On 20. Feb 2024, at 20:06, Steve Awodey <awodey@cmu.edu> wrote:
On Feb 20, 2024, at 9:57 AM, Julian Rohrhuber <rohrhuber@protonmail.com> wrote:
...
What I would be interested in would be in what sense Carnap's mistakes, according to Mac Lane, corresponded to the concept of functor. Or, perhaps, how Carnap's failed attempt to define analyticity corresponds to a wrong concept of functor.
Dear Julian,
the “mistakes” that Mac Lane refers to are not related to Carnap's use of the word “functor”, which was just what we would now call a "function symbol” in a formal language. Rather, they had to do with Carnap’s attempt to define logical validity syntactically, which Saunders showed in his review was mathematically defective. The connection between that and the “purloining” of the word “functor” was, I think, just a playful reminiscence.
Steve
Dear Steve, thank you for the clarification. My suspicion was that Carnap's use of the word functor was too syntactical, and Mac Lane found that for achieving logical validity, functors need to be mathematical objects proper. Would you say that this is a reasonable interpretation? Julian ---------- You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. Leave group: https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=leave&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27