Torsten Wilholt's Number and Reality marks the most sustained treatment of philosophical problems with applied mathematics since Steiner's [1998]The Applicability of Mathematics as a Philosophical Problem. Unlike Steiner though, Wilholt ties questions about applications of mathematics to debates about realist and anti-realist interpretations of mathematics generally. This leads to an argument for a new kind of limited realism about mathematics. My concerns, to be developed below, are that the limited realism he advocates depends on a number of controversial assumptions. While Wilholt's limited realism is certainly a new proposal for understanding mathematics and its applications, it remains to be seen whether it is really superior to the more traditional realist and anti-realist approaches to mathematics.

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Framing the entire discussion are two problems for the...

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