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

TL;DR

The paper explores Sundholm's philosophical approach to logic, emphasizing a contentual view of proofs without object-language distinctions, and applies this to interpret Gentzen's Natural Deduction variants.

Contribution

It introduces a novel interpretation of Gentzen's Natural Deduction through Sundholm's contentual perspective, linking proof-objects and proof-acts without traditional language distinctions.

Findings

Sundholm's approach offers a new perspective on logical meaning.

The interpretation distinguishes proof-objects from proof-acts.

A Martin-Löfian reading underpins the analytic assertion concept.

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.