[4/4] (1.1) (1.2) (1.3) entertains a false opinion. Rubbish! There may be questions concerning which it is impossible deliberately to entertain false opinions. Nobody could well deliberately opine that there is no true opinion, -not, at any rate, unless he were a metaphysician. That arises from the fact that a deliberate opinion is a multiple opinion, - in fact, an endless series of opinions. For to entertain a deliberate opinion implies that one has an opinion that one has that opinion, and so on endlessly. Thus deliberately to opine that there is no opinion would be at once to opine that there is and that there is not an opinion. This is not, properly speaking, a proposition, but is an absurdity. One may commit a mistake, supposing A to be B, when it is not; and then one may opine that something true of A is not true of B, and thus may seem to entertain an absurd opinion. But one does not really do so. But all this does not touch the reader’s opinion, which simply is that a false proposition may be feared as possibly liable to appear as the conclusion of an argument.
What does the reader mean by a false and by a true proposition? This is a difficult and disputed question. The different answers to it that are current are not false: they are only insufficient. They complement one another.
The first answer is this. In the first place a proposition must not be confounded with an assertion or a judgment. An assertion is an act by which a person makes himself responsible for the truth of a proposition. Nobody ever asserted that the moon is made of green cheese; yet this is a familiar proposition. A judgment is a mental act by which one makes a resolution to adhere to a proposition as true, with all its logical consequences. In the next place it is necessary to distinguish between a proposition and a sentence, i.e.: this or that expression of it, in writing, speech, thought, etc. A sentence, in the sense here used, is a single object. Every time it is copied or pronounced, a new sentence is made. But a proposition is not a single thing and cannot properly be said to have any existence. Its mode of being consists in its possibility. A proposition which might be expressed has all the being that belongs to propositions although nobody ever expresses it or thinks it. It is the same proposition every time it is thought, spoken, or written, whether in English, German, Spanish, Tagálog, or how. A proposition consists in a meaning, whether adopted or not, and however expressed. That meaning is the meaning of any sign which should signify that a certain iconic representation, or image (or any equivalent of it), is a (2) sign of something indicated by a certain indexical sign, or any equivalent thereof. To illustrate this, any sentence will answer. Take this:
"Go your way into the village which is over against us, in the which as ye enter, ye shall find an ass tied and a colt with her whereon no man ever yet sat."
As this was said by Jesus to two of his disciples, it created in their imagination the picture of an ass tied and accompanied by a young colt. That picture was the icon which the definition mentions. What was this a picture of? He attaches a legend to it in this way. They were standing looking at the village. Now, says Jesus, you cannot see the colt from where we stand, but go there, and as you enter the village, look about; and you will see what I describe. That injunction put a force upon them which tended to direct their attention to what Jesus was talking about. It acted as an indicating sign or indication. The passage will furnish two further illustrations of the sense of the definition, since two other propositions are contained in it. One of these is that no man had ever yet sat upon that colt. Here the iconic sign is any diagram representing negation. Probably every person has his own way, or ways, of picturing negation to himself. A proposition never presc(r)ibes any particular mode of iconization, although the form of expression may suggest some mode. Here, however, the two disciples are left to picture negation in their own fashions. That method might have been to think one transparent image overlying another and not matching it. Or two separate dots might be pictured as a diagram of non-identity, and each dot might be pictured as having a thread running from it to an image of anything identical with it. They were now to think that they would (3)be allowed to select any instant of the colt’s life they liked, and get information of what its situation was at that instant, - to get a photograph of it, at that instant, or anything equivalent. Then taking this picture and the picture of a colt with a man on its back, to those two the icon of negation would be applicable. Such a complicated idea was expressed by the few words ‘whereon no man ever yet sat’. The other illustration is afforded by the proposition ‘you will go your way into the village which is over against us.’ Jesus does not assert this proposition, that is, does not make himself responsible for it. On the contrary, he enjoins or commands it, that is, makes the two disciples responsible for it. But that does not affect the proposition itself. The icon, or picture excited in the imagination is here that of two men walking to a village. There are two indices, or labels, to show what this is a picture of. One of these is their eye-sight, as Jesus spoke of “that there village over against us”. That label is attached to the village in the icon. The other label is the pronoun “you” (in the Greek merely the termination = ετε of νπαγετε) taken in connection with the look of their master’s countenance, which would have been quite sufficient to show them who the two men of the icon were, for in very many languages the second person of the imperative mood dispenses with all terminations or special indications of the person addressed. These explanations render the nature of a proposition sufficiently clear for our present purpose. It has, I hope, been made tolerably plain to the reader who thinks the matter over carefully for himself, without allowing himself to be disturbed by perplexities as to details (which are endless), that no matter in what other way a proposition may be comprehended, and whether we are going to the very heart of the matter or not, yet it is true (and a significant truth) that every proposition is capable of expression either by means of a photograph, with or without stereoscopic and cinetoscopic elaborations, together with some sign which shall show the connection of these images with the object of some index, or sign or experience, forcing the attention, or bringing some information, or indicating some possible source of information; or else by means of some analogous icon appealing to other senses than that of sight, together with analogous forceful indications, and a sign connecting the icon with these indices. All this shall be more fully considered in the sequel; but thus much may be said at once to advantage.
