Hi Gary F, Thank you very much. I read it once, but I am afraid I will need more than one reading to really understand what Peirce was trying to say.
All the best. Sung On Fri, Dec 18, 2015 at 5:54 PM, <g...@gnusystems.ca> wrote: > NDTR is an acronym for “Nomenclature and Divisions of Triadic Relations,” > EP2:289-99, fifth section of the 1903 Syllabus, and the main text this > thread has been referring to, so far. > > > > Since I included in my post a few quotes from MS 7, which we discussed at > some length back in the spring of 2014, I’ll post my transcription of the > manuscript here (from a photocopy of it posted to the list by Vinicius > Romanini, I think). It’s an interesting text because it prefigures (or > refigures?) many of the things Peirce says about signs in “New Elements,” > which follows immediately after NDTR in EP2. The lack of paragraphing is > Peirce’s. — gary f. > > > > *On the Foundations of Mathematics* > > *MS 7, c. 1903 [gf transcription, 4 Apr 2014, Peirce's underlining > rendered as italics] * > > §1. Mathematics deals essentially with *Signs*. All that we know or think > is so known or thought by signs, and our knowledge itself is a sign. The > word and idea of a sign is familiar but it is indistinct. Let us endeavor > to analyze it. > > It is plain at the outset, first, that a sign is not any particular > *replica* of it. If one casts one's eye down a printed page, every ‘the’ > is the same word, and every e the same letter. The exact identity is not > clear. Secondly, a sign may be complex; and the parts of a sign, though > they are signs, may not possess all the essential characters of a more > complete sign. Thirdly, a sign sufficiently complete must be capable of > determining an *interpretant* sign, and must be capable of ultimately > producing real results. For a proposition of metaphysics which could never > contribute to the determination of conduct would be meaningless jargon. On > the other hand, the cards which, slipped into a Jacquard loom, cause > appropriate figures to be woven, may very properly be called signs although > there is no conscious interpretation of them. If not, it can only be > because they are not interpreted by signs. In fact, in the present > condition of philosophy, consciousness seems to be a mere quality of > feeling which a formal science will do best to leave out of account. But a > sign only functions as a sign when it is interpreted. It is therefore > essential that it should be capable of determining an interpretant sign. > Fourthly, a sign sufficiently complete must in some sense correspond to a > real object. A sign cannot even be false unless, with some degree of > definiteness, it specifies the real object of which it is false. That the > sign itself is not a definite real object has been pointed out under > “firstly”. It is only *represented*. Now either it must be that it is one > thing to *really be* and another to *be represented*, or else it must be > that there is no such thing [a]s *falsity*. This involves no denial that > every real thing may be a representation, or sign, but merely that, if so, > there must be something more in reality than mere representation. Since a > sufficiently complete sign may be false, and also since it is not any > replica or collection of replicas, it is not real. But it refers to a real > *object*. Consequently, a sign cannot have a sign as its sole object; > though it may refer to an object through a sign; as if one should say, > “Whatever the Pope, as such, may declare will be true,” or as a map may be > a map of itself. But supposing the Pope not to declare anything, does that > proposition refer to any real object? Yes, to the Pope. But, *fifthly*, > even if there were no pope, still, like all other signs sufficiently > complete, there is a single definite object to which it must refer; namely, > to the ‘Truth,’ or the Absolute, or the entire Universe of real being. > *Sixthly*, a sign may refer, in addition, and specially, to any number of > parts of that universe. *Seventhly*, every interpretant of a sign need > not refer to all the real objects to which the sign itself refers, but > must, at least, refer to the Truth. *Eighthly*, an interpretant may refer > to an object of its sign in an *indefinite* manner. Thus, given the sign, > ‘Enoch was a man, and Enoch was translated,’ an interpretant of it would be > ‘Some man was translated.’ *Ninethly*, a sign may refer to its > interpretant in such a way that, in case the former sign is incomplete, the > interpretant, being an interpretant of the completer sign, may refer to a > sign to which the first sign does not specially refer, but only > *generally* refers. Thus, the sign ‘Any man there may be is mortal’ does > not refer to any real man, unless it so happens that it is a part of a sign > which otherwise refers to such a real thing. But if it be a part of a sign > of which another part is ‘some man sings,’ the sign ‘some man is mortal’ > becomes an interpretant of it. This may be more conveniently expressed by > speaking of an ‘utterer’ and an ‘interpreter.’ Then the utterer says to the > interpreter, “you are at liberty to understand me as referring to any man > [of] whom you can get any indication, and of him, I say, ‘he is mortal.’” > Tenthly, a sign sufficiently complete must signify some quality; and it is > no more important to recognize that the real object to which a sign refers > is not a mere sign than to recognize that the quality it signifies is not a > mere sign. Take the quality of the odor of attar. There is no difficulty in > imagining a being whose entire consciousness should consist in this alone. > But, it may be objected, if it were contrasted with nothing could it be > recognized? I reply, no; and besides, such recognition is excluded by the > circumstance that a recognition of the smell would not be the pure smell > itself. It may be doubted by some persons, however, whether the feeling > could exist alone. They are the persons whom it ought to be easiest for me > to convince of my point. For they, at least, must admit that *if such > pure homogeneous quality