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.
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