Lowell Lecture 3 of 1903 (3rd draught, MS 464 and 465)

transcribed and edited by Gary Fuhrman, November 2017, from the manuscript copies made available by the SPIN project (link above).
Parts of this lecture are published in CP 1, and for those parts, the CP paragraph numbers are supplied here. But where the CP editors took liberties with Peirce's punctuation and (especially) capitalization, the present transcription follows the manuscript much more closely.
The first and second draughts, MSS 458-9, have been partly published in NEM 3, pp. 331-54.

Peirce began this lecture with his response to a written question about Lecture 1, given as an appendix at the end of that lecture on this site. He then began Lecture 3 with the following invitation:

I desire now to say that, in order to be of as much help as I can to those who may be interested in the subject, it is my intention for the next three Sunday afternoons from 3 to 6 o'clock to be at my room at No 6 Prescott Hall, 474 Broadway, Cambridge, where I shall be extremely happy to see any of you who may wish for any explanation from me.

I was advertized to speak tonight of the three Universal Categories. I will try to say something about them; but my last lecture was not half finished owing to untoward circumstances, and tonight I must begin with the beta part of existential graphs.

I did succeed, last time, in explaining alpha graphs. The black board except such portions as may be separated from the rest by “cuts,” so-called, is the sheet of assertion. Every graph, or proposition, scribed upon it is asserted. If two graphs, or propositions, are scribed upon it, each is asserted independently of the other; and it makes no difference on what part of the sheet a graph is scribed, so long as they are on separate parts of the sheet. The sheet is itself a graph-replica, or the expression of a proposition; namely it is to be interpreted as expressing whatever is well-known to be true concerning the universe of discourse. Every blank part of the sheet is to be understood as forever asserting that.

A cut is a self-returning line which I draw on the board with green chalk, but on paper merely as a fine line. A cut is not a graph-replica: It does not itself assert anything. But the cut together with all that is within it is called an enclosure; and an enclosure is a graph. The surface outside the cut is called its place. The surface inside the cut is called its area.

I gave you 7 Permissions; but I can state these more neatly as follows:

The beta part of the system of existential graphs is distinguished from the alpha-part by the presence of ligatures in its graphs; and it is therefore natural to think that the distinction between alpha-possibility and beta-possibility lies in the latter's taking account of the relation of identity. But it could easily be demonstrated that this is not the truth of the matter. The true distinction lies in the fact that beta possibility takes account of individuals, so that whereas in the alpha part all the spots are regarded simply as propositions and may be general, in the beta part, besides these, individuals which form an entirely different category, enter into the graphs. I now go on to a preface to the gamma part of the subject, which is by far the most important of the three, and which is distinguished by its taking account of abstractions.

I begin by a remark drawn from Phenomenology. Phenomenology is the science which describes the different kinds of elements that are always present in the Phenomenon, meaning by the Phenomenon whatever is before the mind in any kind of thought, fancy, or cognition of any kind. Everything that you can possibly think involves three kinds of elements. Whence it follows that you cannot possibly think of any one of those elements in its purity. The most strenuous endeavors of thinking will leave your ideas somewhat confused. But I think I can help you to see that there are three kinds of elements, and to discern what they are like. I begin with that one

But it is impossible to resolve everything in our thoughts into those two elements. We may say that the bulk of what is actually done consists of Secondness,— or better, Secondness is the predominant character of what has been done. The immediate present, could we seize it, would have no character but its Firstness. Not that I mean to say that immediate consciousness (a pure fiction, by the way), would be Firstness, but that the Quality of what we are immediately conscious of, which is no fiction, is Firstness. But we constantly predict what is to be. Now what is to be, according to our conception of it, can never become wholly past. In general, we may say that meanings are inexhaustible. We are too apt to think that what one means to do and the meaning of a word are quite unrelated meanings of the word [“]meaning,[”] or that they are only connected by both referring to some actual operation of the mind. Prof[essor] Royce especially in his great work The World and the Individual has done much to break up this mistake. In truth the only difference is that when a person means to do anything he is in some state in consequence of which the brute reactions between things will be moulded to conformity to the form to which the man's mind is itself moulded, while the meaning of a word really lies in the way in which it might, in a proper position in a proposition believed, tend to mould the conduct of a person to conformity to that to which it is itself moulded. Not only will meaning always, more or less, in the long run, mould reactions to itself, but it is only in doing so that its own being consists. For this reason I call this element of the phenomenon or object of thought the element of Thirdness. It is that which is what it is by virtue of imparting a quality to reactions in the future.

344. There is a strong tendency in us all to be sceptical about there being any real meaning or law in things. This scepticism is strongest in the most masculine thinkers. I applaud scepticism with all my heart, provided it have four qualities: first, that it be sincere and real doubt; second, that it be aggressive; third, that it push inquiry; and fourth, that it stand ready to acknowledge what it now doubts, as soon as the doubted element comes clearly to light. To be angry with sceptics, who, whether they are aware of it or not, are the best friends of spiritual truth, is a manifest sign that the angry person is himself infected with scepticism,— not, however, of the innocent and wholesome kind, that tries to bring truth to light, but of the mendacious, clandestine, disguised, and conservative variety that is afraid of truth, although truth merely means the way to attain one's purposes. If the sceptics think that any account can be given of the phenomena of the universe while they leave Meaning out of account, by all means let them go ahead and try to do it. It is a most laudable and wholesome enterprise. But when they go so far as to say that there is no such idea in our minds, irreducible to anything else, I say to them, “Gentlemen, your strongest sentiment, to which I subscribe with all my heart, is that a man worthy of that name will not allow petty intellectual predilections to blind him to truth, which consists in the conformity of his thoughts to his purposes. But you know there is such a thing as a defect of candor of which one is not oneself aware. You perceive, no doubt, that if there be an element of thought irreducible to any other, it would be hard, on your principles, to account for man's having it, unless he derived it from environing Nature. But if, because of that, you were to turn your gaze away from an idea that shines out clearly in your mind, you would be violating your principles in a very much more radical way.”

