From Proof-Objects to Grounds

The paper is devoted to an examination of the epistemic account of the notion of deductive inference recently provided by D. Prawitz, and based on the notion of ground. This is part of the general scenario constituted by the “Proof-theoretic semantics”, presented since the ’70s of the last century as an alternative to the standard model-theoretic explication of the notion of logical consequence. Our argument pivots on the so-called “Curry–Howard Correspondence”, which exploited the idea of considering proofs as proper mathematical objects in a remarkable way. A sort of rational reconstruction of this idea is outlined, tracing it back to Hilbert and Husserl’s investigations.