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Motivating Wittgenstein's perspective on mathematical sentences as norms

Friederich, S. (2011) Motivating Wittgenstein's perspective on mathematical sentences as norms. Philosophia Mathematica, 19 (1). pp. 1-19.

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The later Wittgenstein's perspective on mathematical sentences as norms is motivated for sentences belonging to Hilbertian axiomatic systems where the axioms are treated as implicit definitions. It is shown that in this approach the axioms are employed as norms in that they function as standards of what counts as using the concepts involved. This normative dimension of their mode of use, it is argued, is inherited by the theorems derived from them. Having been motivated along these lines, Wittgenstein's perspective on mathematical language may appeal also to those who are not friends of or experts on Wittgenstein's later philosophy of mathematics.

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Item Type: Published Article or Volume
Keywords: Wittgenstein, Hilbert, axiomatics, mathematical language as normative
Subjects: Specific Sciences > Mathematics
Depositing User: Dr. Simon Friederich
Date Deposited: 03 Nov 2015 16:51
Last Modified: 03 Nov 2015 16:51
Item ID: 11748
Journal or Publication Title: Philosophia Mathematica
Publisher: Oxford University Press
Official URL:
DOI or Unique Handle: 10.1093/philmat/nkq024
Subjects: Specific Sciences > Mathematics
Date: 10 January 2011
Page Range: pp. 1-19
Volume: 19
Number: 1

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