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IUSS Philosophy Seminars - eMath Project


08 lug

11:00 AM

Scuola Universitaria Superiore IUSS Pavia
Centro di Ricerca in Neurocognizione, Epistemologia e Sintassi teorica (NEtS)

Dottorato in Neuroscienze Cognitive e Filosofia della Mente
(IUSS e Università “Vita-Salute” San Raffaele di Milano)

Iuss Philosophy Seminars
eMath Project - Epistemology of Mathematics and Logic

joint work with Michael Glanzberg
July 8th, 2020, 11 – 13

Lorenzo Rossi – Munich Center for Mathematical Philosophy (MCMP)

Theories of self-applicable truth have been motivated in two main ways. First, if truth-conditions provide the meaning of a large class of expressions, then self-applicable truth is instrumental to provide the semantics of semantically closed languages (such as natural languages). Second, the truth predicate is argued to fulfill a fundamental expressive role, enabling speakers to express claims that would not be expressible without it (and without resorting to infinitary languages) — for instance, “All the theorems of ZFC are true” can be used to express the infinite conjunction of all the theorems of ZFC via a single, finitary sentence. In order to play these two roles, however, theories of truth must extend beyond the framework of first-order logic in which they have been traditionally studied. In other words, if the truth predicate is to be used to provide the meaning of sentences of natural languages, and to fulfill its expressive role, it must be studied in combination with linguistic constructs that are actually found in natural languages and which, as it is well known, extend beyond first-order logic — modals, indicative conditionals, arbitrary quantifiers, and more. Here, we focus on truth and quantification. More precisely, we provide an extension of the Kripkean approach to self-applicable truth to Generalized Quantifier Theory. We develop a theory of self-applicable truth for the whole class of type <1> and type <1, 1> quantifiers to be found in natural languages such as English. As a result, we will be able to 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.


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