Chapter

Logic and Semantics in the Twentieth Century

Gabriel Sandu and Tuomo Aho

in The Development of Modern Logic

Published in print June 2009 | ISBN: 9780195137316
Published online September 2009 | e-ISBN: 9780199867912 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780195137316.003.0040
 Logic and Semantics in the Twentieth Century

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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

Chapter.  23908 words. 

Subjects: Philosophy of Mathematics and Logic

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