Re: Category Theory • Henry Story

HS:

I place Logic within Mathematics and modal logic is a field of Logic,
and so of mathematics.  You will find that modal logic comes up a lot
working with machines, programs, and all state based systems.

Dear Henry,

Just by way of personal orientation, I tend to follow Peirce and assorted classical sources in viewing logic as a normative science whereas mathematics is a hypothetical descriptive science.  That gives a picture of their relationship like the one I drew in the following post.

Definition and Determination • 4

Normative science rests largely on phenomenology and on mathematics;
metaphysics on phenomenology and on normative science.

❧ Charles Sanders Peirce • Collected Papers, CP 1.186 (1903)
Syllabus • Classification of Sciences (CP 1.180–202, G-1903-2b)

The way I see it, then, logic is more an application of mathematics than a subfield of it.

cc: Category Theory • Cybernetics • Ontolog • Structural Modeling • Systems Science
cc: FB | Inquiry Driven Systems • Laws of Form • Peirce List (1) (2) (3)