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The Development of Modern Logic$
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Leila Haaparanta

Print publication date: 2009

Print ISBN-13: 9780195137316

Published to Oxford Scholarship Online: September 2009

DOI: 10.1093/acprof:oso/9780195137316.001.0001

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Logic and Semantics in the Twentieth Century

Logic and Semantics in the Twentieth Century

Chapter:
(p.562) 13 Logic and Semantics in the Twentieth Century
Source:
The Development of Modern Logic
Author(s):

Gabriel Sandu

Tuomo Aho

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780195137316.003.0040

This chapter explores logical semantics, that is, the structural meaning of logical expressions like connectives (it is not the case that, either or, if … then), quantifiers (there is, for all, etc.), and modalities (it is necessary that, it is possible that). It focuses on truth-theoretical semantics for formalized languages, a tradition emerging from Carnap's and Tarski's work in the first half of the last century that specifies the meaning of these expressions in terms of the truth-conditions of the sentences in which they occur. It considers Tarski-style definitions of the semantics of a given language in a stronger metalanguage, Tarski's impossibility results, and attempts to overcome them in the post-Tarskian tradition.

Keywords:   logic, Frege, Russell, Tarski, truth-definition, Rudolf Carnap, Herzberger, impossibility results, truth-conditions

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