Talk (Work in Progress): Elio La Rosa (MCMP)

Title:

Epsilon Modal Logics

Abstract:

In this talk, I present a new class of Modal logic structurally analogous to Hilbert’s Epsilon Calculus and based on what i call ‘epsilon modalities’. These consist of connectives indexed by formulas selecting a world-witness satisfying their index (if any) through an arbitrary choice function. The obtained ‘Epsilon Modal logics’ are conservative extension of their Modal logic bases, and generalise many of Epsilon Calculus’ properties at the propositional level. Remarkably, the two systems can be proven mutually embeddable. This correspondence spreads to applications. The epsilon terms of Epsilon Calculus have been interpreted as indefinite descriptions in linguistics, as ‘ideal objects’ of mathematical properties in Hilbert’s Program, and used to explicitly define the ‘theoretical terms’ of scientific theories over their own laws by Carnap. On intensional grounds, epsilon modalities can be read as indefinite description of states, as ‘ideal worlds’ of structures of Feferman’s Conceptual Structuralism, and used to explicitly define ‘theoretical contexts’ of scientific theories respectively.