345. I will sketch a proof that the idea of Meaning is irreducible to those of Quality and Reaction. It depends on two main premisses. The first is that every genuine triadic relation involves meaning, as meaning is obviously a triadic relation. The second is that a triadic relation is inexpressible by means of dyadic relations alone. Considerable reflexion may be required to convince yourself of the first of these premisses, that every triadic relation involves meaning. There will be two lines of inquiry. First, all physical forces appear to subsist between pairs of particles. This was assumed by Helmholtz in his original paper on the Conservation of Forces. Take any fact in physics of the triadic kind, by which I mean a fact which can only be defined by simultaneous reference to three things, and you will find there is ample evidence that it never was produced by the action of forces on mere dyadic conditions. Thus, your right hand is that hand which is toward the east, when you face the north with your head toward the zenith. Three things, east, west, and up, are required to define the difference between right and left. Consequently chemists find that those substances which rotate the plane of polarization to the right or left can only be produced from such active substances. They are all of such complex constitution that they cannot have existed when the earth was very hot, and how the first one was produced is a puzzle. It cannot have been by the action of brute forces. For the second branch of the inquiry, you must train yourself to the analysis of relations, beginning with such as are very markedly triadic, gradually going on to others. In that way, you will convince yourself thoroughly that every genuine triadic relation involves thought or meaning. Take, for example, the relation of giving. A gives B to C. This does not consist in A's throwing B away and its accidentally hitting C, like the date-stone, which hit the Jinnee in the eye. If that were all, it would not be a genuine triadic relation, but merely one dyadic relation followed by another. There need be no motion of the thing given. Giving is a transfer of the right of property. Now right is a matter of law, and law is a matter of thought and meaning. I there leave the matter to your own reflection, merely adding that, though I have inserted the word “genuine,” yet I do not really think that necessary. I think even degenerate triadic relations involve something like thought.

346. The other premiss of the argument that genuine triadic relations can never be built of dyadic relations and of Qualities is easily shown. In Existential Graphs, a spot with one tail —X represents a quality, a spot with two tails —R— a dyadic relation. Joining the ends of two tails is also a dyadic relation. But you can never by such joining make a graph with three tails. You may think that a node connecting three lines of identity is not a triadic idea. But analysis will show that it is so. I see a man on Monday. On Tuesday I see a man, and I exclaim, “Why, that is the very man I saw on Monday.” We may say, with sufficient accuracy, that I directly experienced the identity. On Wednesday I see a man and I say, “That is the same man I saw on Tuesday, and consequently is the same I saw on Monday.” There is a recognition of triadic identity; but it is only brought about as a conclusion from two premisses, which is itself a triadic relation. If I see two men at once, I cannot by any such direct experience identify both of them with a man I saw before. I can only identify them if I regard them, not as the very same, but as two different manifestations of the same man. But the idea of manifestation is the idea of a sign. Now a sign is something, A, which denotes some fact or object, B, to some interpretant thought, C.

347. It is interesting to remark that while a graph with three tails cannot be made out of graphs each with two or one tail, yet combinations of graphs of three tails each will suffice to build graphs with every higher number of tails.

348. As to the common aversion to recognizing thought as an active factor in the real world, some of its causes are easily traced. In the first place, people are persuaded that everything that happens in the material universe is a motion completely determined by inviolable laws of dynamics; and that, they think, leaves no room for any other influence. But the laws of dynamics stand on quite a different footing from the laws of gravitation, elasticity, electricity, and the like. The laws of dynamics are very much like logical principles, if they are not precisely that. They only say how bodies will move after you have said what the forces are. They permit any forces, and therefore any motions. Only, the principle of the conservation of energy requires us to explain certain kinds of motions by special hypotheses about molecules and the like. Thus, in order that the viscosity of gases should not disobey that law we have to suppose that gases have a certain molecular constitution. Setting dynamical laws to one side, then, as hardly being positive laws, but rather mere formal principles, we have only the laws of gravitation, elasticity, electricity, and chemistry. Now who will deliberately say that our knowledge of these laws is sufficient to make us reasonably confident that they are absolutely eternal and immutable, and that they escape the great law of evolution? Each hereditary character is a law, but it is subject to development and to decay. Each habit of an individual is a law; but these laws are modified so easily by the operation of self-control, that it is one of the most patent of facts that ideals and thought generally have a very great influence on human conduct. That truth and justice are great powers in the world is no figure of speech, but a plain fact to which theories must accommodate themselves.

349. The child, with his wonderful genius for language, naturally looks upon the world as chiefly governed by thought; for thought and expression are really one. As Wordsworth truly says, the child is quite right in this; he is an

“eye among the blind,”
“On whom those truths do rest
Which we are toiling all our lives to find.”

thought as a real power, or as anything but a fantastic figment, were really natural, it would make an argument of no little strength against its being acknowledged as a real power.

