List: (N.B. 1: This message contains technical arguments that may be incomprehensible to non-technical readers.) (N.B. 2: This message also contains Peircian coinages that may be incomprehensible to non-Peircian readers.)
The scientific origins of the meaning of the unique CSP-created logic terms "decisign" and "legisign" has puzzled me for over a decade. I have a sought to identify the mathematical and scientific concepts which motivated CSP to coin these terms. A recent post searching to find the meaning of the critical CSP coinage, decisign, in a mere crossword puzzle struck me as being unsound as pragmatism is scientifically and mathematically grounded and crossword puzzles are not. Crossword puzzles are linguistically grounded. Knowledge of mathematics is NOT essential to solving a crossword puzzle. So, how do the terms "decisign and legisigns" relate to science and mathematics? Surely, if we understand the deep philosophical tensions underlying the genesis of these two terms, we could apply that understanding to other aspects of CSP's metaphysics, philosophies and their relations to other Peircian coinages. The reasoning (necessary to show that the concept of a crossword puzzle is unsound) motivated a comparison of the three similarities of the associative logics of the indices, rhemata and icons of three sorts of puzzles- the crossword puzzles, the Sudoku puzzles and the chemical puzzles. The arguments used here are constructed about a triadically triadic triad of terms, which could be identified as a sinsign. A Peician 9-fold way? :-) :-) :-) The metaphor of a "cross-word puzzle" for a triadic triad is grossly inadequate because a cross word puzzle only allows one letter in each rhematic blank box. The combinatorial solution of a crossword puzzle, given a clue for the number of letters and the length of each word, is constrained to the choice of any one of 26 letter (symbols) for each open box. The solution of a crossword puzzle depends on a correspondence relations among a large set of correspondence relations among the individual rhematic blanks AND a global coherence for all the choices for rhematic blanks SUCH THAT the entire puzzle is a perfect match between rhematic blanks such that a medad is created. Thus, the crossword puzzle is, from a mathematical perspective (e.g., iconic) a combinatorial puzzle with constraints among the symbol system being restricted to alphabetic symbol system. The count of the combinatorial possibilities for a correct solution of a cross word puzzle is mathematically simple because the number of rhematic blanks is countable and the number of possible symbols for each rhematic blank is countable, that is, 26 in English. A stronger metaphor (at least stronger than the crossword puzzle) for the triadic triad is the Sudoku puzzle. The Sudoku is a stronger metaphor because it is formed (created, generates) by indexes and entails containment of boxes within boxes, such that the puzzle solver must attempt to identify potentially emergent mathematical propositions about number sequences. In summary, a Sudoku puzzle is a problem in combinatorial sequences. The largest box is one object. The 9-subboxes are clearly separate and distinct objects, meeting the Descartian constraint on concept formation. The arrangement of the intermediate size boxes constitute a Peircian triadic triad with three rows and three columns. The solution of Sudoku puzzle requires both coherence among the three rows and three columns. The smallest objects are triadic triads of the intermediate boxes, that is, each of the smallest boxes contains three rows and three columns. The Sudoku puzzle is hierarchical in structure. Thus, in Peircian logical terms, the Sudoku puzzle is a triadically triadic triad which corresponds with the single box of the object as a whole, an intermediate size set of boxes that correspond with the number three squared and the smallest boxes corresponding with the number three cubed. (Thus, the structure of a Sudoku puzzle consists of starting with a single box and partitioning it into smaller boxes and a second partitioning of it into even smaller boxes such that the total number of boxes is extended from 1 to 9 and then to 81.) The puzzle requires coherence and correspondence for each of the 9 smallest boxes such that the coherence and correspondence for the intermediate size boxes and the global box are consistent with the sequences (and sums) of the numbers 1,2,3,4,5,6,7,8, and 9. The solution of a Sudoku puzzle must necessary emerge from the bottom up; each entry in to a box must satisfy mathematical propositions related to fundamental constraints of arranging partitions of number sequences of 1,2,3,4,5,6,7,8, and 9. Several similarities exist between these