# Science and mathematics: the scope and limits of mathematical fictionalism

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## Christopher Pincock

Fictionalism about mathematics allows a philosopher to reject a commitment to any specifically mathematical, abstract objects like numbers, sets and functions while at the same time continuing to accept our ordinary scientific theories and practices. Those raised in the Quinean tradition often suspect that fictionalism is either incoherent or so revisionary of our standards of doing metaphysics that it is not worth taking seriously. This can contribute to a kind of philosophical standoff between fictionalists and non-fictionalists. Mary Leng has done an excellent job in *Mathematics and Reality*of explaining to the Quinean what it takes to be a fictionalist. She goes far beyond previous expositions of the fictionalist position by setting out the fictionalist’s conception of pure mathematics and clarifying what attitude towards our ordinary scientific theories the fictionalist can take. While there have been extensive discussions of fictionalism already in the work...

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