Chapter

Analysis and Consistency: The Case of Geometry

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/9780199891610.003.0005
Analysis and Consistency: The Case of Geometry

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This chapter examines Frege’s dispute with David Hilbert over consistency- and independence-proofs in the foundations of geometry. It is argued that if one understands logical entailment in the way that Frege does, as a relation that can be partly revealed by conceptual analysis, then one can see that Frege’s much-misunderstood complaints against Hilbert are in fact decisive. Hilbert’s method of proving consistency does not demonstrate what Frege understood as “consistency.” It is argued that we see here an important distinction between two ways of understanding entailment and consistency, and that the now-unfamiliar Fregean understanding is a rich and valuable one in its own right.

Keywords: consistency; independence; Hilbert; geometry; parallels; models; relative consistency proof

Chapter.  13236 words. 

Subjects: Philosophy of Mathematics and Logic

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