two forms of combinatorial puzzles. Analogously, the puzzle solver is given a number of clues that provide the logical propositions for solving either puzzle. Like the cross-word, the puzzle solver, the number of clues varies from puzzle to puzzle, thereby creating the potential for an almost unbound number of possible puzzles and possible solutions. But the clues are expressed in different symbol systems. Like the cross word puzzle, the Sudoku puzzle is solved by identifying the propositional clues with a symbol for one or more of the rhematic boxes. But the clues are expressed in different symbol systems, alphabet symbols or numerical symbols. The logical operations for the intrinsic propositions of a crossword puzzle require an interpretation of words as both meaning and letters. In other words, the correct choice of terms are always based on substitution of one meaning for another meaning, in the sense of mathematical substitution of terms. The logical operations for solving the propositions of the Sudoku puzzle are deductive. The medad of every row and every column is the same. The clues are arranged such that each medad of deductive propositions is possible. The number of clues for a Sudoku puzzle is usually from 40 to 15. Given that 81 boxes exist, the solution requires that the puzzle solver need to find a range of mathematical proposition to solve the puzzle, usually from 41 (since 40 +41 = 81) to 66 (since 15 + 66 =81). The Peircian triadic triad can be used as a metaphor for solving the puzzle of the relationships between physical atoms and physical molecules and the vastly more difficult puzzle of the relations between chemical molecules and living cells. The clues for solving the chemical problems are the physical facts related to one-another by physical laws and chemical indices. The mathematical clues are crucial triad, indices, medads as rhemata, and icons and the associated logic of the mathematical symbols. (The concept of an icon associates the visual images of mathematical graphs and chemical graphs.) The crucial clue for the scientific grounding of the chemical puzzle is the physical existence of electrical patterns among chemical indices - a source of both qualisigns and relatonomics. As I noted several months ago on this list, the logic/metaphysical/scientific origins of the triadic triad was successfully resolved. I discussed portions of resolution in my papers (on the logics of the perplex number system) given in Baden-Baden last August. The foundational logic for solving chemical puzzles was previously published in a well-respected mathematics journal (as Ben noted) and was given the name synductive logic to associate with the puzzles of chemical synthesis. Open questions: Are the following hypotheses true or false? "CSP used his knowledge of chemical phenomena to seed the logic of the triadic triad as the foundation for his philosophy of pragmatism." and: "The inquiry into the signs, signals and representations emerging from living systems is grounded in the physics of electricity." Cheers Jerry On Oct 1, 2014, at 12:04 PM, Gary Richmond wrote: > Gary F, lists, > > Gary wrote that in rereading the Speculative Grammar part of the Syllabus > that this struck him: > > GF: that the interpretant of a dicisign or proposition represents the sign > itself as well as its object, and represents it as an index — which, strictly > speaking, lacks the generality which makes the argument a symbol and thus > more genuine. > > I think that your rewording is helpful (but then see the CP 2.293-4 quoted > below which tends to complicate the matter for me); and, further, that your > notion that the reason that Peirce did so much self-rewording was "to get > through to the real, general, genuine Thought that was . . . a piece of the > Truth" and not a more (mere) personal expression of it, makes good sense. I'm > not sure that his re-wordings always made his thinking more transparent, but > often enough they did. > > You also asked why I thought that Peirce's comment that "A proof or genuine > argument is a mental process which is open to logical criticism" > > GR: . . . is in any way incompatible with the notion that the dicisign might > be described as 'degenerate' relative to the argument. > > First, would you say that a 'proof' is but a species of genuine argument? > While it makes a kind of sense to me to say that the dicisign is degenerate > relative to the argument, I wonder if this isn't straining Peirce's > terminology a bit. Perhaps I was thinking that Peirce speaks in places of > degenerate symbols per se. For example: > > . . . while the complete object of a symbol, that is to say, its meaning, is > of the nature of a law, it must denote an individual, and must signify a > character. A genuine symbol is a symbol that has a general meaning. There are > two kinds of degenerate symbols, the Singular Symbol whose Object is an > existent individual, and which signifies only such characters as that > individual may realize; and the Abstract Symbol, whose only Object is a > character. CP 2.293 > > I think the meaning here is fairly clear, that there is one kind of genuine > symbol (one having a "general meaning"--but that would seem to apply to > symbols other than the 'proof' would it not?) and two kinds of degenerate > symbols, the Singular (its object being an individual) and the Abstract (its > object being a character). But in speaking of" the immediate interpretant of > an index," Peirce goes on to say: > > Although the immediate Interpretant of an Index must be an Index, yet > since its Object may be the Object of an Individual [Singular] Symbol, the > Index may have such a Symbol for its indirect Interpretant. Even a genuine > Symbol may be an imperfect Interpretant of it. So an icon may have a > degenerate Index, or an Abstract Symbol, for an indirect Interpretant, and a > genuine Index or Symbol for an imperfect Interpretant. CP 2.294 > > I'm having considerable difficulty parsing this second paragraph, especially > as to how he's using the terms 'imperfect' and 'indirect' (as opposed to > 'intended'?) But it seems to me that it might be important--especially in > getting at the concept of "genuine"--to try to grasp Peirce's meaning here. > > Best, > > Gary R > > > Gary Richmond > Philosophy and Critical Thinking > Communication Studies > LaGuardia College of the City University of New York > C 745 > 718 482-5690 > > On Wed, Oct 1, 2014 at 11:31 AM, Gary Fuhrman <[email protected]> wrote: > Gary R, > > > > Yes, that quote at the end of your post (CP2.231, also EP2:282-3) is worth > reflecting on in this context; but then that’s true of the whole Speculative > Grammar section of the Syllabus. Every time I read part of it, it seems that > another word in the crossword puzzle gets filled in, because of clues I’ve > picked up since the previous reading. This time around, what comes to the > fore is that the interpretant of a dicisign or proposition represents the > sign itself as well as its object, and represents it as an index — which, > strictly speaking, lacks the generality which makes the argument a symbol and > thus more genuine. I’m not making it any more clear than Peirce did, just > rewording it, but that seems to help make the words more transparent, so that > we can see through them to what we’re talking about. Maybe that’s why Peirce > did so much rewording of his own thought — to get through to the real, > general, genuine Thought that was not merely his, and not merely his > momentary brain activity, but a piece of the Truth … > > > > But then I must be missing something too, because I don’t see why Peirce’s > remark that “A proof or genuine argument is a mental process which is open to > logical criticism” is in any way incompatible with the notion that the > dicisign might be described as 'degenerate' relative to the argument. Can you > maybe reword that part of your message? > > > > gary f. > > > > From: Gary Richmond [mailto:[email protected]] > Sent: 30-Sep-14 7:11 PM > To: [email protected] > Cc: Peirce List > Subject: [biosemiotics:7038] Re: Natural Propositions, Chapter 3.3 > > > > Gary, lists, > > > > GF: By shifting the emphasis (in his definition of “fact”) from that > Secondness to its structure — which is that of a proposition or dicisign, and > therefore partakes of Thirdness — I think Peirce was adding another dimension > to the mode of being of “fact”. > > > > I would tend to agree that Peirce did indeed add exactly this new dimension > to the mode of being a fact in his reflections ca. 1904, moving from his late > 19th century emphasis on its existential 2ns to examining its structure as a > dicisign at the beginning of the 20th. > > > > Continuing with our ongoing analysis of genuineness and degeneracy in this > regard, you wrote regarding a passage you quoted (EP2:274): > > > > GF: [That t]his shows at least that genuineness and degeneracy are not > absolute qualities but always relative to a function. So even though Peirce > gave the icon and index the “disparaging name” of “degenerate” in KS, he also > pointed out that they (especially when combined!) can carry out semiotic > functions that the symbol is incapable of except by involving them. > > > > Yes, no doubt mathematical ideas related to degeneracy can help us overcome a > linguistic tendency to think perhaps a bit disparagingly of degeneracy in > semiotic relations when such is not at all Peirce's intent. But this is still > a vexing issue for me. For example, you