Motivating Wittgenstein's Perspective on Mathematical Sentences as Norms

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Philosophia Mathematica, ISSN: 0031-8019, Vol: 19, Issue: 1, Page: 1-19

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Simon Friederich
Oxford University Press (OUP); Oxford University Press
Mathematics; Arts and Humanities
article description
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. © The Author [2011]. Published by Oxford University Press. All rights reserved.