A proposition is the signification of a sign which represents that an icon is applicable to that which an index indicates. The proposition itself does not strictly speaking exist. It is mere possibility. But in order that it should be either true or false, the object of the index to which the proposition refers must exist and react upon the supp(o)rter of the proposition. Without that, a proposition can have no positive truth or falsehood. It is not in such case really a proposition; for an index is a forceful sign and things non-existent exert no force. It is only an empty shell of a proposition, - a form which is like that of the expression of a proposition but with no matter.
The existence of this subject of the proposition which is the object of the indexical sign, that is, the forceful sign, consists in its actually putting forth force. The existence of a genuine index is a sufficient guarantee of the existence of the subject; for the force with which the index acts upon us is only an aspect of the force with which the subject acts on the index. I meet a near neighbor; - living here in the open country. I have only farmers as for neighbors. We begin chatting about familiar things. One of us asks(:) "How is that sow coming on?" Nothing could be more inane and impertinent than the remark of some imaginary young philosopher whom I might bring with me who should doubt the existence of the sow. How should the indication "that sow" have forced my neighbor’s attention and mine in a certain way, if no force was in that which the phrase "that sow" indicates? And how could the non-existent exercize force? A pretty sort of non-existence would that be.
But not only must the subject of the proposition exist, but, in order that the proposition should be true rather than false, it must exist in a special manner, which only the proposition itself can describe. It may be that the cordial acceptance of the proposition helps to bring about this state of things. But I care not though such acceptance should be indispensible to the fact: it still does not constitute ipso facto that reality in which the truth of the proposition in turn consists. The truth of the proposition consists in its accordance with a real state of things; and this reality consists in its existing in what manner it does independently of what you or I or any generation of men may think about it. That is to say, that whether the acceptance of the proposition is helpful to, or is even a necessary and sufficient condition of the reality of the fact or not, no such acceptance of that same proposition constitutes, or goes toward constituting, the fact which the proposition, if asserted, would assert.
An empty shell of a proposition may fail to contain any genuine proposition for either of two reasons. It may simply fail to prescribe any icon at all. Or on the other hand it may prescribe more than can be fulfilled, at once, not because of any weakness of our imagination or mind, for such difficulties can always be evaded, but because the items prescribed are of their own nature incompatible. How insignificant difficulties of the former kind are could be shown in many ways. But not to loiter over a secondary matter, let us content ourselves here with noticing that it has not prevented mathematicians, all whose reasonings are diagrammatic, from studying space of four dimensions. Mr. Stringham has even drawn pictures of the regular solids in four dimensions, and has enumerated and described all the regular solids in spaces of all dimensions. No doubt, a considerable mathematical force is required for such studies; but it may be said to be now established that no degree of complexity, even if it be infinite, will conquer the mathematical imagination, so long of course as there is some regularity in the complication. An utterly irregular infinity could probably be proved to involve a contradiction, as it is already certain that a complication transcending all multiplicity and yet irregular is contradictory. The kind of prescription which is so excessive that no icon can fulfill it is that which demands that a character shall be at once present and absent. It is not because we cannot think it that such a prescription cannot be fulfilled, but because, as we clearly and fully perceive, (but because) the prescription calls upon the imagination not to obey it; like a pope who should pronounce ex cathedra, requiring all the faithful to believe him under pain of damnation, that no pope ever did or ever would make any pronouncement ex cathedra that any Christian ought to believe. The shell of a proposition which thus fails of being a proposition through prescribing too much is said to be absurd. The shell of a proposition which fails of being a proposition through not prescribing anything is said to be empty or meaningless. But in a wider sense the absurd may also be said to be meaningless. As an example of an empty enunciation, we may take this: ‘Whatever phenix there may be is a phenix’. As an example of an absurd enunciation we may take this: ‘some phenix exists which is not a phenix’. Every denial of an empty enunciation is absurd, and vice versa. An enunciation like 'Every phenix is a bird', may be understood in such a sense as to be a proposition conveying positive information. For it may mean that the name ‘phenix’ would not properly be applied to anything not a bird. It is different with the enunciation, Every phenix is a phenix; for this uses the word phenix as if its meaning were known. If in the enunciation ‘Every phenix is a bird’, the word phenix be supposed to be understood through its definition as a bird, then this also is an empty formula, and not a genuine proposition.
