Three solutions to the knower paradox

Francesca Poggiolesi (1)

1 IHPST - Institut d'Histoire et de Philosophie des Sciences et des Techniques

In this paper I shall present three solutions to the Knower Paradox which, despite important points in common, differ in several respects. The first solution, proposed by C. A. Anderson [1] is a hierarchical solution, developed in the framework of first-order arithmetic. However I will try to show that this solution is based on an incorrect argument. The second solution, inspired by a book of R.M. Smullyan [14], is developed in the framework of modal logic and it is based on the idea of interpreting one of the basic systems of the modal logic of provability in an epistemic way. I shall give arguments in support of this solution. The third solution, proposed by P. Egrèé [8] attempts to connect the first and the second solutions. I will show that this attempt fails for philosophical and formal reasons.

Mots clés: hierarchy solutions; Knower Paradox; self-reference; provability logic

Domaines: Histoire, Philosophie et Sociologie des sciences

Francesca Poggiolesi. Three solutions to the knower paradox. Annali del Dipartimento di Filosofia - Nuova Serie, 2008, XIII, pp.147-163. ⟨10.13128/Annali_Dip_Filos-2840⟩. ⟨halshs-00775810⟩