Three Different Solutions to the Knower Paradox

Francesca Poggiolesi
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
more » ... 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.
doi:10.13128/annali_dip_filos-2840 fatcat:o45wwf7o6jal5o34msalarvesu