Review of Stewart Shapiro, philosophy of mathematics: Structure and ontology
|Abstract||This book is an important contribution to the philosophy of mathematics. It aims to clarify and answer questions about realism in connection with mathematics, in particular whether there exist mathematical objects (ontological realism) and whether all meaningful mathematical statements have objective and determinate truth-values (truth-value realism). The author develops a novel structuralist account of mathematics that answers both questions affirmatively. By regarding mathematics as ‘the science of structure’ (p. 5), he attempts to render both forms of realism naturalistically respectable. The resulting philosophy of mathematics is extremely interesting and deserves the attention of anyone with a serious interest in the field.|
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