Chapter

Thoughts and Sharp Boundaries

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/9780199891610.003.0003
Thoughts and Sharp Boundaries

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It is often claimed that Frege requires all function-expressions to be everywhere defined. This, if true, poses a difficulty for Frege’s idea (as claimed in this book) that arithmetical function-expressions, both ordinary and formal, are not so defined. The purpose of this chapter is to argue that Frege does not require total definition of function-expressions, but instead that he imposes a much weaker requirement, here called that of “linguistic completeness,” and that the requirement is imposed just on formal languages. The importance of this point is twofold. First: only under such an understanding can Frege’s logicist project be understood, as urged here, as an attempt to establish the purely-logical status of ordinary arithmetical truths. Secondly: only under such an understanding can we take Frege at his word when he says that ordinary arithmetical sentences express truths and falsehoods.

Keywords: sharp boundaries; total definition; functions; concepts; reference

Chapter.  9933 words. 

Subjects: Philosophy of Mathematics and Logic

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