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, ... , t_n that”, where t₁, ... , t_n 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, ... , t_n that”.