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TULIPS – The Utrecht Logic in Progress Series

Upcoming Talks

2020

Validity in Context. Logical Pluralism and 2D-Semantics

Logical pluralism – the view that there is more than one correct logic – is typically connected to claims about the semantics of the logical vocabulary. A number of authors have claimed that the alleged plurality of correct logical systems can be traced back to the context-sensitivity of the expression “valid” in natural language. In the talk, I explore in what ways the most prominent account of context-sensitivity – Kaplan’s logic LD – can be employed to support this claim. I develop three possible readings of the Kaplanian character of “valid” and assess their weaknesses and strengths.

Time: 16.00 – 17.15

Location: The talk will take place in our dedicated MS Teams team “TULIPS – The Utrecht Logic in Progress Series.” Contact the organizers for information about how to join the online meeting.

 

A Note on Synonymy in Proof-theoretic Semantics

The topic of identity of proofs was put on the agenda of general (or structural) proof theory at an early stage. The relevant question is: When are the differences between two distinct proofs (understood as linguistic entities, proof figures) of one and the same formula so inessential that it is justified to identify the two proofs? The paper addresses another question: When are the differences between two distinct formulas so inessential that these formulas admit of identical proofs? The question appears to be especially natural if the idea of working with more than one kind of derivations is taken seriously. If a distinction is drawn between proofs and disproofs (or refutations) as primitive entities, it is quite conceivable that a proof of one formula amounts to a disproof of another formula, and vice versa. The paper develops this idea.

Time: 16.00 – 17.15

Location: The talk will take place in our dedicated MS Teams team “TULIPS – The Utrecht Logic in Progress Series.” Contact the organizers for information about how to join the online meeting.

 

  • October 13, Lorenzo Rossi(Munich), [joint work with Michael Glanzberg]

Truth and Quantification

Theories of self-applicable truth have been motivated in two main ways. First, if truth-conditions provide the meaning of (several 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 expressible in natural languages without it. In order to fulfill their semantic and expressive roles, we argue, the truth predicate has to be studied in its interaction with linguistic 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 to for the language of Generalized Quantifiers 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 such as ‘Most of what Jane 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.

Time: 16.00 – 17.15

Location: The talk will take place in our dedicated MS Teams team “TULIPS – The Utrecht Logic in Progress Series.” Contact the organizers for information about how to join the online meeting.