Those of you, ladies and gentlemen, who are interested in philosophy, as most of us are, more or less, would do well to get as clear notions of the three elements of Firstness, Secondness, and Thirdness as you can.

521. Very wretched must be the notion of them that can be conveyed in one lecture. They must grow up in the mind, under the hot sun-shine of hard thought, daily, bright, well-focussed, and well aimed thought; and you must have patience, for long time is required to ripen the fruit. They are no inventions of mine. Were they so, that would be sufficient to condemn them. Confused notions of these elements appear in the first infancy of philosophy, and they have never entirely been forgotten. Their fundamental importance is noticed in the beginning of Aristotle's De Caelo, where it is said that the Pythagoreans knew of them.

522. In Kant they come out with an approach to lucidity. For Kant possessed in a high degree all seven of the mental qualifications of a philosopher,
1^st, the ability to discern what is before one's consciousness;
2^nd, Inventive originality;
3^rd, Generalizing power;
4^th, Subtlety;
5^th, Critical severity and sense of fact;
6^th, Systematic procedure;
7^th, Energy, diligence, persistency, and exclusive devotion to philosophy.

523. But Kant had not the slightest suspicion of the inexhaustible intricacy of the fabric of conceptions, which is such that I do not flatter myself that I have ever analyzed a single idea into its constituent elements.

524. Hegel, in some respects the greatest philosopher that ever lived, had a somewhat juster notion of this complication, though an inadequate notion, too. For if he had seen what the state of the case was, he would not have attempted in one lifetime to cover the vast field that he attempted to clear. But Hegel was lamentably deficient in that 5^th requisite of critical severity and sense of fact. He brought out the three elements much more clearly. But the element of Secondness, of hard fact, is not accorded its due place in his system; and in a lesser degree the same is true of Firstness. After Hegel wrote, there came fifty years that were remarkably fruitful in all the means for attaining that 5^th requisite. Yet Hegel's followers, instead of going to work to reform their master's system, and to render his statement of it obsolete, as every true philosopher must desire that his disciples should do, only proposed, at best, some superficial changes without replacing at all the rotten material with which the system was built up.

525. I shall not inflict upon you any account of my own labors. Suffice it to say that my results have afforded me great aid in the study of logic.

I will, however, make a few remarks on these categories. By way of preface, I must explain that in saying that the three, Firstness, Secondness, and Thirdness, complete the list, I by no means deny that there are other categories. On the contrary, at every step of every analysis, conceptions are met with which presumably do not belong to this series of ideas. Nor did an investigation of them occupying me for two years reveal any analysis of them into these as their constituents. I shall say nothing further about them, except incidentally.

526. As to the three Universal Categories, as I call them, perhaps with no very good reason for thinking that they are more universal than the others, we first notice that Secondness and Thirdness are conceptions of complexity. That is not, however, to say that they are complex conceptions. When we think of Secondness, we naturally think of two reacting objects, a first and a second. And along with these, as subjects, there is their Reaction. But these are not constituents out of which the Secondness is built up. The truth is just reverse, that the being a First or a Second or the being a Reaction each involves Secondness. An Object cannot be a Second of itself. If it is a Second, it has an element of being what another makes it to be. That is, the being a Second involves Secondness. The Reaction still more manifestly involves the being what an other makes a subject to be. Thus, while Secondness is a fact of complexity, it is not a compound of two facts. It is a single fact about two objects. Similar remarks apply to Thirdness.

527. This remark at once leads to another. The secondness of the Second, whichever of the two objects be called the Second, is different from the Secondness of the first. That is to say it generally is so. To kill and to be killed are different. In case there is one of the two which there is good reason for calling the First, while the other remains the Second, it is that the Secondness is more accidental to the former than to the latter; that there is more or less approach to a state of things in which something, which is itself First, accidentally comes into a Secondness that does not really modify its Firstness, while its Second in this Secondness is something whose being is of the nature of Secondness and which has no Firstness separate from this. It must be extremely difficult for those who are untrained to such analyses of conceptions to make any sense of all this. For that reason, I shall inflict very little of it upon you — just enough to show those who can carry what I say in their minds that it is by no means nonsense. The extreme kind of Secondness which I have just described is the relation of a quality to the matter in which that quality inheres. The mode of being of the quality is that of Firstness. That is to say, it is a possibility. It is related to the matter accidentally; and this relation does not change the quality at all, except that it imparts existence, that is to say, this very relation of inherence, to it. But the matter, on the other hand, has no being at all except the being a subject of qualities. This relation of really having qualities constitutes its existence. But if all its qualities were to be taken away, and it were to be left quality-less matter, it not only would not exist, but it would not have any positive definite possibility — such as an unembodied quality has. It would be nothing, at all.

