A feature of particular interest to me in Robert Marty’s paper is the resonance he finds between category theory, as it’s known in contemporary mathematics, and the study of Peirce’s Categories. I’ve long felt the cross-pollination of these two fields was naturally bound to bear fruit. In that light I’ll refer again to the “brouillon projet” I wrote on the Precursors of Category Theory, where I trace a common theme uniting the function of categorical paradigms from Aristotle through Peirce to present day logic and math.
By way of orientation to the perspective I’ll adopt in reading Marty’s “Podium” paper, here’s the first of the excerpts I collected, from a primer of category theory on the shelves of every student of the subject, giving a thumbnail genealogy of categories from classical philosophy to current mathematics.
Now the discovery of ideas as general as these is chiefly the willingness to make a brash or speculative abstraction, in this case supported by the pleasure of purloining words from the philosophers: “Category” from Aristotle and Kant, “Functor” from Carnap (Logische Syntax der Sprache), and “natural transformation” from then current informal parlance.
— Saunders Mac Lane, Categories for the Working Mathematician, 29–30.