or seem to perceive, objects differently from how they really are, accommodating them to their manifest intention. Proofreaders get high salaries because ordinary people miss seeing misprints, their eyes correcting them. We can repeat the sense of a conversation, but we are often quite mistaken as to what words were uttered. Some politicians think it a clever thing to convey an idea which they carefully abstain from stating in words. The result is that a reporter is ready to swear quite sincerely that a politician said something to him which the politician was most careful not to say.
I should tire you if I dwelt further on anything so familiar, especially to every psychological student, as the interpretativeness of the perceptive judgment. It is plainly nothing but the extremest case of Abductive Judgments. (CP5-185)

If this third cotary proposition be admitted, the second, that the perceptual judgment contains general elements, must be admitted; and as for the first, that all general elements are given in perception, that loses most of its significance. For if a general element were given otherwise than in the perceptual judgment, it could only first appear in an abductive suggestion, and that is now seen to amount substantially to the same thing. I not only opine, however, that every general element of every hypothesis, however wild or sophisticated it may be, [is] given somewhere in perception, but I will venture so far as to assert that every general form of putting concepts together is, in its elements, given in perception. In order to decide whether this be so or not, it is necessary to form a clear notion of the precise difference between abductive judgment and the perceptual judgment which is its limiting case. The only symptom by which the two can be distinguished is that we cannot form the least conception of what it would be to deny the perceptual judgment. If I judge a perceptual image to be red, I can conceive of another man's not having that same percept. I can also conceive of his having this percept but never having thought whether it was red or not. I can conceive that while colors are among his sensations, he shall never have had his attention directed to them. Or I can conceive that, instead of redness, a somewhat different conception should arise in his mind; that he should, for example, judge that this percept has a warmth of color. I can imagine that the redness of my percept is excessively faint and dim so that one can hardly make sure whether it is red or not. But that any man should have a percept similar to mine and should ask himself the question whether this percept be red, which would imply that he had already judged some percept to be red, and that he should, upon careful attention to this percept, pronounce it to be decidedly and clearly not red, when I judge it to be prominently red, that I cannot comprehend at all. An abductive suggestion, however, is something whose truth can be questioned or even denied. (CP5-186)

Long before I first classed abduction as an inference it was recognized by logicians that the operation of adopting an explanatory hypothesis -which is just what abduction is --was subject to certain conditions. Namely, the hypothesis cannot be admitted, even as a hypothesis, unless it be supposed that it would account for the facts or some of them. The form of inference, therefore, is this:

The surprising fact, C, is observed;
But if A were true, C would be a matter of course,
Hence, there is reason to suspect that A is true.

Thus, A cannot be abductively inferred, or if you prefer the expression, cannot be abductively conjectured until its entire content is already present in the premiss, "If A were true, C would be a matter of course." premiss, "If A were true, C would be a matter of course." (CP5-189)

§3. PRAGMATISM --THE LOGIC OF ABDUCTION
If you carefully consider the question of pragmatism you will see that it is nothing else than the question of the logic of abduction. That is, pragmatism proposes a certain maxim which, if sound, must render needless any further rule as to the admissibility of hypotheses to rank as hypotheses, that is to say, as explanations of phenomena held as hopeful suggestions; and, furthermore, this is all that the maxim of pragmatism really pretends to do, at least so far as it is confined to logic, and is not understood as a proposition in psychology. For the maxim of pragmatism is that a conception can have no logical effect or import differing from that of a second conception except so far as, taken in connection with other conceptions and intentions, it might conceivably modify our practical conduct differently from that second conception.
Now it is indisputable that no rule of abduction would be admitted by any philosopher which should prohibit on any formalistic grounds any inquiry as to how we ought in consistency to shape our practical conduct. Therefore, a maxim which looks only to possibly practical considerations will not need any supplement in order to exclude any hypotheses as inadmissible. What hypotheses it admits all philosophers would agree ought to be admitted. On the other hand, if it be true that nothing but such considerations has any logical effect or import whatever, it is plain that the maxim of pragmatism cannot cut off any kind of hypothesis which ought to be admitted. Thus, the maxim of pragmatism, if true, fully covers the entire logic of abduction. It remains to inquire whether this maxim may not have some further logical effect. If so, it must in some way affect inductive or deductive inference. But that pragmatism cannot interfere with induction is evident; because induction simply teaches us what we have to expect as a result of experimentation, and it is plain that any such expectation may conceivably concern practical conduct. In a certain sense it must affect deduction. Anything which gives a rule to abduction and so puts a limit upon admissible hypotheses will cut down the premisses of deduction, and thereby will render a reductio ad absurdum and other equivalent forms of deduction possible which would not otherwise have been possible. But here three remarks may be made.
First, to affect the premisses of deduction is not to affect the logic of deduction. For in the process of deduction itself, no conception is introduced to which pragmatism could be supposed to object, except the acts of abstraction. Concerning that I have only time to say that pragmatism ought not to object to it.
Secondly, no effect of pragmatism which is consequent upon its effect on abduction can go to show that pragmatism is anything more than a doctrine concerning the logic of abduction.
Thirdly, if pragmatism is the doctrine that every conception is a conception of conceivable practical effects, it makes conception reach far beyond the practical. It allows any flight of imagination, provided this imagination ultimately alights upon a possible practical effect; and thus many hypotheses may seem at first glance to be excluded by the pragmatical maxim that are not really so excluded. (CP5-196)

