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Philosophy and Model Theory$
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Tim Button and Sean Walsh

Print publication date: 2018

Print ISBN-13: 9780198790396

Published to Oxford Scholarship Online: May 2018

DOI: 10.1093/oso/9780198790396.001.0001

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(p.387) 16 Quantifiers
Philosophy and Model Theory

Tim Button

Sean Walsh

Oxford University Press

Typically the existential and universal quantifiers are regarded as logical expressions. But there are straightforward semantic means for defining all sorts of new quantifiers that have roughly the same syntax as the more familiar quantifiers. This raises the question: Which of these new quantifiers are relevantly similar to the existential and universal quantifiers to count as logical? After introducing generalised quantifiers, we use notions of indiscernibility to investigate how to classify quantifiers as logical or non-logical, focussing especially on the famous Tarski-Sher thesis. Roughly, this thesis states that quantifiers are logical provided they exhibit a certain kind of invariance. We argue that intuitions about non-discrimination are insufficient to establish Tarski-Sher. Then, by considering infinitary logics and closure principles, we raise some further difficulties for attempts to establish Tarski-Sher.

Keywords:   Generalised quantifiers, Tarski’s thesis, Tarski-Sher, non-discrimatory, principle of closure, McGee’s squeezing argument

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