Truth, Demonstration and Knowledge. A Classical Solution to the Paradox of Knowability

After introducing semantic anti-realism and the paradox of knowability, the paper offers a reconstruction of the anti-realist argument from understanding. The proposed reconstruction validates an unrestricted principle to the effect that truth requires the existence of a certain kind of “demonstration”. The paper shows that that principle fails to imply the problematic instances of the original unrestricted feasible-knowability principle but that the overall view underlying the new principle still has unrestricted epistemic consequences. Appealing precisely to the paradox of knowability, the paper also argues, against the BHK semantics, for the non-constructive character of the demonstrations envisaged by semantic anti-realism, and contends that, in such setting, one of the most natural arguments for a broadly intuitionist revision of classical logic loses all its force