The Paradox of Knowability from an Intuitionistic Standpoint

Abstract

An intuitionistic solution to the Paradox of Knowability is given. It consists (i) in accepting α→ K α, the ordinary formalization of the principle of Radical Anti-Realism (RAR) that “Every truth is known”, since, intuitionistically understood, it means that proofs are epistemically transparent; and (ii) in accepting (RAR) itself, on the basis of the fact that knowledge is an intuitionistic internal truth notion. Some neo-verificationist approaches are criticized. Finally the problem of how to frame a rational discussion between Classicism and Intuitionism is briefly discussed.