Discovering knowability

a semantic analysis

Sergei Artemov

Tudor Protopopescu

pp. 3349-3376

in: Synthese 190 (16), 2013.

Abstract

In this paper, we provide a semantic analysis of the well-known knowability paradox stemming from the Church–Fitch observation that the meaningful knowability principle all truths are knowable, when expressed as a bi-modal principle ({diamondsuit}), yields an unacceptable omniscience property all truths are known. We offer an alternative semantic proof of this fact independent of the Church–Fitch argument. This shows that the knowability paradox is not intrinsically related to the Church–Fitch proof, nor to the Moore sentence upon which it relies, but rather to the knowability principle itself. Further, we show that, from a verifiability perspective, the knowability principle fails in the classical logic setting because it is missing the explicit incorporation of a hidden assumption of stability: ‘the proposition in question does not change from true to false in the process of discovery.’ Once stability is taken into account, the resulting stable knowability principle and its nuanced versions more accurately represent verification-based knowability and do not yield omniscience.