Logicians, who are much given to formalities, have wished to extend the rule that every proposition is true or false so as to make it include empty and absurd enunciations, calling the empty ones true and the absurd ones false. Nor are they without some tolerably sound reasons for this extension. For our present purpose, however, such extension is unadvisable. It would compel us to give up the statement that every proposition represents a reality independent of what may be affirmed or denied of it, thus losing sight of a very important truth. Indeed it obscures all the fundamental parts of logic very seriously. It leads directly to that class of difficulties, which the logicians themselves have given the name of the Insolubilia. In order to exemplify these difficulties, let us suppose that three witnesses A, B and C, are called in a law suit. We will suppose that owing to exclusions of testimony by the court, the testimony as it stands is reduced to this: A testifies that B’s testimony is not altogether true; B testifies that C’s testimony is not altogether true; and C testifies that A’s testimony is not altogether true. They testify nothing else. None of the three witnesses has any reality in view; that is, nothing which has a manner of existence independent of what is asserted of it. Properly speaking, then, there are no propositions and nothing is testified. But the logicians, by insisting that every enunciation is either true or false, become wound up as follows. Suppose A’s testimony to be altogether true. Then, since he testifies that B’s testimony is not entirely true, this must be admitted to be true. But B testifies to nothing else than that C’s testimony is not altogether true. Hence, this will not be true; that is, we must admit that C’s testimony is altogether true. Now C(‘s) testifies that A’s testimony is not altogether true. Hence, we must admit that A´s testimony is not altogether true, reducing our supposition that it was altogether true to an absurdity. We are then driven to suppose that A´s testimony is not altogether true. But A testifies to nothing except that B’s testimony is not altogether true. If therefore A’s testimony is not altogether true, we must admit that B’s testimony is altogether true, and therefore we must accept the substance of it, which is that C’s testimony is not altogether true. But C testifies to nothing except that A´s testimony is not altogether true. Therefore, it can (not) only be amended by admitting that A’s testimony is altogether true. This, however, is contrary to our second hypothesis. Thus, it is equally absurd that A’s testimony is altogether true and that it is not altogether true. Two solutions of this puzzle are worth mention. The first, which is stated in various ways, comes simply to this, that the reasonings are good and that they prove that the hypothesis that three witnesses should so testify is absurd. But this is not so: it is perfectly imaginable that three witnesses should so testify, although at least one of the three must be a liar, to be willing to testify about a fact which has not yet occurred. Moreover, the reasonings are not good. The whole of them turn upon the fact that the three propositions of the three witnesses are asserted. Eliminate the element of assertion and no puzzle remains. For an assertion involves an endless series of enunciations, or at any rate two; namely, the assertion involves the enunciation asserted and also the enunciation asserting it. And this asserting enunciation is itself asserted. Consequently, though A testifies merely that B’s testimony contains something false, if we suppose that A’s testimony is not altogether true, we are still not obliged to take B’s testimony as not containing anything false. For the falsity of A’s testimony may lie in the asserting and not in the ultimate asserted proposition. It is therefore open to us to suppose that all three witnesses testify truly, in the sense that the propositions to which they testify are true, but all testify falsely since their asserting enunciations are false. It is somewhat paradoxical, no doubt, to say that the assertion of a true proposition is false. Yet it is evident that it is the act of act of assertion by each witness which reverses the truth or falsity of the proposition to which he testifies. For example, suppose that the testimony of each witness is that the next one in cyclical order testifies to something not true. Then, if A had not testified at all, the testimony of C that A testifies to something not true would have been false; for A would testify to nothing. Consequently the testimony of B that C testifies something untrue would be entirely true, and the proposition to which A testifies would be utterly false if he did not testify to it. It is this lying act of assertion which renders it true, and if this asserting enunciation had not been false, - that is, if he had testified, as he ought, that B’s testimony is true, there would have been no difficulty. But his asserting enunciation being false, the asserted enunciation of C becomes true; only the asserting enunciation of C remains false. As to the asserting enunciation of B, that is rendered false only by A’s false act of assertion. Suppose on the other hand that what each witness asserts is that if the next in cyclical order testifies to anything he testifies to something false. Then, if A had asserted nothing, C would assert nothing false, and consequently B’s testimony would be down right false, and what A in fact asserts would have been true. But his act of asserting it renders C’s testimony false, except so far as A’s asserting enunciation justifies it. This does justify C’s asserted enunciation, but fails to justify C’s asserting enunciation, and thus B’s asserted enunciation in its turn is rendered true, though his asserting enunciation is false. If the number of witnesses testifying in cyclical order, each to the falsity of the next, had been even, it would be possible to suppose that every other one spoke true and every other one false. But there would be no ground in fact for saying that either half of the witnesses spoke truly rather than falsely. The only proper solution is, as before, that the asserting enunciation of each is false and the asserted enunciation true.
Such are the subtleties, one might almost say quibbles, into which we are inevitably led if we follow the logicians in considering anything in the form of a proposition as being necessarily true or false, without regard to whether it represents a reality, i.e.: something not constituted by a representation of it, or not. I do not say that the logicians do wrong. Within their technique there may be, there are, advantages in the course they take. But in any broad view such as we are now taking how much simpler and how much truer it is to say that a proposition, as that which is either true or false, so soon as the individual subject to which it relates has any sort of existence, is something which conforms, or professes to conform, to a reality not constituted by any assignable representation of it.
If philosophers can show us that the realities are so overgrown with thoughts about them that it is impossible by any direct process to compare the thoughts with the naked realities, that need not at all disturb us. If idealists can prove that the thought is the cause of the reality which is its object, even that will not disturb us so long as the reality does not consist in what is thought about it. If a Berkeley can show that all reality is of the nature of thought, still our opinion is untouched, so long as it is one a possible thought which constitutes the reality, and not this or that definite existent thought about that very thing.
The second answer to the question what the reader means by a true and by a false proposition ought to be understood as fully admitting the correctness of the first answer, but as further explaining what this reality is to which the proposition professes to conform and which in itself is does not consist in any actual representation of it. In order to understand that, we must first ask what is the meaning of any statement, what is the meaning of any word or of any sign whatever. Until we have a clear idea of what we mean by "meaning", it is useless to inquire what the meaning of any particular sign is. It is evident that in order to answer a question we must understand what the question is; and we cannot understand what it is to ask for the meaning of true and false until we know what is meant by meaning.