of feeling were to exist alone*, it would not be > a sign. Everybody ought to admit it because it would be alone, and > therefore would have no object different from itself. Besides, there would > be no possible replica of it, since each of two such things would be > nonexistent for the other; nor could there be any third who should compare > them. So, then, the whole question of whether such a quality is a sign or > not resolves itself into the question of whether there could be such a > tinge upon the consciousness of a being, supposing the being could be > conscious (for I shall show presently that the fact that he would be asleep > is only in my favor). In order to decide this question, it will be > sufficient to look at any object parti-colored in bright red and bright > blue and to ask oneself a question or two. Would there be any possibility > of conveying the idea of that red to a person who had no feeling nearer to > it than that blue? Plainly not, the quality of the red is in the red > itself. The proximity of the blue heightens the shock up[on] the seer[']s > organism, emphasizes it, renders it vivid, perhaps slightly confuses the > feeling. But the red quality is altogether positive and would remain if the > blue were not there. If every other idea were removed, there would be no > shock, and there would be sleep. But the quality of that sleep would be > red, in this sense, that if it were taken away frequently and brought back > so as to wake the being up, the tinge of his consciousness would be of that > quality. A quality, in itself, has no being at all, it is true. It must be > embodied in something that exists. But the quality is as it is positively > and in itself. That is not true of a sign, which exists only by bringing an > interpretant to refer to an object. A quality, then, is not a sign. > *Eleventhly*, we may assume that this is as true of what is, with > excusable inaccuracy, called a composite quality as of a simple one. In > itself, one quality is as simple as another. A person who should be > acquainted with none but the spectral colors would get no idea of white by > being told that it was the mixture of them all. One might as well tell him > to make a mixture of water, patriotism, and the square root of minus one. > Find a man who has had no idea of patriotism; and if you tell him that it > is the love of one's country, if he knows what love is, and what a man's > country, in its social sense, is, he can make the experiment of connecting > ideas in his imagination, and noting the quality of feeling which arises > upon this composition. Tell him this in the evening, and he will repeat the > experiment several times during the night, and in the morning he will have > a fair idea of what patriotism means. He will have performed an experiment > analogous to that of mixing colored lights in order to get an idea of > white. If a treasure is buried in the midst of a plain, and there are four > signal poles, the place of the treasure can be defined by means of ranges, > so that a person who can take ranges and set up new poles can find the > treasure. In like manner the name of any color may be defined in terms of > four color disks so that a person with a color-wheel can experimentally > produce the color and thereafter be able to use the name. Every definition > to be understood must be treated as a precept for experimentation. The > imagination is an apparatus for such experimentation that often answers the > purpose, although it often proves insufficient. No point on the plain where > the treasure is hid is more simple than other. Colors may be defined by > various systems of coördinates, and we do not know that one color is in > itself simpler than another. It is only in a limited class of cases that we > can define a quality as simply a mixture of two qualities. In most cases, > it is necessary to introduce other relations. But even when that is the > case, if a quality is defined as being at once *a* and *b*, there will > always be another way of defining it as that which is at once *c* and *d*. > Now all that is either *a* or *c* will have a certain quality *p*, common > and peculiar to that class; the class of possible objects that are *b* or > *c* will be similarly related to a quality, *r*; and the class of > possible objects that are either *b* or *d* will be similarly related to > a quality, *s*. Then that quality which was defined as, at once, *a* and > *b*, can be more analytically defined as that which is at once *p, q, r,* > and *s*; and so on *ad infinitum*. We may not be able to make out these > qualities; but there is reason to believe that any describable class of > possible objects has some quality common and peculiar to it. It is certain > that a pure quality, in its mode of being as a pure quality, does not cease > to be because it is not embodied in anything. Every situation in life > appears to have its peculiar flavor. This flavor is what it is positively > and in itself. For the experiment by which it may be reproduced an adequate > prescription may be given; but the definition will not itself have that > flavor. To say that a flavor, or pure quality, is composed of two others, > is simply to say that on experimentally mixing these others in a particular > way, that first flavor will be reproduced. Every sufficiently complete sign > determines a sign to the effect that on a certain occasion, that is, in a > certain object a certain flavor or quality may be observed. > > This attempt to begin an analysis of the nature of a sign may seem to be > unnecessarily complicated, unnatural, and ill-fitting. To that I reply that > every man has his own fashion of thinking; and if such is the reader's > impression let him draw up a statement for himself. If it is sufficiently > full and accurate, he will find that it differs from mine chiefly in its > nomenclature and arrangement. [Not unlikely he might insist on distinctions > which I avoid as irrelevant.] He will find that, in some shape, he is > brought to recognize the same three radically different elements that I do. > Namely, he must recognize, first, a