Jon, list, Today I’d like to get back to your post of 31 March and follow up on some of your comments in your reply to a prior post of mine — just to check my impression that we’re singing the same song, as it were, in this thread:
GF (earlier): The upshot of this, if I understand it, is that a spot of teridentity may be regarded either as a rhema, which is a general concept, or as a denoted individual, which (by definition) is not general, but is identical to the three extremities of the graph of teridentity. JAS: I suggest that a Spot of Teridentity by itself is a Seme for the continuous predicate, "_____ is identical to _____ and to _____"; while a Graph of Teridentity--a Spot of Teridentity with three loose-ended Lines of Identity attached--represents the Proposition, "something is identical to something and to something." GF (now): As Peirce says in the Prolegomena (CP 4.561), “Two lines cannot abut upon the same peg other than a point of teridentity. (The purpose of this rule is to force the recognition of the demonstrable logical truth that the concept of teridentity is not mere identity. It is identity and identity, but this “and” is a distinct concept, and is precisely that of teridentity.)” This distinct concept is of course triadic, and is indecomposable in a way analogous to Thirdness as a type of indecomposable element of the phaneron. One thing that distinguishes it from the dyadic line of identity is that by combining teridentities in various ways, we can produce concepts of any -adicity (as illustrated on EP2:364). We might say that teridentity is the root of plurality, or better, of complexity in systems. My post previous to this one quoted Peirce’s statement that the line of identity should be understood “to be potentially the graph of teridentity by which means there always will virtually be at least one loose end in every graph. In fact, it will not be truly a graph of teridentity but a graph of indefinitely multiple identity” (CP 4.583). One of Peirce’s drafts for that April 1906 address provides some background thinking that leads up to this idea, and brings other logical, semiotic, cognitive and metaphysical dimensions to the explanation of EGs: [[ In this system, every sign, and every complete part of a sign, that is, everything which if it stood alone would be a sign, is of a nature to be fully interpreted in a proposition. We shall see how that perfectly provides for arguments and for names of all kinds. … The signs it represents are signs presented as cognitive, that is as conformed to a real object. By real, I always mean that which is such as it is whatever you or I or any generation of men may opine or otherwise think that it is. There must not be any confusion between reality and exteriority[:] that is real which is as it is no matter what one may think about it. The external is that which is as it is whatever one may think about anything. No doubt there are grades of reality, meaning that objects of signs may yield with more or less resistance to opinion or other representation. According to the definition absolute resistance is essential to reality. But an approach to reality, something that is not in the slightest of the nature of pretense is found wherever an object of thought is sufficiently obstinate to enable us to say, it has not these characters, but it does have these. There is already a lesson in logic. Namely that one may lay down the very best of definitions, going to the very heart of things; and yet there will be, as it were, a little living mouse of a quasi-exception which will find or make a hole to get in when all seemed hermetically closed. This mouse will not be a mere pest to be got rid of and forgotten. It will be a fellow being to be remembered and to be appraised. ] MS 498, Pietarinen transcription published in Synthese (2015) ] That little living mouse is, for me anyway, another metaphor for the “at least one loose end in every graph, and for the mode of being represented in EGs by the potential for the line of identity to be a graph of teridentity or multiple identity. Reality in logic and metaphysics is primarily a matter of “resistance” (Secondness), but cognitive reality is always a matter of Thirdness — Thirdness crucially involving Secondness but allowing for degrees of reality. There’s much more to say about your March 31 post, Jon (and those which followed it), but that’s all I have time for right now. Gary f. From: Jon Alan Schmidt <jonalanschm...@gmail.com> Sent: 31-Mar-19 20:18 To: peirce-l@list.iupui.edu Subject: Re: [PEIRCE-L] Phaneroscopy and logic Gary F., List: …
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