Philosophy of Mathematics Seminar


Philosophy of Mathematics seminar


Giovanna Corsi, Bologna

From Kripke to Lewis and beyond: A foundational study of quantified modal logic


The approach to quantified modal logic we present leads both to a generalization of Kripke semantics, the so called “transition or counterpart semantics” and to the introduction of modal languages with indexed modalities: “it is necessary that” is replaced by “it is necessary for t1, ... , tn that”, where t1, ... , tn are terms of the language. A key theme will be the interplay between substitution, quantification and identity once indexed modalities are present. We will show which properties of the counterpart relation correspond to which modal sentences (the Barcan formula, the Ghilardi formula, the necessity of identity, etc). Indexed epistemic modalities will be introduced with the intended reading “t knows of t1, ... , tn that”.