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.

Uniform Interpolation and Admissible Rules

“…This is the road that Artemov and Protopopescu (2016) take and that we follow here. This is not a mainstream standpoint in the discussion on Church-Fitch paradox, but is defended in (Martino and Usberti, 1994;Usberti, 2016;Khlentzos, 2004;Artemov and Protopopescu, 2016). Also in the work of Hart (1979) and Williamson (1988) similar arguments are lined out, but are still questioned.…”