Analytic frameworks, our various theories of categories, sets, sorts, and types, have their uses but they tend to become à priori, autonomous, top-down, and top-heavy unless they are supported by a robust population of concrete examples arising in practical experience, one of the things the maxim of pragmatism advises us to remember. That is why Peirce’s tackling of information and inquiry is even-handed with respect to their extensional and intensional sides. And it’s why we need to pay attention when anomalies accumulate and the population of presenting cases rebels against the dictates of Procrustean predicates. Times like that tell us we may need to reconceive our customary conceptual frameworks.
As it happens, I’ve been thinking a lot lately about a particular class of sign sequences, namely, proofs in propositional calculus regarded as cases of sign process, or semiosis. Naturally I’ve been thinking of delving more deeply into Robert Marty’s work on paths through the lattice of sign classes but so far I’m still in the early stages of that venture.
For what they’re worth, here are my blog posts so far on Proof As Semiosis.