Chapter

Frege and Models

Patricia A. Blanchette

in Frege’s Conception of Logic

Published in print April 2012 | ISBN: 9780199891610
Published online May 2012 | e-ISBN: 9780199933211 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199891610.003.0006
Frege and Models

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This chapter discusses the question of how modern model-theoretic methods should be assessed from a Fregean point of view. It is argued that while the central features of mathematical theories, from a post-Fregean point of view, have essentially to do with features of those theories’ classes of models, this is not the case from Frege’s point of view. Given a Fregean starting-point, from which logical relations are borne not by sentences but by thoughts, and from which conceptual analysis is relevant to the discovery of logical relations, classes of models are not sensitive to the crucial logically-significant features of theories. Hence the important logical properties of theories as Frege understands them cannot be cashed out in standard modern terms. For similar reasons, model-theoretic entailment in a sufficiently rich language will diverge from logical entailment as understood by Frege

Keywords: models; consistency; semantic entailment; model-theoretic entailment; Tarski; logical entailment

Chapter.  6954 words. 

Subjects: Philosophy of Mathematics and Logic

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