Meaning is the character of a sign; and therefore in order to find what meaning is we must consider what a sign is. Before entering on that inquiry, however, let us note that meaning is something allied in its nature to value. I do not know whether we ought rather to say that meaning is the value of a word, - a phrase often used, - or whether we ought to say that the value of anything to us is what it means for us, - which we also sometimes hear said. Suffice it to say that the two ideas are near together. Now value is the measure of desirability; and desire always refers to the future. That leads us to inquire whether meaning does not always refer to the future. We cannot answer this question with certainty until we have inquired into the nature of a sign; but it will help us to bear it in mind. If a man is brave now, his present possession of that character cannot mean that he behaved in certain ways in the past; for though he acted as a brave man would have done, still, it was only upon a limited number of occasions; and therefore it might have been accidental that from quite other motives and causes he then happened to act as if he were brave. But braveness does not mean that, it is a quality which would make the man act in a certain way every time no matter what the multitude of the occasions. It means that we can predict with certainty how he will act whenever an occasion shall present itself. To say that a man is brave means that a certain kind of conduct is to be expected of him. Here, then, is a case in which meaning refers to the future; and there are evidently multitudes of similar cases. The question is whether or not all meaning refers to the future**.
What is a sign? It is anything which in any way represents an object. This statement leaves us the difficulty of saying what “representing” is. Yet it affords help by pointing out that every sign refers to an object. Let us begin by looking at his word object. It came in with scholasticism, and is somewhat remarkable as a fundamental term of philosophy that is not translated from the Greek. Its earliest occurrence is in a translation from the Greek; but there is no corresponding word in the original. Another somewhat noticeable circumstance about the word is how little it has been deflected from its original meaning, of that which a representation in some sense reproduces or aims to exhibit in its true light. Aquinas already slightly distorts the meaning, but by a hardly perceptible deviation; and very little further distortion has taken place. Aquinas, in using the word, commonly illustrates his meaning by a reference to the object of sight. This use of the word belongs to our familiar speech: we detect nothing out of the common in the sentence, "Think on thy Proteus, when thou haply seest some rare note-worthy object in thy travels." This use of the word arose from the fact that vision is conceived as furnishing images, pictures, of outward things. Our idea of an object of sight is a trifle closer to the original sense than is the idea of Aquinas. For he thought that the rays shoot out from the eye and on being reflected by the object bring back with them the species, or appearance. His notion of sight, therefore, does not altogether set aside the element of active looking. Consequently it does not strike him that an object is essentially a correlate of a sign: he considers it to be the correlate of any power or habit. Let us turn over a few familiar locutions in which the word object is used. A person loved is the lover’s "beloved object". In the delirium of his fever, an image painted in roseate hue appears to him as the faithful representation of the person loved. Hence she is only said to be his beloved object. She is for all the world a woman who is loved; but she is the beloved object of his delirious fancy. So we speak of an “object of pity”; because pity depends upon a lively imaginative representation of the plight of the person pitied. But when we speak of an "object of wrath", we are thinking rather of the person or thing to which the angry person is aiming his injuries. The thing of which a shooter aims is called the "object" at which he aims. This, we may suppose, is due to the circumstance that the shooter has to look along his arrow or his gun and make that thing the object of distinct vision while he is sighting along his weapon. From applying the word "object" to the thing aimed at, we soon pass to speaking of the "object" of endeavors and of contrivances in general. But there is another way in which the word is appropriate here. For in all serious endeavor it is requisite that which should form as distinct an idea as possible of precisely the state of things that we desire to bring about and then try to make the actual results of our labor as close a copy of that "object" as we can. Thus it comes about that a lover’s "beloved object" and the "object of his desire" are phrases of quite different meanings. The one is the cause of his conduct, the other the effect of it. As for the present use of the word "object" in grammar, it is almost recent. Thus the Port Royal Grammar, which was used into the nineteenth century, says: "The accusative denotes the subject that receives the action of the verb"; and this use of the word subject remains quite correct to this day. What is often called the subject of a sentence is properly called "the subject nominative" or the "principal subject". These remarks are intended to impart a preliminary rough idea of the sense in which I shall endeavor consistently (4) to employ the word "object", namely, to mean that which a sign, so far as it fulfills the function of a sign, enables one who knows that sign, and knows it as a sign, to know.
