OK, thanks, Jerry. I don’t disagree. It may well be worthwhile to look at metalanguage to understand further what is going on in the process of hypostatic abstraction. I would want to look at the difference in how something is represented and what it is, as I suggested in my response below. This itself involves semiotics, of course, giving the issue an involuted*, but that makes it complex in Robert Rosen’s sense of involving irreducible impredicatiivity (Essays on Life Itself). It would follow that it can’t be dealt with fully in 1st order logic. My suggestion (below) was to go to 2nd order logic (which quantifies over properties), following Ramsey’s method (used in structural realism and some other forms of structuralism), but this has known problems itself. Perhaps the basic problem is that 2nd order logic is incomplete, and thus impredicative. The bump in the rug doesn’t go away easily.
I suspect that there is no way to deal with it fully, but I think it is still helpful to think of the grammar of semiotic properties in terms of relations by using Peirce’s hypostatic abstraction. Switching back and forth can help to get past the issues of the particular language, which are not essential to the subject. As for any possible application to the logic of chemistry, that is outside of my areas of expertise, but I would guess that shifting back and forth between chemical properties and relations via hypostatic abstraction might be informative by eliminating some accidents of representation system. That is just a guess on my part, though. *From the Free Dictionary: 1. a. The act of involving. b. The state of being involved. 2. Intricacy; complexity. 3. Something, such as a long grammatical construction, that is intricate or complex. John Collier Professor Emeritus, UKZN http://web.ncf.ca/collier From: Jerry LR Chandler [mailto:jerry_lr_chand...@icloud.com] Sent: Tuesday, 05 January 2016 6:07 AM To: John Collier; Peirce List Subject: RE: [PEIRCE-L] RE: signs, correlates, and triadic relations - meta-languages and propositions of triadicity John, List: My response follows the original message ----- Original Message ----- From: John Collier To: Jerry LR Chandler ; Peirce List Cc: Gary Richmond Sent: Monday, December 28, 2015 5:41 PM Subject: RE: [PEIRCE-L] RE: signs, correlates, and triadic relations - meta-languages and propositions of triadicity All I can say, Jerry, is to read it more carefully. There are no contradictions, so you must be misreading what I said. I have no idea why you relate what I said to Tarski’s views, with which I am quite familiar. The move that I think lies behind the connection between the triadic relations of the sign and the relations that I think Edwina is talking about is hypostatic abstraction, which is a technical device for reinterpreting a property as a relation. Other than that, I was trying to get how the two implied relations to the representamen become three, and it seemed to me that that the third is on a more abstract level, a relation of relations, again, and perhaps even more obviously if I am right about that, though Edwina seems to differ than the relations it relates. The third relation I am referring to seems to me to be the relation between the object the interpretant. The object and interpretant are properties (despite the grammatical nominatives used to refer to them), which are turned into relations by the abstraction, which is a standard method for understanding things, especially for semiotic vehicles, in Peirce’s work. Taken this way there is a sense in which I am suggesting that it is “meta”, but so are the relations related, as they also are grasped through hypostatic abstraction. If there is an apparent inconsistency I am pretty sure that it arise from not understanding and being able to recognize hypostatic abstraction, and confusing the way in which something is picked out with its essential nature. The same thing can be both a property and a relation, depending on how we look at it. This is not possible to represent in the language of first order logic due to its formal limitations. Second order logic makes the possible, e.g., in the Ramsification of theories (which basically replaces properties with relational structures). Ramsey tried to get a logic grounded solely in relations, but he was unsuccessful. I have little hope of doing what Ramsey failed to do despite his being one of the most insightful logicians of the first half of the last century, so I did not try, and I won’t try now, either. But I will say that Peirce’s hypostatic abstraction is probably the key. Tarski’s satisfaction notion of truth, though it fits nicely with Ramsey’s work on the nature of theories and their reference, doesn’t need hypostatic abstraction to be stated. “Snow is white” is true if and only if snow is white involves only properties. Unless, like Frege, one thinks that to be true is a relation between a proposition and the True, which goes a good deal further, and may involve hypostatic abstraction. But it is late and I am not going to think that through right now. John Collier Professor Emeritus, UKZN http://web.ncf.ca/collier After considering your post, I would withdraw my assertion about about contradictions. It was a poor choice of terms. My concern, however, remains vital. That is, what are the forms of logic associated with the notion of “relation”. In this regard, Tarski’s notion of truth is not a substantial issue for me. It is Tarski’s assertion that a meta-language is necessary to associate a truth in one logic with another. This is one approach to creating a sense of congruency among forms of logic. Tarski’s “meta-language” hypothesis is stronger than CSP’s notion of “hypostatic abstraction” and is well differentiated from the notion of degeneracy in either lines-cones or QM orbital arrangements. The logic of chemistry is not a first order logic so that is not my concern. Cheers Jerry
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