NUMBERS AS PICTURES OF EXTENSIONS
NUMBERS AS PICTURES OF EXTENSIONS

Summary/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.

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