mode of being in itself, corresponding > to my *quality*; secondly, a mode of being constituted by opposition, > corresponding to my *object*; and thirdly, a mode of being of which a > branching line Y is an analogue, and which is of the general nature of a > mean function corresponding to the sign. > > §2. Partly in hopes of reconciling the reader to my statement, and partly > in order to bring out some other points that will be pertinent, I will > review the matter in another order. > > The reference of a sign to the quality which is its *ground*, reason, or > *meaning* appears most prominently in a kind of sign of which any replica > is fitted to be a sign by virtue of possessing in itself certain qualities > which it would equally possess if the interpretant and the object did not > exist at all. Of course, in such case, the sign could not be a sign; but as > far as the sign itself went, it would be all that [it] would be with the > object and interpretant. Such a sign whose significance lies in the > qualities of its replicas in themselves is an *icon*, image, analogue, or > copy. Its object is whatever that resembles it its interpretant takes it to > be the sign of, and [it is a] sign of that object in proportion as it > resembles it. An icon cannot be a complete sign; but it is the only sign > which directly brings the interpretant to close quarters with the meaning; > and for that reason it is the kind of sign with which the mathematician > works. For not only are geometrical figures icons, but even algebraical > arrays of letters have relations analogous to those of the forms they > represent, although these relations are not altogether iconically > represented. > > The reference of a sign to its object is brought into special prominence > in a kind of sign whose fitness to be a sign is due to its being in a real > reactive relation,—generally, a physical and dynamical relation,—with the > object. Such a sign I term an *index*. As an example, take a > weather-cock. This is a sign of the wind because the wind actively moves > it. It faces in the very direction from which the wind blows. In so far as > it does that, it involves an icon. The wind forces it to be an icon. A > photograph which is compelled by optical laws to be an *icon* of its > object which is before the camera is another example. It is in this way > that these indices convey information. They are *propositions*. That is > they separately indicate their objects; the weather-cock because it turns > with the wind and is known by its interpretant to do so; the photograph for > a like reason. If the weathercock sticks and fails to turn, or if the > camera lens is bad, the one or the other will be *false*. But if this is > known to be the case, they sink at once to mere icons, at best. It is not > essential to an index that it should thus involve an icon. Only, if it does > not, it will convey no information. A cry of “Oh!” may be a direct reaction > from a remarkable situation. But it will convey, perhaps, no further > information. The letters in a geometrical figure are good illustrations of > pure indices not involving any icon, that is they do not force anything to > be an icon of their object. The cry “Oh!” does to a slight degree; since it > has the same startling quality as the situation that compells it. The index > acts compulsively on the interpretant and puts it into a direct and real > relation with the object, which is necessarily an individual event (or, > more loosely, a thing) that is *hic et nunc*, single and definite. > > A third kind of sign, which brings the reference to an interpretant into > prominence, is one which is fit to be a sign, not at all because of any > particular analogy with the quality it signifies, nor because it stands in > any reactive relation with its object, but simply and solely because it > will be interpreted to be a sign. I call such a sign a *symbol*. As an > example of a symbol, Goethe's book on the Theory of Colors will serve. This > is made up of letters, words, sentences, paragraphs etc.; and the cause of > its referring to colors and attributing to colors the quality it does is > that so it is understood by anybody who reads it. It not only determines an > interpretant, but it shows very explicitly the special determinant, (the > acceptance of the theory) which it is intended to determine. By virtue of > thus specially showing its intended interpretant (out of thousands of > possible interpretants of it) it is an *argument*. An index may be, in > one sense, an argument; but not in the sense here meant, that of an > *argumentation*. It determines such interpretant as it may, without > manifesting a special intention of determining a particular interpretant. > It is a perfection of a symbol, if it does this; but it is not essential to > a symbol that it should do so. Erase the conclusion of an argumentation and > it becomes a proposition (usually, a copulative proposition). Erase such a > part of a proposition that if a proper name were inserted in the blank, or > if several proper names were inserted in the several blanks, and it becomes > a rhema, or term. Thus, the following are *rhematic*: > > Guiteau assassinated ______ > ______ assassinated ______ > > Logicians generally would consider it quite wrong for me to call these > *terms*; but I shall venture to do so. > > > > *From:* sji.confor...@gmail.com [mailto:sji.confor...@gmail.com] *On > Behalf Of *Sungchul Ji > *Sent:* 18-Dec-15 16:22 > > Gary F, Jeff, List, > > > > Please excuse my ignorance. > > What is NDTR ? > > > > Thanks in advance. > > > > Sung > > > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to > peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L > but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the > BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm > . > > > > > > -- Sungchul Ji, Ph.D. Associate Professor of Pharmacology and Toxicology Department of Pharmacology and Toxicology Ernest Mario School of Pharmacy Rutgers University Piscataway, N.J. 08855 732-445-4701 www.conformon.net
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