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Frege, Neo-Logicism and Applied Mathematics

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Induction and Deduction in the Sciences

Part of the book series: Vienna Circle Institute Yearbook ((VCIY,volume 11))

Abstract

A little over one hundred years ago (the letter is dated July 28, 1902), Frege wrote to Russell in the following terms1: I myself was long reluctant to recognize ranges of values and hence classes; but I saw no other possibility of placing arithmetic on a logical foundation. But the question is how do we apprehend logical objects? And I have found no other answer to it than this, We apprehend them as extensions of concepts, or more generally, as ranges of values of functions. I have always been aware that there are difficulties connected with this, and your discovery of the contradiction has added to them; but what other way is there?

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Authors
  1. Peter Clark
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Editors and Affiliations

  1. University of Vienna and Institut Vienna Circle, Austria

    Friedrich Stadler

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Clark, P. (2004). Frege, Neo-Logicism and Applied Mathematics. In: Stadler, F. (eds) Induction and Deduction in the Sciences. Vienna Circle Institute Yearbook, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2196-1_11

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  • DOI: https://doi.org/10.1007/978-1-4020-2196-1_11

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  • Print ISBN: 978-90-481-6555-1

  • Online ISBN: 978-1-4020-2196-1

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