Sung, The short answer is that many functions, all of which are dyadic relations, are also triadic relations.
I can see where a statement like that might lead one to suspect that the whole mess of concepts concerned with adicity, arity, relational type, functional type, ad indefinitum, are totally incoherent, but I think it is possible to understand what is going on here if we realize that relational types are not absolute categories so much as aspectual or interpretive categories. Let's look at a concrete example. Consider the "binary operation" of real number addition, +(x, y) = x + y, where the arguments x, y, and the result x + y are elements of the real number domain R. Then + is a function from the cartesian product R × R to R, and we express this by writing the type specification + : R × R → R. But the definition of + : R × R → R also defines a triadic relation, namely, the set of triples (x, y, z) in R × R × R such that z = x + y. Just to give this triadic relation a name, we can refer to it as [+] ⊆ R × R × R. Now, you can say that the function + and the relation [+] are distinct mathematical objects, and there are certainly contexts in which it might be useful to distinguish them, but there are just as certainly other, more abstract contexts in which it is useful to identify them. Regards, Jon 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 Peircean 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 > -- academia: http://independent.academia.edu/JonAwbrey my word press blog: http://inquiryintoinquiry.com/ inquiry list: http://stderr.org/pipermail/inquiry/ isw: http://intersci.ss.uci.edu/wiki/index.php/JLA oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey facebook page: https://www.facebook.com/JonnyCache
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