Logic Supergroup — Online Colloquium, April 2, 2021 https://sites.google.com/view/logicsupergroup/ Lorenzo Rossi (MCMP, LMU Munich) – Truth and Quantification Joint work with Michael Glanzberg (Rutgers). Theories of self-applicable truth have been motivated in two main ways. First, if truth-conditions provide the meaning of (many kinds of) natural language expressions, then self-applicable truth is instrumental to develop the semantics of natural languages. Second, a self-applicable truth predicate is required to express generalizations that would not be otherwise expressible in natural languages. In order to fulfill its semantic and expressive role, we argue, the truth predicate has to be studied in its interaction with constructs that are actually found in natural languages and extend beyond first-order logic — modals, indicative conditionals, arbitrary quantifiers, and more. Here, we focus on truth and quantification. We develop a Kripkean theory of self-applicable truth (strong Kleene-style) for the language of Generalized Quantifier Theory. More precisely, we show how to interpret a self-applicable truth predicate for the full class of type ⟨1, 1⟩ (and type ⟨1⟩) quantifiers to be found in natural languages. As a result, we can model sentences which are not expressible in theories of truth for first-order languages (such as ‘Most of what Jane’s said is true’, or ‘infinitely many theorems of T are untrue’, and several others), thus expanding the scope of existing approaches to truth, both as a semantic and as an expressive device. Along the way, we will point at the relations between our work and recent works in similar directions (by Hartry Field, Bruno Whittle, and others).