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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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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 28 October 2021

Logics and languages

Logics and languages

Chapter:
(p.7) 1 Logics and languages
Source:
Philosophy and Model Theory
Author(s):

Tim Button

Sean Walsh

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198790396.003.0001

This chapter introduces the concepts of signature and structure, and describes the semantics for first- and second-order logic. We outline three different but extensionally equivalent treatments of quantifiers and variables (the Tarskian approach, the Robinsonian approach, and a hybrid approach) and discuss their philosophical merits concerning compositionality, and Fine’s antinomy of the variable. We also outline two extensionally distinct semantics for second-order logic (Henkin, full). The appendix to the chapter presents the formal definitions of some theories of arithmetic and set theory that we employ frequently throughout the remainder of the book.

Keywords:   signature, structure, Tarskian approach to variables, Robinsonian approach to variables, second-order logic (Henkin semantics, full semantics

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