A sign does not function as a sign unless it be understood as a sign. It is impossible, in the present state of knowledge, to say, at once fully, precisely, and with a satisfactory approach to certitude, what it is to understand a sign. Consciousness is requisite for reasoning; and reasoning is required for the highest grade of understanding of the most perfect signs; but in view of the facts adduced by Von Hartmann and others concerning Unconscious Mind, it does not seem that consciousness can be considered as essential to the understanding of a sign. But what is indispensible is that there should be an interpretation of the sign; that is that the sign should, actually or virtually, bring about a determination of a sign of the same object of which it is itself a sign. This interpreting sign, like every sign, only functions as a sign so far as it again is interpreted, that is, actually or virtually, determines a sign of that same object of which it is itself a sign. Thus there is a virtual endless series of signs when a sign is understood; and a sign never understood can hardly be said to be a sign. There is an endless series of signs, at any rate, in the same sense in which Achilles runs over an endless series of distances in overtaking the tortoise. It may be asked why we are not immediately conscious of this infinite process. To begin with, let us not be too sure we are not conscious of it in that kind of understanding into which consciousness enters. We have no direct means of ascertaining what we have been conscious of during a movement of thought. It is only the resting places which affect the memory. But let us consider roughly what must pass within us, when we read a sentence. It is a significant fact that those languages in which the prevailing form of sentence places the predicate first, -the kind of sentence called in Arabic , -like 'Then came Omar', are read with more pleasure and less fatigue than our own languages. The reason is that a picture begins to be painted in the imagination almost as soon as the utterance begins and details are put (in) it as it proceeds, and finally a label is attached to the picture; while with a German or Latin sentence, the materials for building up the idea are brought one after another, stored away somewhere in the mind; and it is not until the sentence is done that we can survey our materials and consider how they have to be put together, and having decided, try that way of building up the meaning, in order to see whether it makes probable sense. English is not quite so bad; but it has the same fault. In either case, the process of understanding is quite a gradual operation. Ideas in crowds, that lie hid in the depths of memory have to be brought up toward the surface of consciousness; and this increase of vividness is a gradual process. They have to be adjusted somewhat nicely, no one being made too prominent. During all this time there must be a sign before the mind, and there must besides be a sign that that sign is not yet quite the sign wanted. When we do understand the sentence, our sense of understanding it is a consciousness that we have begun at the uttered sounds and gradually transmuted them, without a breach of continuity, into the idea we gain. We feel that every step was reasonable. Now a reason for which there is no reason is no reason at all. Perfect reasonableness implies an, at least virtual, endless series of reasons. Moreover, when the meaning of the sentence is one understood, let us suppose that all memory, record, or possibility of effect of the sentence should utterly perish, so that neither the listener nor anybody else should have their consciousness, ideas, or conduct, in any way shaped or modified by it, but everything should necessarily be precisely as if it had never been uttered. In that case, I ask, Could it properly be regarded as a sign at all? Has it not been, in that case, absolutely insignificant, non significant? Is it not essential to a sign’s being a sign that its influence should never cease finally to live, as lending strength to a habit, law, or rule which is ready to produce action when occasion may arise even although the truth of the sign (if it is a subject of truth or falsehood) be forever denied? What is anything that has perished and left not a wrack behind but a forgotten dream? Let the earth be struck by a comet and reduced to gas, let the whole universe, and space itself be annihilated and forgotten, yet still one or other of two alternatives remain, either it is a living law that if any mind should discover and read the first Book of Euclid, the 42nd proposition would produce its effect, pro or con, upon that mind, or else that proposition is utter nonsense and has no meaning. In this sense, every sign must be followed by an absolutely endless virtual succession of interpretant signs, or else not be in very truth a sign.
In the light of these considerations it is easy to see that the object of a sign, that to which it virtually at least professes to be applicable, can itself be only a sign. For example, the object of an ordinary proposition is generalization from a group of perceptual facts. It represents those facts, these perceptual facts are themselves abstract representatives, through we know not precisely what intermediaries, of the percepts themselves; and these are themselves viewed and are, - if the judgment has any truth, -representations, primarily of impressions of sense, ultimately of a dark underlying something, which cannot be specified without its manifesting itself as a sign of something below. There is, we think, and reasonably think, a limit to this, an ultimate reality, like a zero of temperature. But, in the nature of things, it can only be approached, it can only be represented. The immediate object which any sign seeks to represent is itself a sign.
The sign is never the very object itself. It is, therefore a sign of its object only in some aspect, in some respect. Thus, a sign is something which brings another sign into objective relation to that sign which it represents itself, and brings it into that relation in some measure in the same respect or aspect in which it is itself a sign of the same sign. If we attempt to say what respect or aspect it is in which a sign is a sign of its object, that respect or aspect must then appear itself as a sign. Its own full aspect, the sign cannot evoke or endeavor to evoke. It is only some aspect of that aspect that it can aim to reproduce. Here again there will be an endless series. But this aspect is only a character of the necessary imperfection of a sign. A sign is something which in some measure and in some respect makes its interpretant the sign of that of which it is itself the sign. It is like a mean function in mathematics. We call (P)x,y a mean function of x and y, if it is such a function that when x and y are the same, it is itself that same. So a sign which merely represents itself to itself is nothing else but that thing itself. The two infinite series, the one back toward the object, the other forward toward the interpretant, in this case collapse into an immediate present. The type of a sign is memory, which takes up the deliverance of past memory and delivers a portion of it to future memory.
