Mary, Edwina, Gary R, list,
Getting back to Mary's question, I dug out my copy of The Meaning of Meaning, and found no triangle diagram in it; the brief summary of Peirce's work in the Appendix contains no diagram at all. So I don't know where that diagram started its career, except that it wasn't with Peirce. But then the three-spoke diagram of the "semiosic triad" (as Edwina calls it) didn't start with Peirce either. Edwina's given us a very free translation of what Peirce says in Lowell 3.4 (aka CP 1.347), and I'd like to direct attention back to what Peirce actually said (included below, diagrams and all). Peirce does give a little diagram of "a node connecting three lines of identity": . This is what he elsewhere calls a "point of teridentity," which is entirely different from a "spot with three tails" (it's not a spot at all). He uses both diagrams, in different ways, to prove (or rather "sketch a proof" of) the irreducibility of Thirdness, which he refers to here as "Meaning," which "is obviously a triadic relation." (At least, that should be obvious to any student of the logic of relations.) To establish the truth of his first premiss, "that every genuine triadic relation involves meaning," he asks us to take "any fact in physics of the triadic kind." It's clear enough that "Three things, east, west, and up, are required to define the difference between right and left"; but his reference to the chemistry of "active substances" is not very clear, at least to me. Maybe some of the chemists on the list can comment on that. The relation of "giving," which he also uses elsewhere as an exemplary triadic relation, would be represented by a "spot with three tails," because "giving" is a triadic rheme, a predicate which requires three subjects. But it's the "other premiss of the argument" - "that genuine triadic relations can never be built of dyadic relations and of Qualities" - that Peirce elects to illustrate with Existential Graphs, and in two different ways. First, you can't make a triadic rheme by joining the tails of two (or more) dyadic spots; that would just give you two dyadic rhemes (or a chain of them, which is still dyadic. Second, you do have a triadic relation if three lines of identity are joined at a spot of teridentity. This is what would occur in the transformations of a sequence of beta graphs that would diagram the series of events Peirce narrates, leading to the conclusion: "On Wednesday I see a man and I say, "That is the same man I saw on Tuesday, and consequently is the same I saw on Monday. There is a recognition of triadic identity; but it is only brought about as a conclusion from two premisses, which is itself a triadic relation." The key word that makes this a triadic relation is "consequently"; the whole sequence is an argument, or inference, which is unquestionably triadic. And of course an argument is a sign - a sign which cannot be fully represented by a single existential graph, but only by a sequence of them. Semiosis takes time. Then, as an "interesting" afterthought, Peirce adds that while no "complexus of dyadic relations" (as he put it in the Syllabus) can constitute a genuine triadic relation, a complexus of triadic relations can give you any higher -adicity - the point being, again, that Thirdness is an irreducible element but there is no irreducible Fourthness. This brings us back to Phenomenology, with perhaps a deeper understanding of its mathematical aspect. As for semiotics, there is no diagram here of the triad object-sign-interpretant. If someone can point to such a diagram anywhere in Peirce's writings (either triangular or three-spoked), I will thank them profusely, for refuting my claim that neither of those diagramming habits started with Peirce. Gary f. From: g...@gnusystems.ca [mailto:g...@gnusystems.ca] Sent: 12-Dec-17 07:01 To: peirce-l@list.iupui.edu Subject: [PEIRCE-L] Lowell Lecture 3.4 Continuing from Lowell Lecture 3.3, https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-464-465-1903-low ell-lecture-iii-3rd-draught/display/13884 I will sketch a proof that the idea of Meaning is irreducible to those of Quality and Reaction. It depends on two main premisses. The first is that every genuine triadic relation involves meaning, as meaning is obviously a triadic relation. The second is that a triadic relation is inexpressible by means of dyadic relations alone. Considerable reflexion may be required to convince yourself of the first of these premisses, that every triadic relation involves meaning. There will be two lines of inquiry. First, all physical forces appear to subsist between pairs of particles. This was assumed by Helmholtz in his original paper on the Conservation of Forces. Take any fact in physics of the triadic kind, by which I mean a fact which can only be defined by simultaneous reference to three things, and you will find there is ample evidence that it never was produced by the action of forces on mere dyadic conditions. Thus, your right hand is that hand which is toward the east, when you face the north with your head toward the zenith. Three things, east, west, and up, are required to define the difference between right and left. Consequently chemists find that those substances which rotate the plane of polarization to the right or left can only be produced from such active substances. They are all of such complex constitution that they cannot have existed when the earth was very hot, and how the first one was produced is a puzzle. It cannot have been by the action of brute forces. For the second branch of the inquiry, you must train yourself to the analysis of relations, beginning with such as are very markedly triadic, gradually going on to others. In that way, you will convince yourself thoroughly that every genuine triadic relation involves thought or meaning. Take, for example, the relation of giving. A gives B to C. This does not consist in A's throwing B away and its accidentally hitting C, like the date-stone, which hit the Jinnee in the eye. If that were all, it would not be a genuine triadic relation, but merely one dyadic relation followed by another. There need be no motion of the thing given. Giving is a transfer of the right of property. Now right is a matter of law, and law is a matter of thought and meaning. I there leave the matter to your own reflection, merely adding that, though I have inserted the word "genuine," yet I do not really think that necessary. I think even degenerate triadic relations involve something like thought. The other premiss of the argument that genuine triadic relations can never be built of dyadic relations and of Qualities is easily shown. In Existential Graphs, a spot with one tail -X represents a quality, a spot with two tails -R- a dyadic relation. Joining the ends of two tails is also a dyadic relation. But you can never by such joining make a graph with three tails. You may think that a node connecting three lines of identity is not a triadic idea. But analysis will show that it is so. I see a man on Monday. On Tuesday I see a man, and I exclaim, "Why, that is the very man I saw on Monday." We may say, with sufficient accuracy, that I directly experienced the identity. On Wednesday I see a man and I say, "That is the same man I saw on Tuesday, and consequently is the same I saw on Monday." There is a recognition of triadic identity; but it is only brought about as a conclusion from two premisses, which is itself a triadic relation. If I see two men at once, I cannot by any such direct experience identify both of them with a man I saw before. I can only identify them if I regard them, not as the very same, but as two different manifestations of the same man. But the idea of manifestation is the idea of a sign. Now a sign is something, A, which denotes some fact or object, B, to some interpretant thought, C. 347. It is interesting to remark that while a graph with three tails cannot be made out of graphs each with two or one tail, yet combinations of graphs of three tails each will suffice to build graphs with every higher number of tails. And analysis will show that every relation which is tetradic, pentadic, or of any greater number of correlates is nothing but a compound of triadic relations. It is therefore not surprising to find that beyond these three elements of Firstness, Secondness, and Thirdness, there is nothing else to be found in the phenomenon. http://gnusystems.ca/Lowell3.htm }{ Peirce's Lowell Lectures of 1903
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