"Category theory," "theory of categories," and even "categorial theory" could be hard to distinguish in some languages. Anyway, we're getting into the territory of distinctions that are semantically nontrivial yet confusingly expressed, such as that between "relation algebra" and "relational algebra," and that between "algebraic topology" and "topological algebra."
Another option would be to use Peirce's word "categorics" generally for philosophical category theories, rather than keeping it to Peirce-style categorics. Problem is that the accompanying adjective is "categorical" rather than "categorial." Less sonorous options include "categoriacs," "categoristics," and "categoriology." Another option would be to resist the transference of the sense of either "philosophical" or "mathematical" to phrases like "category theory," and instead speak of "mathematical categorics" and "philosophical categorics." Those phrases are rather long. My guess is that the best bets for philosophical theory of categories, Peircean or otherwise, are "categoristics" and "categoriology." "Categoristics" has fewer syllables than "categoriology," and its correlated adjective "categoristical" has quite that advantage over "categoriological." Best, Ben ----- Original Message ----- From: "Gary Fuhrman" To: <PEIRCE-L@LISTSERV.IUPUI.EDU> Sent: Thursday, July 21, 2011 2:11 PM Subject: Re: [peirce-l] Slow Read: "Is Peirce a Phenomenologist?" I don't think "Doctrine of Categories" would work because the word "doctrine" no longer means what it did in Peirce's time. As for "Theory of Categories", a quick internet search shows that it's used by some mathematicians as a synonym for "Category Theory", so unless they can be broken of that habit, that difference in name isn't enough to distinguish between the two disciplines. Maybe Gary needs to come up with an ugly neologism as Peirce would have done -- "trichotomologics"? -- if he needs to avoid confusing mathematicians. (I don't think "category theory" would be ambiguous for anybody else.) Gary F. -----Original Message----- From: Irving Sent: July-21-11 10:55 AM Not to continue to be overly fussy, but I propose "Doctrine of Categories" or "Theory of Categories" for the philosophical use, whether speaking of Aristotle, or Kant (Kategorienlehre) or Peirce, and reserve "Category Theory" for the the that branch of abstract algebra that formalizes a number of algebraic properties of collections of transformations between mathematical objects (such as binary relations, groups, sets, topological spaces, etc.) of the same type, subject to the constraint that the collections contain the identity mapping and are closed with respect to compositions of mappings, ... unless and until it is demonstrated that the philosophical concept, whether Aristotle's, Kant's, or Peirce's, is equivalent to, or at least in some important sense related to, the algebraists' concept. --------------------------------------------------------------------------------- You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU --------------------------------------------------------------------------------- You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
