CEFISES Seminar: Lorenzo Rossi, “Supervaluational truth and quantifiers”

Livestream https://www.youtube.com/@CEFISES

Series: OLOFOS

Speaker: Lorenzo Rossi (University of Turin)

Title: “Supervaluational truth and quantifiers”

Abstract

Quantification has long been both a stumbling block and a testing ground in semantics. Building on Frege, Tarski developed the modern model-theoretic semantics for first-order logic (FOL), but many quantifiers (because of the Compactness and Löwenheim–Skolem Theorems) cannot be expressed within FOL. Mostowski and Lindström extended Tarski’s framework to capture quantifiers such as “finitely many” and “most”, giving rise to Generalized Quantifier Theory (GQT), now a standard tool in formal and natural language semantics. Still, challenges remain, especially where semantic indeterminacy arises. We focus on three sources of indeterminacy: (P) presupposition failure, (V) vagueness, and (L) semantic paradoxes. To address them, we propose a general supervaluational framework for quantifier semantics in the presence of indeterminacy, and we develop two formal systems that (a) meet key desiderata for handling P, V, and L, and (b) recover a substantial fragment of GQT. Note: Joint work with Johannes Stern (University of Bristol).