We have now a general notion of what a sign is. But this idea can be rendered much more distinct by pointing three radically different types of signs. No sign, perhaps, can perfectly realize any one of these types. They are like chemical elements, which the very laws of chemical reaction prohibit us from obtaining in absolute purity, but to the purification of which we can so far approximate as to get tolerably accurate ideas of their nature, and which present themselves habitually in such a degree of purityl, that we have no hesitation in saying, this is gold, that silver, and the other copper; or this is iron, that nickel, and the third cobalt; although all are strictly mixtures of the three. The three types of signs are icons, which are the simplest; next indices; third and highest, symbols. Let us begin with the Index. An Index is a thing which having been forcibly affected by its object, forcibly affects its interpretant and causes that interpretant to be forcibly affected by the object, and to affect its interpretant in turn; and which, further, so far as it is a sign, becomes a sign in this way. So far as it is a sign in any other way or sense it belongs to one of the other types of sign and is not a pure Index. For example, a man in a town happens to spy a balloon and goes into the middle of the street and stares up at it. He is forced, by virtue of his natural instincts to do so, and others seeing him so intent in his gaze, are forced in their turn to look up and see what he sees; and they attract still other gazers. That man’s upward gaze is a tolerably pure Index. A man driving a pair of horses rapidly through a tangled and crowded thoroughfare, sees himself in danger of running over an old woman. "Hi!" he shouts, quite automatically; and she automatically flees to the sidewalk, and exclaims, as automatically, "Ah! A narrow escape!" whereupon passers by automatically turn their eyes and look at her. Here, the man’s "Hi!" is an index, but of a somewhat more perfect kind, -not a more perfect index, but a more perfect sign, -than the other man’s upward gaze. Because that upward gaze did not tell anything. Ther was no profession of seeing any specific kind of thing in the upward gaze. But the exclamation "Hi!" both the syllable itself, and the urgent tone in which it is uttered suggest, -even assert, -danger. The "hi!" might be true or false; the gaze could not be either.
An icon is a pure image, not necessarily visual. Being a pure image it involves no profession of being a sign; because such profession would be a sign not of the nature of an image. There is no known cause making it an image of its object; for if there were it would in part have a significant character of the Indexical type. I take ship and sail into the tropics for the first time. The first time we come into port, I lean over the toprail and gaze at the scene. There is no reason known to me why that scene should be typical of the tropics, in general; and it does not occur to me that is perhaps so. Yet a general impression is produced in my imagination, a generalized picture of the picture before me; and in point of fact I already know the tropics, or that which is most distinctive of that clime. Although I have only seen some palm-trees from a distance, I already without suspecting it, have an idea which I shall find fits the whole vegetable kingdom of the Tropics, and its animals aswell, including its men and women, their physique, their dispositions, their manners and customs, and their whole life. That view from the toprail is and Icon of the Tropics. All icons, from mirror-images to algebraic formulae, are much alike, committing themselves to nothing at all, yet the source of all our information. They play in knowledge a part iconized by that played in evolution, according to the Darwinian theory, by fortuitous variations in reproduction.
It will be observed that an Icon represents whatever object it may represent by virtue of its own quality, and determines whatever interpretant it may determine by virtue of its own quality; while an Index represents its object by virtue of a real relation with it and determines whatever interpretant may be in a real relation with it and the object. A Symbol differs from both of those types of sign inasmuch as it represents its object solely by virtue of being represented to represent it by the interpretant which it determines. But how can this be, it will be asked. How can a thing become a sign of an object to an interpretant sign which itself determines by virtue of the recognition of that, its own creation? The reply to this question is best given in the form of an illustration. Certain facts are stated in such a way as to convince a person of the reality of a certain truth, that is, the argumentation is designed to determine in his mind a representation of that truth. Now if in the acknowledgement of that truth he recognizes that that argumentation is a sign of that truth then it has really functioned as a sign of it; but if he does not then the argumentation fails to be for him a sign of that truth. Next consider, not an argumentation or statement, expressly designed to lead to a given belief, but a mere statement of fact, a true proposition. That proposition may not be admitted by anybody. In that case, it does not function as a sign to anybody. But to whomsoever shall believe it, it will be a sign that, under certain circumstances, with a view to certain ends, certain lines of conduct are to be embraced, and the interpretant of it will be a rule of conduct to that effect established, not in consciousness necessarily, but in the nature and soul of the believer.
(1.1) … entertains a false opinion. Rubbish!. There may be questions concerning which it is impossible deliberately to entertain false opinions. Nobody could well deliberately opine that there is no true opinion, - unless he was a metaphysician. But that does not come near conflict with the readers opinion which relates to what may be feared as the conclusion of an argument.
What does the reader mean by a false and by a true proposition? This is one of the disputed questions. Two answers often supposed to conflict seem to be true, and a third is perhaps not false.
First answer. The truth or falsity of a proposition is not such a character that the proposition must first exist in speech, writing, thought or otherwise, and then, or thereby, acquire the character. On the contrary, the proposition though it never comes into existence will be true or false. Yet, in general, something must exist in order that a proposition should be true or false ( ). For example, the proposition "There is no such bird as a phenix", means that there is no such bird in the created universe; because there is such a bird in fable. Therefore the proposition could not be positively true or false if the universe did not exist. Were it meant that there was no such bird in fable, this world of fable would have to have such mode of being as it has to confer positive truth or falsity upon the proposition. If this "subject" to which the proposition applies exists, the proposition is either true or false; but which it is depends upon how that subject exists. If it exists in one manner the proposition is true; if in any other manner, false. But it is impossible to say or think what these manners are except by means of the proposition or some equivalent of it. An equivalent of a proposition is the same proposition, differently materialized. For the proposition consists in its meaning.
(1.2) … entertains a false opinion. But that is aside from the point. You might grant them that nobody entertains any opinion and still maintain your ground that there are false opinions and that there are true opinions; since it is sufficient to cover your meaning that it should be possible to write down two propositions the one precisely denying the other; such as
For as long as a false proposition can be written down it is l …
(1.3) … entertains a false opinion. Surely, this is rubbish. There may perhaps be questions concerning which it is impossible deliberately to entertain false opinions. Perhaps nobody can deliberately opine that there is no such thing as an opinion; though I would not warrant that a metaphysician could not. But that is not the point of the reader’s opinion in question, which relates to what may turn up as the conclusion of an argument.
