John, List: I agree that Peirce's categories are *much broader* from a philosophical standpoint than modern mathematical categories, and obviously monadic/dyadic/triadic relations are not the *only *mathematical categories. However, the question on the table, as originally stated by Gary R., was about "the conceptual relationship between Peirce's trichotomic category theory and contemporary mathematical category theory if any." Goguen's "first dogma" provides an answer that I find helpful--monadic/dyadic/triadic relations are three different species of mathematical structure, objects having each structure belong to the corresponding category (1ns/2ns/3ns), and morphisms of each category preserve that structure.
Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Fri, May 8, 2020 at 11:03 PM John F. Sowa <[email protected]> wrote: > Jon, > > Peirce was using the word 'category' in rhe tradition from Aristotle to > Kant. That tradition is still alive and well in philosophy. > > It's unfortunate that the 20th c mathematicians used the same term for a > different kind of mathematical theory. But as Robert M. hass been saying, > it's possible to apply the mathematical category theory to analyze Peirce's > theories. > > JAS> "A Categorical Manifesto" provides the kind of clear and succinct > definition that I have been seeking. > > JG: To each species of mathematical structure, there corresponds a > category whose objects have that structure, and whose morphisms preserve > it. (p. 2) > > That simple statement may look clear and succinct, but underneath there's > the kind of complexity that Robert was talking about. > JAS> Would it then be accurate to say that Peirce's categories > (1ns/2ns/3ns) are mathematical categories in the sense of corresponding to > the structures of the three irreducible forms of relation > (monadic/dyadic/triadic)? > Short answer: No. > The longer answer would be along the lines that Robert was talkinng about. > John >
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