Bob, Sorry for my delayed response.
I would agree that z = f(x, y) is more "triadic" in the Peircesan sense than y = f(x) would be, since x, y and z can form Borromean rings (and a mathematical category) whereas x and y cannot. With all the best. Sung __________________________________________________ Sungchul Ji, Ph.D. Associate Professor of Pharmacology and Toxicology Department of Pharmacology and Toxicology Ernest Mario School of Pharmacy Rutgers University Piscataway, N.J. 08855 732-445-4701 www.conformon.net > How about the surface z = f (x,y) > ______________________ > > Robert K. Logan > Prof. Emeritus - Physics - U. of Toronto > Chief Scientist - sLab at OCAD > http://utoronto.academia.edu/RobertKLogan > www.physics.utoronto.ca/Members/logan > > > > > > > > On 2014-05-16, at 3:52 PM, Sungchul Ji wrote: > >> Jon: >> >> I haven't kept up with your emails, but I do have one 'burning' >> question. >> You wrote: >> >> "Since functions are special cases of dyadic relations . . " (051614-1) >> >> Can there be functions of the type, y = f(x), that are special cases of >> "triadic relations" in the Peircena sense ? In other words can the >> following mapping be considered triadic? >> >> f >> x --------> y (501614-2) >> >> With all the best. >> >> Sung >> ___________________________________________________ >> Sungchul Ji, Ph.D. >> Associate Professor of Pharmacology and Toxicology >> Department of Pharmacology and Toxicology >> Ernest Mario School of Pharmacy >> Rutgers University >> Piscataway, N.J. 08855 >> 732-445-4701 >> >> www.conformon.net >> >> >> >> >>> Post : Peirce's 1870 âLogic Of Relativesâ ⢠Comment 11.12 >>> http://inquiryintoinquiry.com/2014/05/12/peirces-1870-logic-of-relatives-%e2%80%a2-comment-11-12/ >>> Posted : May 12, 2014 at 2:00 pm >>> Author : Jon Awbrey >>> >>> Peircers, >>> >>> Since functions are special cases of dyadic relations and since the >>> space of dyadic relations is closed under relational composition â >>> that is, the composition of two dyadic relations is again a >>> dyadic relation â we know that the relational composition of two >>> functions has to be a dyadic relation. If the relational composition of >>> two functions is necessarily a function, too, then we would be justified >>> in speaking of ''functional composition'' and also in saying that the >>> space of functions is closed under this functional form of composition. >>> >>> Just for noveltyâs sake, let's try to prove this for relations that >>> are functional on correlates. >>> >>> The task is this â We are given a pair of dyadic relations: >>> >>> ⢠P â X à Y and Q â Y à Z >>> >>> The dyadic relations P and Q are assumed to be functional on >>> correlates, a premiss that we express as follows: >>> >>> ⢠P : X â Y and Q : Y â Z >>> >>> We are charged with deciding whether the relational composition P â Q >>> â X à Z is also functional on >>> correlates, in symbols, whether P â Q : X â Z. >>> >>> It always helps to begin by recalling the > >
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