John, List: > 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.
Huh? Yes, as stated, I agree with your sentence. And that a function can be defined as an order pair between two mathematical objects. But, there is nothing in either mathematics or physics that requires the pair of symbols, "m" and "a" to be ordered as "m multiplied by a" as to be distinguished from the pair "a multiplied by m". Both calculations give the same number for force, do they not? The usual requirement for ordering, at least as I understand it, is the sense of a transitive relation, a<b<c or a>b>c. A practical example of ordering is the counting all possible combinations of pairs of parentheses, aligned along the a number line such as the Catalan numbers are generated. Further, the concept of ordered pairs or ordered triplets, or... does NOT REQUIRE an extension to higher counts, such as the set of all integers. I point these distinctions out because the concept of order is used in a DRAMATICALLY different manner in the chemical sciences, even in the 19th Century views of CSP, as evidenced by the routine use of "molecular formula" as contrasted with "molecular weights". Think about it... do these two chemical terms imply the same concept of order or ordered pairs? By way of contrast, physical symbols, such as those you use, as well as many, many other physical symbols, pre-suppose that the concept of order and number are virtually synonymous, as amply documented by the International System of Units. At least until catastrophe/chaos/fractal theories arrived in the 1960s - 1970s. In pure philosophical discourse (metaphysics?) it would appear to me that the concept of "order" is a matter of personal judgment. Consequently, the discipline has an unending source of stimulations about the relative importance of different ideas and the "difference that makes a difference". Would you disagree with this generality? Cheers Jerry On Jan 29, 2015, at 2:52 AM, John Collier wrote: > 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:[email protected]] > Sent: January 28, 2015 7:07 PM > To: [email protected]; '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? > [....] > > > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] > . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] > with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at > http://www.cspeirce.com/peirce-l/peirce-l.htm . > > > >
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