Now what does the reader mean by a false proposition and a true proposition? A false proposition is unsatisfactory, a true one satisfactory, in some respect. When is this satisfaction to be experienced; in the past, the present, or the future, relatively to the time of utterance of the proposition.
(2) … sign (or any equivalent thereof.) For an example any proposition will do. Take this:
"Go your way into the village which is over against you: in the which as ye enter into it, ye shall find an ass tied a colt with her, where no man ever yet sat."
(3) … be allowed to select any man they pleased, and that they would be allowed to select any instant of the colt’s past life they please. Those two permissions would constitute the indication of what was the subject to which the proposition related; and the proposition itself was the meaning of any sign which should signify that to the position of the man chosen at the instant chosen and to the being on the colt’s back the icon of negation would be applicable as a sign. It was thus a highly complex idea that was expressed by saying that no man had ever yet sat on the colt’s back.
(4) … to employ the word ‘object’ to mean that of which a sign, - so far as it fulfills the function of a sign, - enables one to know who knows the sign and knows it as a sign.
A sign does not function as a sign unless it is understood as a sign, that is to say, unless it determines an idea to be itself a sign of the same object. This, of course, implies an infinite series of sign after sign. Now so wretchedly inaccurate has been the thought even of eminent philosophers that the prevailing notion is that an infinite series cannot be completed, and that the idea of an infinite series cannot be completely formed. The classical example of Achilles and the Tortoise, instead of serving, as it ought to have served, to show that both these notions were unfounded, and to suggest the simple solution of the sophism, has, by a league between babyhood and pedantry, been held up as a support of the absurdity it ought to have refuted. It is truly astonishing to find that powerful minds, as they seem to be, should be taken in by this silly trick. One can understand that even a Kant should not see precisely how it is that there is no contradiction in an endless series being completed; but that a mind like his should think that a mere definition could arrest the course of real events is amazing. Our wonder is still greater when we find those the whole theme of whose song is that “abstract” ideas have not the life that belongs to "concrete" ideas, boggling over this most abstract of abstractions. An endless series is so called because it cannot be completed by successive additions of units. That does not hinder its being otherwise completed. Achilles runs. We apply a certain method of measuring his run. This does not hamper him. If the method of measurement turns out to be inadequate, it is that which has to be abandonned: Achilles will not stop without some force stops him. Does no glimmer of the light of reality reach the minds of philosophers, that they should imagine it otherwise? Those who deny that an endless series exists take two separate grounds; and still a third might be taken, which stronger than either. Let us examine them in succession. Some go so far as to say that an endless series is a logical impossibility embodying a contradiction. Others admit that in itself it is possible, but that its actualization would involve absurdity. These are the two positions actually taken. The latter is easily refuted. To be possible means no more nor less than to be possibly actual. There is no distinction. Actuality is not a peculiar character which can be in contradiction with another character. Therefore, to say that a hypothesis involves no contradiction and yet that its being true does involve contradiction is to use a phrase to which no meaning can be attached. As a step toward rendering this clear, let us examine two possible objections to it. Namely, it might, in the first place, be objected that to say that a thing is neither black nor not black involves no contradiction; that a horse that is wished for, and not actualized, may be indeterminate as to whether, in its state of being conferred upon it by the desire, that is, in its mere possibility, it shall be black or not black; yet as soon as the desire is fulfilled, and the wished for horse is actualized, it must be either a black horse or a non-black horse. In the second place, it might be objected that if actuality could bring no contradiction with it, to predicate actuality would have no meaning. But we find that, on the contrary, it does mean something, whether it be true or not, to say that Washington might have made himself the emperor of the United States, but that in fact he did not do so. The Emperor Washington involves no contradiction. It is a non-actual possibility. Now add actuality to this, and it would become an actual non-actual possibility, which involves a contradiction in terms. These two objections are as plain, and clear, and bright as snow; but they cannot be handled with melting away like the snow of congealed air. It is true that one can wish for a horse without wishing it to be black nor wishing it not to be black; but one cannot even wish it to be neither black nor non black; and the reason is that this is in conflict with the meaning of negation; for to wish it to be neither black nor not black would be to wish it to be not black and at the same time not not black, which is a flat contradiction. An indeterminate logical possibility is an indeterminate which without developing any contradiction may be determined in one way or another; but if it could not be determined in any way without contradiction resulting, then it cannot with developing a contradiction be determined, that is, it is not logically (5) possible. As to the second objection, a hypothesis may, no doubt, be free from self-contradiction as far as we can see and yet not be true. Thus our Moon may itself have a moon. There seems to be no absurdity in the supposition. A moon’s moon, then, is a logical possibility. But if, as a matter of fact, there is no such thing, it is a non-actual possibility. But what is possible in one state of information is not so in another. The possible is that which in a given state of information is not known not to be true. Logical possibility refers to a state of information in which nothing would be known of positive facts, except so much as is necessary to know the meanings of words and sentences. A man may know what is meant by the Moon and not know that the Moon has itself no moon. In this sense, the Moon’s moon is a possibility. But a man in the same state of complete ignorance will not know that the Moon has a moon, any more than that it has not a moon. It is, therefore, logically possible that the possible Moon’s moon should not be actual. The ignorant logician would not know but that a man who was sufficiently informed would know that there was no Moon’s moon. It is, therefore, logically possible that the possible Moon’s moon should not be actual. But even the ignorant logician knows that no man however sufficiently informed at once knows that there is a Moon’s moon and knows that there is not a Moon’s moon. Thus, it is logically impossible that the same thing should be at once actual and non-actual. But this is no objection to the principle that if anything is logically possible, it is logically possible that it is actual. To say that a thing is logically possible is to say that a good logician, if sufficiently ignorant, may not know it to be non-existent. That is the same as to say that he does not know but that it actually exists. The logical possibility of a thing and the logical possibility of its actually existing are absolutely the same. If you grant that the idea of an endless series involves no absurdity, you grant that the most perfect logician may not know that it does not actually exist; and consequently you grant that there is no absurdity in its actual existence.
