ABSTRACT. In his middle period Wittgenstein wrote that numbers are pictures of extensions. We interpret and defend this claim and develop Wittgenstein’s critique of referential accounts of number signs. Wittgenstein argues that the sign of an extension is a list and that number signs schematize lists. Number signs do this either directly, by having a sub-expression which corresponds to each element in this list; or else they do so indirectly, in virtue of symbolic conventions for their reduction to signs of the first sort. Accordingly, the function of number signs in number ascriptions is to provide samples of the appropriate multiplicity.

Keywords: Gottlob Frege; Ludwig Wittgenstein; class; concept; extension; number

How to cite: Büttner, Kai Michael, and David Dolby (2018). “Numbers as Pictures of Extensions,” Analysis and Metaphysics 17: 95–115.

Received 10 February 2018 • Received in revised form 13 March 2018
Accepted 15 March 2018 • Available online 5 April 2018

doi:10.22381/AM1720184