Admitting, then, that the question of Pragmatism is the question of Abduction, let us consider it under that form. What is good abduction? What should an explanatory hypothesis be to be worthy to rank as a hypothesis? Of course, it must explain the facts. But what other conditions ought it to fulfill to be good? The question of the goodness of anything is whether that thing fulfills its end. What, then, is the end of an explanatory hypothesis? Its end is, through subjection to the test of experiment, to lead to the avoidance of all surprise and to the establishment of a habit of positive expectation that shall not be disappointed. Any hypothesis, therefore, may be admissible, in the absence of any special reasons to the contrary, provided it be capable of experimental verification, and only insofar as it is capable of such verification. This is approximately the doctrine of pragmatism. But just here a broad question opens out before us. What are we to understand by experimental verification? The answer to that involves the whole logic of induction. (CP5-197)

Different opinions which we actually find men holding today:
*In the first place, we find men who maintain that no hypothesis ought to be admitted, even as a hypothesis, any further than its truth or its falsity is capable of being directly perceived. This is what was in the mind of Auguste Comte, who is generally assumed to have first formulated this maxim. Of course, this maxim of abduction supposes that we "are to believe only what we actually see"; and that it is unscientific to make predictions --unscientific, therefore, to expect anything. One ought to restrict one's opinions to what one actually perceives. I need hardly say that that position cannot be consistently maintained. It refutes itself, for it is itself an opinion relating to more than is actually in the field of momentary perception. (CP5-198)
*In the second place, there are those who hold that a theory which has sustained a number of experimental tests may be expected to sustain a number of other similar tests, and to have a general approximate truth, the justification of this being that this kind of inference must prove correct in the long run, as I explained in a previous lecture. But these logicians refuse to admit that we can ever have a right to conclude definitely that a hypothesis is exactly true, that is that it should be able to sustain experimental tests in endless series; for, they urge, no hypothesis can be subjected to an endless series of tests. They are willing we should say that a theory is true, because, all our ideas being more or less vague and approximate, what we mean by saying that a theory is true can only be that it is very near true. But they will not allow us to say that anything put forth as an anticipation of experience should assert exactitude, because exactitude in experience would imply experiences in endless series, which is impossible. (CP5-199)
* In the third place, the great body of scientific men hold that it is too much to say that induction must be restricted to that for which there can be positive experimental evidence. They urge that the rationale of induction as it is understood by logicians of the second group, themselves, entitles us to hold a theory, provided it be such that if it involve any falsity, experiment must some day detect that falsity. We, therefore, have a right, they will say, to infer that something never will happen, provided it be of such a nature that it could not occur without being detected. (CP5-200)
*We are thus led to a fourth opinion very common among mathematicians, who generally hold that any one irrational real quantity (say of length, for example) whether algebraical or transcendental in its general expression, is just as possible and admissible as any rational quantity, but who generally reason that if the distance between two points is less than any assignable quantity, that is, less than any finite quantity, then it is nothing at all. If that be the case, it is possible for us to conceive, with mathematical precision, a state of things in favor of whose actual reality there would seem to be no possible sound argument, however weak. For example, we can conceive that the diagonal of a square is incommensurable with its side. That is to say, if you first name any length commensurable with the side, the diagonal will differ from that by a finite quantity (and a commensurable quantity), yet however accurately we may measure the diagonal of an apparent square, there will always be a limit to our accuracy and the measure will always be commensurable. So we never could have any reason to think it otherwise. Moreover, if there be, as they seem to hold, no other points on a line than such as are at distances assignable to an indefinite approximation, it will follow that if a line has an extremity, that extreme point may be conceived to be taken away so as to leave the line without any extremity, while leaving all the other points just as they were. In that case, all the points stand discrete and separate; and the line might be torn apart at any number of places without disturbing the relations of the points to one another. Each point has, on that view, its own independent existence, and there can be no merging of one into another. There is no continuity of points in the sense in which continuity implies generality. (CP5-204)
*In the fifth place it may be held that we can be justified in inferring true generality, true continuity. But I do not see in what way we ever can be justified in doing so unless we admit the cotary propositions, and in particular that such continuity is given in perception; that is, that whatever the underlying psychical process may be, we seem to perceive a genuine flow of time, such that instants melt into one another without separate individuality. (CP5-205)

§4. THE TWO FUNCTIONS OF PRAGMATISM
There are two functions which we may properly require that Pragmatism should perform; or if not pragmatism, whatever the true doctrine of the Logic of Abduction may be, ought to do these two services.
Namely, it ought, in the first place, to give us an expeditious riddance of all ideas essentially unclear. In the second place, it ought to lend support, and help to render distinct, ideas essentially clear, but more or less difficult of apprehension; and in particular, it ought to take a satisfactory attitude toward the element of thirdness. (CP5-206)