wrote: > > > > GF: I wonder, too, if the dicisign and the proposition itself can be > described as “degenerate” relative to the argument, which is the most > complete and complex of all sign-types because it separately indicates its > interpretant — and which, for that very reason, can only be a symbol. Is that > the main reason why the symbol is the most genuine member of the first > (icon/index/symbol) trichotomy of signs? > > > > But in looking for telling passages related to "genuine" relations, I came > across this. > > > > A proof or genuine argument is a mental process which is open to logical > criticism. CP 2.26 > > > > Perhaps one needn't make too much of this apparent equivalence of 'proof' and > 'genuine argument', but it does make me abit unsure about your thought that > the dicisign might be "described as 'degenerate' relative to the argument." I > think there may be good reasons to think that that's a pretty good abduction, > but I'm not yet entirely convinced. > > > > At CP 5.76 Peirce refers to the symbol as the "relatively genuine form of > Representamen" in relation to the index and the icon. Again one needn't make > too much of the phrase 'relatively genuine', but I'm not exactly certain now > how much to make of it. Maybe it simply means what we've always taken it to > mean in this context, but why then "relatively"? > > > > As for the 'genuine index' in consideration of the dicisign, although you (or > Frederik?) may have already quoted some of this passage, I found it of the > greatest interest, although I not quite yet sure exactly what to make of it. > > > > . . . Now in analyses hitherto proposed, it seems to have been thought that > if assertion [. . .] were omitted, the proposition would be indistinguishable > from a compound general term--that "A man is tall" would then reduce to "A > tall man." It therefore becomes important to inquire whether the definition > of a Dicisign here found to be applicable to the former [. . .] may not be > equally applicable to the latter. The answer, however, comes forthwith. Fully > to understand and assimilate the symbol "a tall man," it is by no means > requisite to understand it to relate [. . .] to a real Object. Its > Interpretant, therefore, does not represent it as a genuine Index; so that > the definition of the Dicisign does not apply to it. It is impossible here > fully to go into the examination of whether the analysis given does justice > to the distinction between propositions and arguments. But it is easy to see > that the proposition purports to intend to compel its Interpretant to refer > to its real Object, that is represents itself as an Index, while the argument > purports to intend not compulsion but action by means of comprehensible > generals, that is, represents its character to be specially symbolic (CP > 2.321, emphasis added). > > > > I want to spend more time reflecting on this passage in consideration of "the > distinction between propositions and arguments" as it seems to me to be of > potential considerable importance in our reflections on the dicisign. I'll be > interested to hear what you or other members of the lists make of this > quotation. > > > > Best, > > > > Gary > > > > > > > > Gary Richmond > > Philosophy and Critical Thinking > > Communication Studies > > LaGuardia College of the City University of New York > > C 745 > > 718 482-5690 > > > > On Mon, Sep 29, 2014 at 2:53 PM, Gary Fuhrman <[email protected]> wrote: > > Gary R, lists, > > > > This is an extremely helpful post, Gary, and I’m still in the process of > following up on it, but thought I’d better (rather than wait any longer) > mention some of the considerations it inspires with particular reference to > dicisigns. > > > > First, your quote from CP 2.275-276 is originally from the “Speculative > Grammar” section of the Syllabus (EP2:272-3) immediately preceding Peirce’s > introduction of the Dicisign as part of the “second trichotomy of > representamens” (EP2:275). Your next quote, CP 1.539, is from the Lowell > Lectures which the Syllabus was intended to accompany. But your third, CP > 1.480 (about “genuine triads”), is from the “Logic of Mathematics” paper > c.1896. It occurs to me that Peirce’s concept of a fact, or his usage of the > word, may have shifted somewhat during the intervening years. > > > > In “Kaina Stoicheia” (1904?), Peirce wrote that “What we call a “fact” is > something having the structure of a proposition, but supposed to be an > element of the very universe itself.” Earlier on, he wrote that > representation is necessarily triadic because “it involves a sign, or > representamen, of some kind, outward or inward, mediating between an object > and an interpreting thought. Now this is neither a matter of fact, since > thought is general, nor is it a matter of law, since thought is living” (CP > 1.480, emphasis altered). This seems to imply that a “matter of fact” lacks > the generality of “thought”, as if the universe of which it is “supposed to > be an element” is only the universe of existence, i.e. of Secondness. By > shifting the emphasis (in his definition of “fact”) from that Secondness to > its structure — which is that of a proposition or dicisign, and therefore > partakes of Thirdness — I think Peirce was adding another dimension to the > mode of being of “fact”. > > > > But I’m not sure how much sense this makes, yet … I think it’s related to a > some other pieces of the puzzle of the “genuine” which turn up in this > neighborhood. One is that although in KS the index is a degnerate sign, > relative to the symbol, it also seems to be true that the linguistic symbol > at least, if related to its object mainly by reference, involves a degenerate > index: the Index is a “Representamen whose Representative character consists > in its being an individual second. If the Secondness is an existential > relation, the Index is genuine. If the Secondness is a reference, the Index > is degenerate” (EP2:274). This shows at least that genuineness and degeneracy > are not absolute qualities but always relative to a function. So even though > Peirce gave the icon and index the “disparaging name” of “degenerate” in KS, > he also pointed out that they (especially when combined!) can carry out > semiotic functions that the symbol is incapable of except by involving them. > > > > The more we take the concept of “degeneracy” back to its purely mathematical > roots, the less disparaging it appears. For instance, we could describe a > circle as a degenerate ellipse, which only means that it is simpler than an > ellipse. I wonder, too, if the dicisign and the proposition itself can be > described as “degenerate” relative to the argument, which is the most > complete and complex of all sign-types because it separately indicates its > interpretant — and which, for that very reason, can only be a symbol. Is that > the main reason why the symbol is the most genuine member of the first > (icon/index/symbol) trichotomy of signs? > > > > It’s difficult to hold all these pieces of the puzzle in mind long enough to > see how it all fits together, and there’s much in the latter part of your > post that I haven’t dealt with here. But I think the joint effort should be > helpful toward a deeper and more exact understanding of Peirce’s doctrine of > the Dicisign. > > > > gary f. > > From: Gary Richmond [mailto:[email protected]] > Sent: 26-Sep-14 3:51 PM > To: [email protected] > Cc: Peirce List > Subject: Re: [biosemiotics:7008] RE: [PEIRCE-L] Natural Propositions, Chapter > 3.3 > > > > Gary F., lists, > > > > This is a very helpful outline of this section, Gary, which, along with the > next, 3.4, seems to me to be at the heart of this chapter, perhaps even at > the heart of NP itself. I've nothing to add or emend to what you've written, > and so I'll move immediately to your now twice asked and doubly vexing > question: > > > > GF: "if a genuine dicisign or “indexical proposition” does not have to be > symbolic in order to fulfill its function of conveying information, why does > Peirce identify the symbol with the genuine sign?" > > > > You conclude the substantive part of your post by giving Peirce's late > definition of a symbol as “a sign which is fit to serve as such simply > because it will be so interpreted” (EP2:307) then commenting: > > > > GF: "Now, the icon/index/symbol trichotomy is supposed to be the list of > possible relations between sign (representamen) and object. Yet this > definition of symbol, on the face of it, seems to be more about the sign’s > relation with its interpretant than with its object. No wonder the relation > between dicisign and symbol seems so complex. > > > > Now as to the symbol seeming "to be more about the sign's relations with its > interpretant than with its object," I find the following quotation suggestive > (and, in consideration of the representamen, increasingly so as I proceed > down the ensuing group of quotes): > > > > . . . . The most fundamental [division of signs] is into Icons, Indices, and > Symbols. Namely, while no Representamen actually functions as such until it > actually determines an Interpretant, yet it becomes a Representamen as soon > as it is fully capable of doing this; and its Representative Quality is not > necessarily dependent upon its ever actually determining an Interpretant, nor > even upon its actually having an Object (emphasis added). > > An Icon is a Representamen whose Representative Quality is a Firstness > of it as a First. That is, a quality