528. Thus we have a division of Seconds into those whose very being, or Firstness, it is to be Seconds, and those whose Secondness is only an accretion. This distinction springs out of the essential elements of Secondness. For Secondness involves Firstness. The concepts of the two kinds of Secondness are mixed concepts composed of Secondness and Firstness. One is the Second whose very Firstness is Secondness. The other is a Second whose Secondness is Second to a Firstness. The idea of mingling Firstness and Secondness in this particular way is an idea distinct from the ideas of Firstness and Secondness that it combines. It appears to be a conception of an entirely different series of categories. At the same time, it is an idea of which Firstness, Secondness, and Thirdness are component parts, since the distinction depends on whether the two elements of Firstness and Secondness that are united as to be One or whether they remain Two. This distinction between two kinds of Seconds, which is almost involved in the very idea of a Second, makes a distinction between two kinds of Secondness; namely, the Secondness of Genuine Seconds, or matters, which I call genuine Secondness, and the Secondness in which one of the seconds is only a Firstness, which I call degenerate Secondness; so that this Secondness really amounts to nothing but this, that a subject, in its being a Second, has a Firstness, or quality. It is to be remarked that this distinction arose from attending to extreme cases; and consequently subdivision will be attached to it according to the more or less essential or accidental nature of the Genuine or the Degenerate Secondness. With this distinction Thirdness has nothing to do, or at any rate has so little to do that a satisfactory account of the distinction need not mention Thirdness.

529. I will just mention that among Firstnesses there is no distinction of the Genuine and the Degenerate, while among Thirdnesses we find not only a Genuine but two distinct grades of Degeneracy.

530. But now I wish to call your attention to a kind of distinction which affects Firstness more than it does Secondness, and Secondness more than it does Thirdness. This distinction arises from the circumstance that where you have a triplet ∴ you have 3 pairs; and where you have a pair, you have 2 units. Thus, Secondness is an essential part of Thirdness though not of Firstness, and Firstness is an Essential element of both Secondness and Thirdness. Hence there is such a thing as the Firstness of Secondness and such a thing as the Firstness of Thirdness; and there is such a thing as the Secondness of Thirdness. But there is no Secondness of Pure Firstness and no Thirdness of Pure Firstness or Secondness. When you strive to get the purest conceptions you can of Firstness, Secondness, and Thirdness,— thinking of Quality, Reaction, and Mediation,— what you are striving to apprehend is Pure Firstness, the Firstness of Secondness,— that is what Secondness is, of itself,— and the Firstness of Thirdness. When you contrast the blind compulsion in an Event of Reaction considered as something which happens and which of its nature can never happen again, since you cannot cross the same river twice, when, I say, you contrast this compulsion with the logical necessitation of a meaning considered as something that has no being at all except so far as it actually gets embodied in an event of thought, and you regard this logical necessitation as a sort of actual compulsion, since the meaning must actually be embodied, what you are thinking of is a Secondness involved in Thirdness.

531. A Firstness is exemplified in every quality of a total feeling. It is perfectly simple and without parts; and everything has its quality. Thus the tragedy of King Lear has its Firstness, its flavor sui generis. That wherein all such qualities agree is universal Firstness, the very being of Firstness. The word possibility fits it, except that possibility implies a relation to what exists, while universal Firstness is the mode of being of itself. That is why a new word was required for it. Otherwise, “Possibility” would have answered the purpose.

532. As to Secondness, I have said that our only direct knowledge of it is in Willing and in the experience of a Perception. It is in Willing that the Secondness comes out most strongly. But it is not pure Secondness. For, in the first place, he who wills has a Purpose; and that idea of purpose makes the act appear as a Means to an end. Now the word Means is almost an exact synonym to the word third. It certainly involves Thirdness. Moreover, he who wills is conscious of doing so, in the sense of representing to himself that he does so. But representation is precisely genuine Thirdness. You must conceive an instantaneous Consciousness that is instantly and totally forgotten and an effort without purpose. It is a hopeless undertaking to try to realize what consciousness would be without the element of representation. It would be like unexpectedly hearing a great explosion of nitroglycerine before one had recovered oneself and merely had the sense of the breaking off of the quiet. Perhaps it might not be far from what ordinary common sense conceives to take place when one billiard ball caroms on another. One ball “acts” on the other; that is, it makes an exertion minus the element of representation. We may say with some approach to accuracy that the general Firstness of all true Secondness is Existence, though this term more particularly applies to Secondness in so far as it is an element of the reacting First and Second. If we mean Secondness as it is an element of the occurrence, the Firstness of it is Actuality. But actuality and existence are words expressing the same idea in different applications. Secondness, strictly speaking, is just when and where it takes place, and has no other being; and therefore different Secondnesses, strictly speaking, have in themselves no quality in common. Accordingly existence, or the universal Firstness of all Secondness, is really not a quality at all. An actual dollar to your credit in the bank does not differ in any respect from a possible imaginary dollar. For if it did, the imaginary dollar could be imagined to be changed in that respect, so as to agree with the actual dollar. We thus see that actuality is not a quality, or mere mode of feeling. Hence Hegel, whose neglect of Secondness was due chiefly [to] his not recognizing any other mode of being than Existence,— and what he calls Existenz is a special variety of it merely,— regarded Pure Being as pretty much the same as Nothing. It is true that the word “existence” names, as if it were an abstract possibility, that which is precisely the not having any being in abstract possibility; and this circumstance, when you look upon existence as the only being, seems to make existence all but the same as nothing.

533. To express the Firstness of Thirdness, the peculiar flavor or color of mediation, we have no really good word. Intention Mentality is, perhaps, as good as any, poor and inadequate as it is.

Here, then, are three kinds of Firstness, Qualitative Possibility, Existence, Mentality, resulting from applying Firstness to the three categories. We might strike new words for them: Primity, Secundity, Tertiality.

534. There are also three other kinds of firstness which arise in a somewhat similar way; namely, the idea of a simple original quality, the idea of a quality essentially relative, such as that of being “an inch long”; and the idea of a quality that consists in the way something is thought or represented, such as the quality of being manifest.

