Thanks for the notice of Carolyn Eisele’s article — it’s always worth reading what she has to say. We’ve had discussions of Peirce’s distinction between theorematic and corollarial reasoning before and I know there’s a respectable amount of literature out there about it. The subject has curiously enough come up just recently in discussions on Facebook and Academia.edu, mostly on account of points brought up by John Corcoran. It’s also related to a number of discussions I’ve had over the years about the difference between “insight” proofs and “routine” proofs, partly in connection with theorem proving apps and Peirce’s logical graphs. Usually these discussions take off into the stratosphere of high-sounding blue-skying about Gödel incompleteness and all that — but I want to keep my focus on more nuts and bolts issues at the moment and I’ll try to avoid going off on those planes.
- Eisele, C. (1982), “Mathematical Methodology in the Thought of Charles S. Peirce”, Historia Mathematica 9, pp. 333–341. Online. PDF.