This article argues for an intermediate standpoint concerning the theory of truth which finds an equilibrium between realist an epistemic conceptions of truth. At the same time it is accepted that truth is a notion with an ultimate realist sense, but it is made clear that this intuitive sense does only have a non-trivial (i.e. non-“disquotational”), reading if the function of “truth” is seen from within the epistemic framework of our practices of belief-formation (i.e. of confirmation and revision). Following the realist line one can reconstruct the unconditional validity attributed to the intuitive concept of truth out of its internal relation with the concept of “reality”; this in turn makes clear that the epistemic strategy of extracting this uncoditionality from an emphatic concept of perfect, infallible knowledge is more than weak. This is because only preserving the decisive function of truth as a corrective, as a fallibilist reserve (incompatible therefore with any concept of “infallible” knowledge) one can see how truth relates to cognitive learning processes. On the other hand, the strategy of this paper shows thus how this is possible avoiding the bad alternative of metaphysical realism and relativism.

Let’s agree in calling “classical demonstration” a deduction that enables us to know the rational necessity that something is the case and cannot be otherwise. I propose to take seriously actual instances of this notion, e.g. some mathematical proofs, and explore certain discoursive and epistemic implications of their existence. Then I will look at questions about characterizing, rigorizing and acknowledging this kind of conclusive proof. Finally, some remarks on the meaning of Provability Logic in this context will be made.