535. I shall not enter into any exact analysis of these ideas. I only wished to give you such slight glimpse as I could of the sort of questions that busy the student of phenomenology, merely to lead up to Thirdness and to the particular kind and aspect of thirdness which is the sole object of logical study. I want first to show you what Genuine Thirdness is and what are its two degenerate forms. Now we found the genuine and degenerate forms of secondness by considering the full ideas of First and Second. Then the genuine Secondness was found to be ReAction, where First and Second are both true Seconds and the Secondness is something distinct from them, while in Degenerate Secondness, or mere Reference, the First is a mere First never attaining full Secondness.

536. Let us proceed in the same way with Thirdness. We have here a First, a Second, and a Third. The first is a Positive Qualitative Possibility, in itself nothing more. The Second is an Existent thing without any mode of being less than existence, but determined by that First. A Third has a mode of being which consists in the Secondnesses that it determines, the mode of being of a Law, or Concept. Do not confound this with the ideal being of a quality in itself. A quality is something capable of being completely embodied. A Law never can be embodied in its character as a law except by determining a habit. A quality is how something may or might have been. A law is how an endless future must continue to be.

537. Now in Genuine Thirdness, the First, the Second, and the Third are all three of the nature of thirds, or Thought, while in respect to one another they are First, Second, and Third. The First is Thought in its capacity as mere Possibility; that is, mere Mind capable of thinking, or a mere vague idea. The Second is Thought playing the rôle of a Secondness, or Event. That is, it is of the general nature of Experience or Information. The Third is Thought in its rôle as governing Secondness. It brings the Information into the Mind, or determines the Idea and gives it body. It is informing thought, or Cognition. But take away the psychological or accidental human element, and in this genuine Thirdness we see the operation of a Sign.

538. Every sign stands for an Object independent of itself; but it can only be a sign of that Object in so far as that object is itself of the nature of a Sign or Thought. For the Sign does not affect the Object but is affected by it; so that the object must be able to convey Thought, that is, must be of the nature of Thought or of a Sign. Every Thought is a Sign. But in the First Degree of Degeneracy the Thirdness affects the Object, so that this is not of the nature of a Thirdness,— not so, at least, as far as this Operation of Degenerate Thirdness is concerned. It is that the Third brings about a Secondness but does not regard that Secondness as anything more than a Fact. In short it is the Operation of executing an Intention. In the last degree of degeneracy of Thirdness, there is Thought, but no conveyance or embodiment of thought at all. It is merely that a Fact of which there must be, I suppose, something like knowledge is apprehended according to a possible idea. There is an instigation without any prompting. For example, you look at something and say, “It is red.” Well, I ask you what justification you have for such a judgment. You reply, “I saw it was red.” Not at all. You saw nothing in the least like that. You saw an image. There was no subject or predicate in it. It was just one unseparated image, not resembling a proposition in the smallest particular. It instigated you to your judgment, owing to a possibility of thought; but it never told you so. Now in all imagination and perception there is such an operation by which thought springs up; and its only justification is that it subsequently turns out to be useful.

539. Now it may be that logic ought to be the science of Thirdness in general. But as I have studied it, it is simply the science of what must be and ought to be true representation, so far as representation can be known without any gathering of special facts beyond our ordinary daily life. It is, in short, the Philosophy of Representation.

540. The analysis which I have just used to give you some notion of Genuine Thirdness and its two forms of degeneracy is the merest rough blackboard sketch of the true state of things; and I must begin the examination of representations by defining representation a little more accurately. In the first place, as to my terminology, I confine the word Representation to the operation of a sign or its relation to the object for the interpreter of the representation. The concrete subject that represents I call a sign or a representamen. I use these two words, sign and representamen, differently. By a sign I mean anything which conveys any definite notion of an object in any way, as such conveyers of thought are familiarly known to us. Now I start with this familiar idea and make the best analysis I can of what is essential to a sign, and I define a representamen as being whatever that analysis applies to. If therefore I have committed an error in my analysis, part of what I say about signs will be false. For in that case a sign may not be a representamen. The analysis is certainly true of the representamen, since that is all that word means. Even if my analysis is correct, something may happen to be true of all signs, that is of everything that, antecedently to any analysis, we should be willing to regard as conveying a notion of anything, while there might be something which my analysis describes of which the same thing is not true. In particular, all signs convey notions to human minds; but I know no reason why every representamen should do so.

541. My definition of a representamen is as follows:

A representamen is a subject of a triadic relation to a Second, called its Object, for a Third, called its Interpretant, this triadic relation being such that the Representamen determines its Interpretant to stand in the same triadic relation to the same Object for some Interpretant.

542. It follows at once that this relation cannot consist in any actual event that ever can have occurred; for in that case there would be another actual event connecting the interpretant to an interpretant of its own of which the same would be true; and thus there would be an endless series of events which could have actually occurred, which is absurd. For the same reason the interpretant cannot be a definite individual object. The relation must therefore consist in a power of the representamen to determine some interpretant to being a representamen of the same object.

543. Here we make a new distinction. You see the principle of our procedure. We begin by asking what is the mode of being of the subject of inquiry, that is, what is its absolute and most universal Firstness? The answer comes, that it is either the Firstness of Firstness, the Firstness of Secondness, or the Firstness of Thirdness.

We then ask what is the Universal Secondness, and what the Universal Thirdness, of the subject [in hand?].