Of these two offices of Pragmatism, there is at the present day not so crying a need of the first as there was a quarter of a century ago when I enunciated the maxim. The state of logical thought is very much improved. Thirty years ago .1 when, in consequence of my study of the logic of relations, I told philosophers that all conceptions ought to be defined, with the sole exception of the familiar concrete conceptions of everyday life, my opinion was considered in every school to be utterly incomprehensible. The doctrine then was, as it remains in nineteen out of every score of logical treatises that are appearing in these days, that there is no way of defining a term except by enumerating all its universal predicates, each of which is more abstracted and general than the term defined. So unless this process can go on endlessly, which was a doctrine little followed, the explication of a concept must stop at such ideas as Pure Being, Agency, Substance and the like, which were held to be ideas so perfectly simple that no explanation whatever could be given of them. This grotesque doctrine was shattered by the logic of relations, which showed that the simplest conceptions, such as Quality, Relation, Self-consciousness could be defined and that such definitions would be of the greatest service in dealing with them. By this time, although few really study the logic of relations, one seldom meets with a philosopher who continues to think the most general relations are particularly simple in any except a technical sense; and of course, the only alternative is to regard as the simplest the practically applied notions of familiar life. We should hardly find today a man of Kirchhoff's rank in science saying that we know exactly what energy does but what energy is we do not know in the least. For the answer would be that energy being a term in a dynamical equation, if we know how to apply that equation, we thereby know what energy is, although we may suspect that there is some more fundamental law underlying the laws of motion. (CP5-207)

I shall take it for granted that as far as thought goes, I have sufficiently shown that thirdness is an element not reducible to secondness and firstness. But even if so much be granted, three attitudes may be taken:
(1) That thirdness, though an element of the mental phenomenon, ought not to be admitted into a theory of the real, because it is not experimentally verifiable;
(2) That thirdness is experimentally verifiable, that is, is inferable by induction, [abduction?] although it cannot be directly perceived;
(3) That it is directly perceived, from which the other cotary propositions can hardly be separated. (CP5-209)

The man who takes the first position ought to admit no general law as really operative. Above all, therefore, he ought not to admit the law of laws, the law of the uniformity of nature. He ought to abstain from all prediction, however qualified by a confession of fallibility. But that position can practically not be maintained. (CP5-210)

The man who takes the second position will hold thirdness to be an addition which the operation of abduction introduces over and above what its premisses in any way contain, and further that this element, though not perceived in experiment, is justified by experiment. Then his conception of reality must be such as completely to sunder the real from perception; and the puzzle for him will be why perception should be allowed such authority in regard to what is real. (CP5-211)

The man who takes the third position and accepts the cotary propositions will hold, with firmest of grasps, to the recognition that logical criticism is limited to what we can control. In the future we may be able to control more but we must consider what we can now control. Some elements we can control in some limited measure. But the content of the perceptual judgment cannot be sensibly controlled now, nor is there any rational hope that it ever can be. Concerning that quite uncontrolled part of the mind, logical maxims have as little to do as with the growth of hair and nails. We may be dimly able to see that, in part, it depends on the accidents of the moment, in part on what is personal or racial, in part is common to all nicely adjusted organisms whose equilibrium has narrow ranges of stability, in part on whatever is composed of vast collections of independently variable elements, in part on whatever reacts, and in part on whatever has any mode of being. But the sum of it all is that our logically controlled thoughts compose a small part of the mind, the mere blossom of a vast complexus, which we may call the instinctive mind, in which this man will not say that he has faith, because that implies the conceivability of distrust, but upon which he builds as the very fact to which it is the whole business of his logic to be true.
That he will have no difficulty with Thirdness is clear enough, because he will hold that the conformity of action to general intentions is as much given in perception as is the element of action itself, which cannot really be mentally torn away from such general purposiveness. There can be no doubt that he will allow hypotheses fully all the range they ought to be allowed. The only question will be whether he succeeds in excluding from hypotheses everything unclear and nonsensical. It will be asked whether he will not have a shocking leaning toward anthropomorphic conceptions. I fear I must confess that he will be inclined to see an anthropomorphic, or even a zoömorphic, if not a physiomorphic element in all our conceptions. But against unclear and nonsensical hypotheses, [of] whatever ægis [he will be protected]. Pragmatism will be more essentially significant for him than for any other logician, for the reason that it is in action that logical energy returns to the uncontrolled and uncriticizable parts of the mind. His maxim will be this:
The elements of every concept enter into logical thought at the gate of perception and make their exit at the gate of purposive action; and whatever cannot show its passports at both those two gates is to be arrested as unauthorized by reason.
The digestion of such thoughts is slow, ladies and gentlemen; but when you come in the future to reflect upon all that I have said, I am confident you will find the seven hours, you have spent in listening to these ideas, have not been altogether wasted. (CP5-212)