Jeff, list, I’m not sure what you are referring to as “the internal character of the relations.” In terms of the chemical analogy, Peirce is treating the “atoms” as indecomposable (i.e. subatomic physics is irrelevant to the analogy), and saying that the most important way of classifying them is according to their -adicities, i.e. the number of monads they typically combine with to form molecules. But you’re not referring to the internal character of the atoms, or the internal character of the elements of the phaneron, are you?
I assume that the “system of mathematical graphs” you are recommending is different from Peirce’s system of EGs, and from the diagrams on EP2:364, but I’d need to see an example or two in order to see what you mean. Gary f. From: Jeffrey Brian Downard <[email protected] <mailto:[email protected]> > Sent: 26-Mar-19 17:09 To: [email protected] <mailto:[email protected]> Subject: Re: [PEIRCE-L] Phaneroscopy and logic Gary F., List, I'd like to respond to the following claim that Gary F. has offered as part of an interpretation of EP2:363-4: "What this shows is that neither medads nor monads are internally simple, because -adicity is entirely a matter of external relations." While relations that are externally considered medads or monads may be composed of triads, let us ask if the internal character of the relations is essential for understanding the elemental forms of relation. In fact, Peirce argues for the conclusion that there are only three elemental forms of relation in the phenomenology, just as he argues against the conclusion that medads are elemental. The division of what is internal or external as a relation is, I think, one that might be worth more of our attention. For my part, I think that it helps to think about the evolution of relations, and how something that is complex internally may be treated as, say, a dyad or triad in virtue of the relations that are are unsaturated that then become saturated by some process of composition of relations. As we seek greater clarity on this matter, I think it might be helpful to start with nothing more than elemental relations--and then to think of how more complex molecular structures might evolve from combinations of such relations. As we think about the process of evolution, I think it helps to impose some kind of notation to mark what is consider internal and what is external at a given stage in the process of the evolution of relations. In an attempt to clarify matters, I recommend working with a system of mathematical graphs that draw on the three kinds of relations that Peirce takes to be elemental. In doing so, one needs to reconsider some of the assumptions that underlie standard graph theory in which there are two kinds of things: nodes and edges. Instead, following Peirce, we might use a graph theory that takes three kinds of things to be fundamental: elemental monadic relations, elemental dyadic relations, and elemental triadic relations. That, at least, is the approach that I've tried to adopt in my own attempts to get clearer on these matters. --Jeff
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