Motivating Wittgenstein's Perspective on Mathematical Sentences as Norms

Philosophia Mathematica 19 (1):1-19 (2011)
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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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Simon Friederich
University of Groningen

References found in this work

Philosophical Investigations.Ludwig Wittgenstein - 1953 - New York, NY, USA: Wiley-Blackwell. Edited by G. E. M. Anscombe.
Remarks on the foundations of mathematics.Ludwig Wittgenstein - 1967 - Oxford [Eng.]: Blackwell. Edited by G. E. M. Anscombe, Rush Rhees & G. H. von Wright.
Remarks on the Foundations of Mathematics.Ludwig Wittgenstein - 1956 - Oxford: Macmillan. Edited by G. E. M. Anscombe, Rush Rhees & G. H. von Wright.

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