Helmut, List ... Here are links to my blog rehashes of the last few exchanges on this thread:
https://inquiryintoinquiry.com/2017/04/16/icon-index-symbol-%e2%80%a2-7/ https://inquiryintoinquiry.com/2017/04/17/icon-index-symbol-%e2%80%a2-8/ https://inquiryintoinquiry.com/2017/04/24/icon-index-symbol-%e2%80%a2-9/ https://inquiryintoinquiry.com/2017/04/25/icon-index-symbol-%e2%80%a2-10/ https://inquiryintoinquiry.com/2017/04/27/icon-index-symbol-%e2%80%a2-11/ Turning now to your next point: HR: > Example: The triadic function “x_1 + x_2 = x_3”, with the > three sets X_1, X_2, X_3 not being classes of any kind, > at least not of the special kind (whatever that is), > that would allow representation, and make it having > to do with the third category. Mathematics is rife with examples of triadic relations having all three relational domains the same. For instance, the binary operation “+” in “x_1 + x_2 = x_3” is associated with a function fun[+] such that fun[+] : X × X → X and also with a triadic relation rel[+] such that rel[+] ⊆ X × X × X. Semiotics, by contrast, tends to deal with relational domains O, S, I where the objects in O are distinct in kind from the signs in S and the interpretant signs in I. As far as S and I go, it is usually convenient to lump them all into one big set S = I, even if we have to partition that set into distinct kinds, say, mental concepts and verbal symbols, or signs from different languages. But even if it's how things tend to work out in practice, as we currently practice it, there does not seem to be anything in Peirce's most general definition of a sign relation to prevent all the relational domains from being the same. So I'll leave that open for now. Regards, Jon On 4/21/2017 4:59 PM, Helmut Raulien wrote: > Jon, List, > I am not so sure, if thirdness is about any triadic relation. > The categories in Peirce's "new list" of them are quality, relation, > representation. Maybe "representation" is a very special kind of > triadic relation. A simple triadic or n-adic relation, I think, > belongs to secondness, and has only two modes, the quality, eg. > function or caprice (intension), and the resulting set of tuples > (extension). Example: The triadic function "x_1 + x_2 = x_3", > with the three sets X_1, X_2, X_3 not being classes of any kind, > at least not of the special kind (whatever that is), that would > allow representation, and make it having to do with the third > category. I guess, that a difference between Peirce's relation > theory, and his semiotics and category theory, is, that the > first is about all triadic relations, and the latter only > about sign relations or representational relations (the > special kind of triadic relations). > Best, > Helmut -- inquiry into inquiry: https://inquiryintoinquiry.com/ academia: https://independent.academia.edu/JonAwbrey oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey isw: http://intersci.ss.uci.edu/wiki/index.php/JLA facebook page: https://www.facebook.com/JonnyCache
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