Now let us examine the position that an endless series involves a contradiction. To hold that is to hold that however ignorant a man may be, if he can put two and two together he will know that any series is not endless. Certainly, if a man is ignorant enough, he may not know but that there is somewhere written, or about to be written, a series of numbers, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, etc. or in the binary notation 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, 10000, 10001, etc. Now if there is a last one of that series, let that last number be N. The regular law of formation of the series shows how another might be added to it, N + 1. How then is the ignorant man to know that there is any number not followed by another number? Where is the contradiction in the assertion that every number of the series is followed by the number one greater than it? It is plain that there is no particular number which may not be followed by another. How, then, can the ignorant man know that there is a particular number that is not followed by another? Again, is not every number which can be produced by successive additions of one to one possible? Evidently it is. Then all numbers which could be produced by counting are possible. But there is no particular place in the series at which counting must stop. Therefore the numbers that might be produced by counting, all of which are possible, constitute an endless series. Therefore, an endless series is possible. Various difficulties have been suggested; and they might be multiplied indefinitely, since they one and all depend upon assuming that the endless series has an end. For example, there are countless easy ways of proving that if an endless series existed, a part could be as great as the whole. Thus, every number has a double, which is an even number. Consequently, for every number there is a distinct and separate even number, so that the even numbers are just as multitudinous as the whole. But what of it? An infinite part may, of course, be equal to its whole: every thinking man has recognized that from the dawn of thought. When we say that the part is less than its whole, we are using the word ‘whole’ in the sense in which it means a whole whose measurement comes to an end.
The two positions which are commonly held against infinite series are, therefore, untenable; but it might be maintained with some show of reason that the evidence of experience is that, as a matter of fact, there is no endless series. Here we must be upon our guard against what may be called the metaphysician’s fallacy which consists in exaggerating enormously his conclusion, -carrying all the way from somewhat to altogether. The question cannot be profitably discussed in all its length and breadth until the principles of reasoning have been thoroughly considered; but this much we may at once say. We none of us in the least doubt the reality of time. When we come to details, as to just how much and what this reality amounts to, there is room for doubt. But in a general way we do believe that time flows. Now we can certainly say that the natural belief that time and motion are continuous, so that a moving body has an innumerable multitude of positions in any lapse of time, has met with nothing whatever in our experience hitherto to cause us any doubt of it. The vibrations of light could not well be as uniform as they are through many hundreds of thousands of vibrations if this were far from the truth. For if it be not true, the simplest motion must be a most intricate and irregular thing. It cannot be said, then, that experience at all disproves, or tends to disprove, the actuality of infinite multitudes.
(5) … possible. As to the second objection, a hypothesis may (as far as we can see) involve no contradiction, and yet not be true. The substance of such hypothesis, that which is supposed, is in that case possible but not actual.
And an additional page: Topics 13, which reads:
The instantaneously present state of things is, at once, just beginning and just ceasing to be. Now what mode of being is it which evades the principle of contradiction? It is possibility. Understand well that our discourse is restricted to what is possible, and ‘I shall sin’ is true and ‘I shall not sin’ is true. The moderately skilled logician will call such an instance puerile. I myself used to laugh merrily over similar remarks in Hegel. I now say that the regulation logician is both right and wrong. Like the scholastic doctors of the middle ages, when they found themselves entangled in contradicition, the logician says Distinguo, and triumphantly cuts the meshes of the snare. This way of looking at the matter is perfectly legitimate, but so is the other. The truth is there are vicious self-contradictions and innocent self-contradictions. A vicious self-contradiction is one which violates the principle of contradiction; an innocent self-contradiction is one to which the principle of contradiction does not apply.
**[Peirce double sidelined this
paragraph in MS pages 26 and 27 whereas he cross-sided the following: MS page
28(1)] [Nota del T.]
Fin de: "Reason's Rules", Charles S. Peirce (1902). Fuente textual en MS 599.
Una de las ventajas de los textos en formato electrónico respecto de los textos impresos es que pueden corregirse con gran facilidad mediante la colaboración activa de los lectores que adviertan erratas, errores o simplemente mejores traducciones. En este sentido agradeceríamos que se enviaran todas las sugerencias y correcciones a firstname.lastname@example.org
Fecha del documento: 6 abril 2006
Ultima actualización: 11 abril 2006