The introduction sets out the attractions and drawbacks of mathematical platonism, then gives an overview of the anti-platonistic argument of the book, paying particular attention to the difficulties a naturalized epistemology faces in accounting for platonism. Chapter 1's distinctions between methodological and ontological naturalism and between informational and metaphysical content are sketched. The content of the remaining chapters is described in turn: Chapter 2 deals with ‘hermeneutic anti-realisms’, anti-realisms which do not deny that the discourse in question is truth-valued; Chapter 3 with the neo-formalist position championed in the book; Chapter 4 looks at objections to neo-formalism and comparisons with other views; Chapter 5 tackles the applicability of mathematics. Chapter 6 develops a concretist syntax, and distinguishes a legitimate from an illegitimate way to idealize such syntax, the former explored in Chapter 7 which additionally argues for infinitary idealizations; Chapter 8 concentrates on key logical issues.
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