Ben, List, I believe that a weaker is required for an ordered triple. Any finite set can be ordered. The Axiom of Choice, which is controversial, implies that any set including infinite ones can be ordered. The order need not be anything like 'more' or 'less' in any intuitive sense. For example in a function, like f=ma, <m,a> is an ordered pair, one from one domain and another from another domain such that their product is in another domain which is the range of the function. Obviously, under the Newtonian interpretation m and a are not either more or less than the other in any intuitive (or even nondegenerate) sense. I think that this is worth remembering when thinking of Peircean triads in particular. I would go further than saying that we should not think of object, sign and interpretant as "falling dominos", since I am not at all clear that there is a unique "order of semiotic determination". This follows from the way I understand irreducible triads as not fully computable, and hence inherently open-ended.
Best, John -----Original Message----- From: Benjamin Udell [mailto:bud...@nyc.rr.com] Sent: January 28, 2015 7:07 PM To: biosemiot...@lists.ut.ee; 'Peirce-L' Subject: Re: [PEIRCE-L] Re: Triadic Relations Jeff, Jon, lists, I think that all that is required for an ordered triple, or an ordering of any length, is a rough notion of 'more' or 'less', for example an ordering of personal preferences, and this is enough for theorems, for example http://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem. Exact quantities are not required. In the case of object, sign, interpretant, insofar as the object determines the sign to determine the interpretant to be determined by the object as the sign is determined by the object, the order of semiotic determination is 'object, sign, interpretant', although object, sign, interpretant are not to be understood as acting like successive falling dominoes. Best, Ben On 1/27/2015 2:08 PM, Jeffrey Brian Downard wrote: [....] Here is the starting question: Doesn't the notion of an ordered triple require that we already have things sorted out in such a way that we are able to ascribe quantitative values to each subject that is a correlate of the triadic relation? [....]
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