that it has qua thing renders it fit to > be a representamen. Thus, anything is fit to be a Substitute for anything > that it is like. (The conception of "substitute" involves that of a purpose, > and thus of genuine thirdness.) [emphasis added CP 2.275-276] > > > > So the first hint here is that a representamen, while not actually > functioning as such, is indeed one "as soon as it is fully capable of > [determining an interpretant]. So, an icon is serving as a representamen when > it merely may substitute for something which it's like, AND the idea of > substitution involves that of purpose, "and thus of genuine thirdness." > > > > But stepping back a bit from signs to categorial thirdness itself, Peirce > writes something telling here in suggesting that logic perhaps "ought to be > the science of Thridness in general": > > > > 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 (CP 1.539). > > > > But philosophy is the work of human minds. Yet, since thirdness involves > secondness and firstness, and since anything which involves the idea of > "purpose" (even the icon as the likeness of something) expresses "genuine > thirdness" (CP2.276), it would seem that to the extent that the dicisign > expresses purpose (which I think it clearly does) it expresses thirdness even > when it is not the symbolic variety of that sign. > > > > Peirce also comments on "genuine triads" in a way which might be pertinent to > this inquiry. He begins the next passage with language seemingly > contradicting that which he used directly above--but note the conclusion of > the passage). > > > > Genuine triads are of three kinds. For while a triad if genuine cannot > be in the world of quality nor in that of fact, yet it may be a mere law, or > regularity, of quality or of fact. But a thoroughly genuine triad is > separated entirely from those worlds and exists in the universe of > representations. Indeed, representation necessarily involves a genuine triad. > For it involves a sign, or representamen, of some kind, outward or inward, > mediating between an object and an interpreting thought. Now this is neither > a matter of fact, since thought is general, nor is it a matter of law, since > thought is living (CP 1.480, emphasis added). > > > > So, every genuine triad "[involving] a sign, or representamen, o > > f > > some kind, outward or inward" (even the now near proverbial “sunflower") has > the potential to become a living thought (see CP 2.276 above). So the idea of > genuine thirdness, the genuine triad, may trump , in certain cases, the idea > of the genuine sign, which is to say the sign completed in its being > interpreted, that is, the symbol. > > So, as the following quote concludes, "take away the psychological or > accidental human element, and in this genuine Thirdness we see the operation > of a sign,” and 'philosophy' as such has nothing to do with it. > > > > > > 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 role of a Secondness, or event. That > is, it is of the general nature of experience or information. The third is > thought in its role 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 (CP1.537). > > > > So, whether or not it is possible that "logic ought to be the science of > Thirdness in general," for me the dicisign concept suggests that this idea > might have some resonance in biosemiotics, or perhaps that semiotics > generally ought be tempered by this idea (or something like it). > > > > Finally, Peirce makes a distinction which may make a difference in this > direction of analysis by defining a sign as "anything which conveys any > definite notion of any object in any way": > > > > . . . 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. [. . . ] All signs convey notions to human minds; but I know no reason > why every representamen should do so (CP1.540, emphasis added). > > > > And this is immediately followed by the following famous definition (which, > note in the context of what I just quoted, is a definition of a representamen > and not of a sign): > > > > 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 (CP1.541). > > > > I am not prepared to draw any definitive conclusions from the above which are > just some preliminary thoughts I had today. In short, I offer these quotes > and comments as suggestions towards a possible answer to the intriguing > question you asked, Gary. For all I know I may be heading in the wrong > direction. > > > > Best, > > > > Gary > > > > > > > > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] > . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] > with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at > http://www.cspeirce.com/peirce-l/peirce-l.htm . > > > >
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