Next we say that Firstness of Firstness, that Firstness of Secondness and that Firstness of Thirdness that have been described have been the Firstness of the Firstness in each case. But what is the Secondness that is involved in it and what is the Thirdness?

So the Secondnesses as they have been first given are the Firstnesses of those Secondnesses. We ask what Secondness they involve and what Thirdness. And so we have endless questions, of which I have only given you small scraps.

The answers to these questions do not come of themselves. They require the most laborious study, the most careful and exact examination. The system of questions does not save that trouble in the least degree. It enormously increases it by multiplying the questions that are suggested. But it forces us along step by step to much clearer conceptions of the objects of logic than have ever been attained before. The hard fact that it has yielded such fruit is the principal argument in its favor.

544. The method has a general similarity to Hegel's. It would be historically false to call it a modification of Hegel's. It was brought into being by the study of Kant's categories and not Hegel's. Hegel's method has the defect of not working at all if you think with too great exactitude. Moreover, it presents no such definite question to the mind as this method does. This method works better the finer and more accurate the thought. The subtlest mind cannot get the best possible results from it; but a mind of very moderate skill can make better analyses by this method than the same mind could obtain without it, by far.

Analyses apparently conflicting may be obtained by this method by different minds, owing to the impossibility of conforming strictly to the requirements. But it does not follow that the results are utterly wrong. They will be two imperfect analyses, each getting a part of the truth.

With this preface let us go on to the division of representamens, remembering that it is as impossible in a lecture to exhibit really fine and precise work of thought as it would be to exhibit before an audience experiments such as are used in researches.

deleted or omitted passages

This is the beginning of the lecture as written in October, up to p. 26, but apparently omitted from the delivery in November 1903.

Ladies and Gentlemen:

At the end of the last lecture I gave a rule for positively ascertaining whether or not a graph is alpha-possible. In case it be so, the rule further furnishes a description of the states of the universe to which its possibility is limited. If I had time to set before you the train of thought which determined the formulation of that rule, it would afford an instructive simple example of methodical reasoning. Unfortunately, there is not time for any such illustration in this course, far less can the scientific methodeutic be touched upon that great third of logic that teaches the principles upon which reasonings are to be arranged into systematic developments of theory. I will only say that in formulating that rule, I considered that of the six fundamental permissible operations, two are non-reversible, namely erasure and insertion. That is where either of these can be performed the reverse operation cannot be performed. I further considered that three of the six fundamental permissible operations complicate the graph, while the other three simplify it. Namely, insertion, iteration, and the introduction of a double cut, complicate the graph, while erasure, deiteration, and the removal of a double cut simplify it. It is necessary for the purpose to modify the non-reversible operations so as to render them reversible; and it fortunately happens that this can be done without erasure, the only one of them that is simplicative, being rendered complicative. In the next place, since the result aimed at must be of extreme simplicity, it is necessary to place restrictions upon the employment of the complicative operations. To this end, each of these was studied and the precise ways in which it could further the general purpose of the rule was ascertained; and thus in place of the complicative operations were substituted a set of operations conducive to the purpose.

The process of the rule is, as I said, probably not the most facile. But since the system of existential graphs is not intended as a calculus or general tool of reasoning, but is only meant for use in the study of logic, where it quite infrequently happens that it is necessary to ascertain whether or not any very complicated graph is alpha-possible, the waste of time due to this rule not being the simplest possible, is not of much importance.

The rule prescribes a routine calling for the exercize of so little intelligence that a machine might be devised to perform it. When we pass to the problem of beta possibility, that is of formulating a rule for positively ascertaining whether a graph with ligatures is logically possible or not, it would be quite easy to formulate a similar routine. But the performance of it would be utterly impracticable owing to the stupendous complications that it would lead to. For example, here is a graph, not particularly intricate:

The red ligatures refer to numbers, the brown ligatures to any universe such that there is a relation that u may be understood to express, that will make the entire graph true.

X is to be understood to be replaceable by any monad graph whatever without altering the truth of the entire graph.

We shall see, in due time, what those five premisses are. Suffice it for the present to say that there are only five. Now if each of them could be efficient and that in only one way, as one would have a right to infer from the account of reasoning given in the text-books, it would necessarily follow that there could not be but 32 theorems of the theory of numbers in all; whereas of highly interesting theorems already known there are hundreds. Euclid's Elements, which was never designed to be more than an introduction to geometry and algebra (or that theory which with the Greeks served the purpose of our algebra) has only 5 postulates, which are the main premisses, together with 9 axioms and 132 definitions. From these Euclid deduces 369 theorems, 96 problems, 17 lemmas, and 27 corollaries. There are also 2 scholia. At the same time, I ought to remark that, while the possible conclusions are innumerable, yet after all premisses have been iterated so as to exhaust all the different ways of using them together with all simpler ways, there will be no more theorems of any particular interest, and the branch of mathematics in question may be said to be substantially exhausted. The theory of conics is an instance. The great geometer Chasles after he attained to a great age continued to grind out, by the bushel-basket full, such theorems as that in a plane, the number of conics that touch five given conics is 3264. I think that when a mathematical theory has nothing new to discover but such propositions as that, it may be said to be exhausted. Every given mathematical theory must, in that sense, eventually become exhausted. Whether or not new theories of interest will continue to offer new problems or not, I am not prepared to say.

But to come back to the matter in hand, I give you without further preface, the following rule for positively ascertaining whether or not a given graph is beta possible.

