The Knowability Paradox and Unsuccessful Updates

Abstract

In this paper we undertake an analysis of the knowability paradox in the light of modal epistemic logics and of the phenomena of unsuccessful updates. The knowability paradox stems from the Church-Fitch observation that the plausible knowability principle, according to which all truths are knowable, yields the unacceptable conclusion that all truths are known. We show that the phenomenon of an unsuccessful update is the reason for the paradox arising. Based on this diagnosis, we propose a restriction on the knowability principle which resolves the paradox.

Keywords

• knowability paradox
• knowability principle
• dynamic epistemic logic
• logic of public announcements
• unsuccessful update
• successful formulas