Philosophical Review 108 (1):106 (1999)
AbstractThis is the first systematic survey of modern nominalistic reconstructions of mathematics, and for this reason alone it should be read by everyone interested in the philosophy of mathematics and, more generally, in questions concerning abstract entities. In the bulk of the book, the authors sketch a common formal framework for nominalistic reconstructions, outline three major strategies such reconstructions can follow, and locate proposals in the literature with respect to these strategies. The discussion is presented with admirable precision and clarity, and should be accessible even to readers with only minimal background in logic and mathematics. There will be many who will turn directly to these pages and use them as a brief manual on the state of the art of nominalism in mathematics. But the most intriguing parts of this elegant book—at least in my view—are the introduction and the conclusion, where the authors examine the significance of reconstructive nominalism.
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Citations of this work
On What Grounds What.Jonathan Schaffer - 2009 - In David Manley, David J. Chalmers & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press. pp. 347-383.
Mathematical Explanation in Science.Alan Baker - 2009 - British Journal for the Philosophy of Science 60 (3):611-633.
Go Figure: A Path Through Fictionalism.Stephen Yablo - 2001 - Midwest Studies in Philosophy 25 (1):72–102.
Existence as a Real Property: The Ontology of Meinongianism.Francesco Berto - 2012 - Synthèse Library, Springer.
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