In the first place, find in the graph every lexis, (regarding as a lexis,) of which one replica is oddly enclosed (that is, is within an odd number of cuts) and another evenly enclosed, (i.e. is within an even number of cuts) the latter not being enclosed by every cut that encloses the former; and call every such pair of spots an adaptible pair. An adaptible pair is said to be conjoined when, and only when, every hook of one of its spots is joined by a ligature to the corresponding hook of the other spot. Your object will be as far as possible to leave no adaptible pair unconjoined, and if this be impossible, at any rate to produce every possible combination of conjunctions in some replica of an evenly enclosed part of the graph, unless you see clearly that a given combination would not serve your purpose in any degree. In order to do this you are permitted to perform an of the following operations upon ligatures, provided that before performing a non-reversible operation you iterate an evenly enclosed part of the graph including every part that will be affected by the operation and only operate upon the new replica so produced.

Operation A Two oddly enclosed lines of identity on the same area may be joined; and an evenly enclosed line of identity may be severed. These operations are irreversible.

Operation B. From any line of identity lying just outside a cut a branch may be made extending into the cut; and this operation is reversible.

Operation C. A disconnected line of identity ligature can anywhere be scribed or erased.

But what is generally useful is to iterate an evenly enclosed partial graph within an even number of additional cuts, or an oddly enclosed partial graph within an odd number of additional cuts, to extend a branch from an evenly enclosed line of identity into an odd number of cuts and there join it to another. Of course, this operation is irreversible.

Secondly, when all possible combinations of conjunctions of applicable pairs have been made, the second part of the rule is to be applied, all spots not conjoined by all their corresponding hooks being treated as replicas of different lexeis and all spots that are so conjoined being treated as replicas of the same lexis, and no further attention being paid to the ligatures during the process.

The process will be found to be simpler in practice than it sounds in an abstract statement. I regret that the brevity of the course forbids my illustrating it.

This next section, crossed out by Peirce, follows the paragraph published as CP 1.524 (above). MS page numbers are given in {brackets}.

{74} Things were in that condition when I devoted two years of daily hard labor, with active, wide-awake, thought, to making out, as well as I could, what the first categories really were. I have near a ream of carefully pondered statements of my work, and the result was a paper printed in 1867 and filling ten pages. When that was done, I dismissed the matter from my thoughts very largely and when I thought of [it] cultivated {76} a critical and depreciatory attitude toward [my] doctrine. In fact, I have done that with everything I have printed. Then, after some years, I reëxamined the subject and became more confident than before of the substantial truth of my original statement. I thus alternated periods in which I endeavored to develope my doctrine with periods in which I emdeavored to destroy it for many years, until I finally quite ceased to doubt. That was a good many years ago; and since then, I have devoted a large part of my study to improving the doctrine. But with me this is very slow work; for I require the thought to be exact and strong. I tell you these things in order to persuade you that the subject is worth a good deal of thought. If I could only induce

From this point on, the text on the even-numbered pages is not crossed out, but seems to be an alternate draft that was replaced by the text written on the unnumbered pages, up to p. 104.

{78} another person of sufficient natural aptitude to train himself to this work, he would bring to light truths which I have not been able to discover.

There are a few comments upon the Categories that I had better add, because they will be pertinent to questions that will come before us.

I have already shown you that this list of categories is complete, and that there is no Fourthness, as a distinct element. But I have never said nor thought that this list of categories is the only list. On the contrary, it has always appeared to me that there must be at least one other; and I have given much time to attempts to make out the others. But I have nothing to communicate about them, being {80} desirous that the little I publish should be of genuine value.

I have spoken of two peculiar modes of consciousness, the consciousness of Reaction in Volition and in Perception, as Secondness par excellence. But, in truth, all consciousness is ipso facto Secondness. I have sometimes called Qualities of Feeling immediate consciousness; but this immediate consciousness is a fiction of the psychologists. Consider your memory or imagination of a red color. You may have a very dim imagination of a brilliant scarlet. You may have an intensely vivid imagination of an ashes of roses color, or very dull reddish grey. The vividness or dimness of the image does not affect the quality. The {82} vividness is the force of the reaction upon you of the object of imagination. It is of the nature of compulsion, or Secondness. It is a character of the consciousness as a fact. The quality per se has no vividness nor dimness. It is not a mode of consciousness but is a possible mode of the object felt. Thirdness is neither consciousness nor a possible immediate object of consciousness. It governs consciousness. A graph, if it were seriously meant to convey information would be a good example of a thing of Thirdness, because it might shape your conduct in regard to the thing the graph represents. The graph would thus establish a reaction between two other things, which is the essential characteristic of Thirdness. But I have already called attention {84} to the distinction between a graph and a graph-replica. Your consciousness at a given moment may be a graph-replica. But the graph itself can never come into your mind except by the mediation of a replica.

