Sundholm's explanation of meaning: logical atavism and the nature of proofs

Abstract

I provide an overview of some of Sundholm's remarks on the history and philosophy of logic. In particular, I focus on Sundholm's proposal to explain meaning with no object-language/metalanguage distinction, and to provide a consequently contentual approach to formalisms for proofs. When applied to Gentzen's Natural Deduction in its two 1935 and 1936 variants, this triggers a reading of each variant as pointing to one of the poles in the distinction between proof-objects and proof-acts, also introduced by Sundholm. I suggest that the basis of this picture is given by a Martin-Loefian reading of the notion of analytic assertion.