Room P3.10, Mathematics Building

Alexandre Costa-Leite, U Neuchâtel, Switzerland

The Church-Fitch paradox and combining logics

The Church-Fitch paradox shows that "If there is some true proposition which nobody knows (or has known or will know) to be true, then there is a true proposition which nobody can know to be true." (Fitch, F. A Logical Analysis of Some Value Concepts. Journal of Symbolic Logic, 1963.) Indeed, the paradox shows that the verification principle "All true propositions can be known" implies the collapse principle "All true propositions are known." In my talk, I argue that the correct set to state the paradox is composed syntactically by a fusion of modal languages and logics and semantically by a product of Kripke models. I also argue that if we replace "possibility" and "knowledge" by the hybrid modality of "knowability" obtained by introducing in the language of the paradox a new operator $\boxminus$, then we can state the verification principle without leading to the collapse principle.