We can seldom find any phenomenon in which one of the categories is so predominant as to improve our notion of the category. One might expect to find them illustrated by our apprehension of past, present, and future time. But the past and present appear under aspects too various. One might say that the past as a whole is what it is in itself, which is a Firstness, while the present has no other being or at least is not otherwise known to us, than as the last bit of the past. But the whole Time rather illustrates Thirdness. The Future, at any rate, which is able to bring about what never will be capable of having been brought about, {86} which has no end, certainly has a prominent aspect which well illustrates the mode of being of Thirdness, which I have sometimes called the esse in futuro. Every Thirdness consists in the truth that something will be brought about, if the conditions present themselves. A graph, or speech, has no real meaning unless it will influence conduct. The manner in which the future influences the present also erves to make the mode of being of Thirdness clearer. The first step of the process of that influence is that we make a forecast, which at the outset is a mere suggestion, the resultant of various mental habits acting on perceptions and memories. “Yes,” objects somebody; “that is just it. It is {88} the forecast that influences us, itself the result of past perceptions and habits, and the future as fact, contradistinguished from the mere representation of it, does not influence us in the least.” To which I reply, “My dear sir, you say you agree with my remark, and in my turn I fully assent to yours. The future, as fact, naturally does not influence us; because a fact, factum, is what is already done; and the future is not a fact at all. But that is not to say that it has no reality, unless you are determined to shut your eyes to every category but Secondness. The future has a present, real being which consists in the present certainty of its destined {90} coming to pass. This certainty, like all certainty, is of the nature of a sign. It is not, however, a certainty in our minds. It is certainty in the nature of things. It is an eternal law to which the events of the universe really will conform. It is this certainty, this law which in pervading the whole universe, and in thus pervading our mental natures with the rest, enables us, no matter by what machinery, to make our guess. Your objecting,— I continue in reply, your objecting, which is the only element of what you say that I find to object to, is due to your bad habit of thinking that there are no realities but facts, thus overlooking these realities which alone impart to facts any significance. You must become as {92} a little child in order to understand these things. Yet well as the future, under this aspect of it, illustrates Thirdness, if one looks upon a future contingent proposition, as Aristotle did, with more reason than modern men can easily appreciate, as a proposition which is not yet either true or false, then the future seems to show Firstness. If on the other hand we say that when a man is in a struggle of effort, it is the future that he is struggling to affect, then we detect an element of Secondness in the Future.

A quality, or Firstness, has mere logical possibility,— that is, such being as an idea can contain in itself. But it is a positive determinate possibility. A fact, or Secondness, has actuality. A sign, or Thirdness, as bringing about facts, has power, or necessity, but a kind of necessity which is neither a mere absence of possibility nor a blind compulsion, but an intellectual necessity.

Where Secondness is predominant, dichotomies {94} or distinctions between two kinds prevail; and that might perhaps have been expected. But it is rather surprising that where the element of Thirdness is predominant, trichotomies, or the divisions into three kinds prevail. In saying this, I am speaking of divisions of form, not mere divisions according to matter. The dichotomies of secondness all have a general likeness, the one species being more external, the other more internal. The trichotomies of thirdness also have a general likeness, one species being decidedly intellectual and having trichotomic subdivisions, another more factual and having dichotomic subdivisions, and the third more qualitative, and these have [mere?] divisions according to matter. Thus, in what has the form of fact, Secondness is the predominant {96} element; and accordingly we find two kinds of what has the form of facts, real facts and fictions. Real facts subdivide, not, you will observe, merely materially, or according to the matter they relate to, but formally or in their nature as facts, into hard facts, not directly controllable, and facts of volition which are what we call ‘free,’ meaning directly controllable by the power of self-control. Hard facts are again divisible into those of the external real things and facts of sensation. Now let us pass to the consideration of law. The predominant element in law, or uniformity, is Thirdness; and accordingly we find a trichotomic division into normative laws, which determine what ideally, or in reason, should be; compulsive laws, which determine how facts must take place; {98} and uniformities of classification, which determine the connections of qualities. Subdivision of the first class should, by the rule, be trichotomic, that of the second dichotomic, and that of the third merely according to the subjects to which the laws apply. Accordingly, normative laws are found to be either logical, relating to what thought should in reason be, ethical, relating to what conduct should ideally be, and esthetical, relating to what qualities of works of art should ideally be; and although this sounds like a mere material division yet the characters of the three kinds of laws, as laws, are essentially different. Compulsive laws divide by dichotomy into purely Physical laws and Psychological laws. These have very different characters {100} as laws. For the purely physical laws are of this nature, that they determine accelerations, that is to say what the position of a particle shall be at a given instant relatively to its positions at two instants indefinitely near to the instant in question; while physiological laws, that is to say, habits and heredities, simply determine that the event (usually a complex event) of one time shall be like the event of a previous time (usually long previous). There is also another great difference between these laws which the majority of those whose opinions are of weight believe to be merely apparent, but which I believe to be real. It is that the purely physical laws are absolutely compulsive, while the physiological laws are {102} subject to variations, and these variations, it has not been sufficiently remarked in connection with this difference of opinion, is quite indispensible to their regular action. I can hardly understand how there could be such a thing as an unchangeable habit. The great psychologist, Hume, said that the law of the association of ideas was a “gentle force.” It seems to me to be essentially so.

I dwell upon this rule of division, because, however it may be in other fields, in logic I am pretty sure that the divisions [it leads to are ?] the most important. At any rate, though I have never relied upon it, not seeing any clear reason why it should be so, and feeling sure that nothing in logic can be universally true without a reason, yet I have invariably found its {104} suggestions to be useful. They certainly ought not to be neglected.

The dichotomies of secondness often present a curious phenomenon. Namely while the two fold division is very evident, yet owing to the external part being itself bisected, there is in effect a division into three classes, although it is perfectly evident that this is due to two dichotomies, and then there is a cross division of the same kind producing nine classes. But the smallest attention to the character of these divisions will convince anybody of their dichotomic origin.

Lowell Lecture 4