Howard, Thanks to Jon A. for taking up your question from the mathematical side (much more effectively than i could). If i were to point to a Peirce text that deals directly with your question, it would be EP2:169-77 (1903), but it's only helpful if you follow the argument step by step, diagrams and all. CP 1.345-7 is much more concise but less mathematical and "leaves the matter to your own reflection", so is unlikely to inform you if your focus is on graph theory. Its argument is in terms of Peirce's existential graphs, not mathematical graph theory.
But since we're looking into this in a broader logical/semiotic context, i think we need to approach it from the "Phenomenological" side as well, as Peirce does in his Syllabus section on Triadic Relations (EP2:289-299, which defines the famous ten classes of signs). This approach (in stark contrast to Edwina's) is very tentative both conceptually and terminologically, as you can see from the first two pages of it, introducing "the most important class of triadic relations, those of signs, or representamens, to their objects and interpretants." I would recommend at least one careful reading of those pages before resorting to second-hand versions of Peirce's views on triadic relations. The one comment i'll make is that any *explicit* two-dimensional diagram of an *actual* triadic relation has to omit the element of time which is essential any such actual relation, and trust the interpreter to read that element back into it (by decoding symbols). This is why Peirce emphasized that one needs a *connected sequence* of graph-instances in order to represent *iconically* the process of reasoning or of semiosis, which obviously takes time because it involves change. That's why he referred to his existential graphs as "moving pictures of thought." gary f. -----Original Message----- From: Howard Pattee [mailto:[email protected]] Sent: 16-Dec-14 8:58 PM At 02:07 PM 12/16/2014, Gary Fuhrman wrote: > The reason that "people keep saying you [Edwina] support dyads" is > that your three "relations" have only two "members" each, to use > Peirce's term. A triadic relation has three members, not two; and a > complexus of three dyadic (two-member) relations is not, according to > Peirce, "a triadic relation." All these claims are unclear to me. Why are these two descriptions inconsistent? Is there a graph theory representation of a triadic relation that does not have a dyadic subgraph? Howard
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