Edited by Rafal Urbaniak (University of Ghent, University of Gdansk)
|Summary||One way to avoid epistemic challenges that mathematical platonism runs into (how can mundane human beings have knowledge of aspatial and atemporal abstract objects?) and to develop a more naturalistically acceptable account of mathematical knowledge is to deny the existence of mathematical objects. The main challenge, if you follow this path, is to make sense of mathematics, of mathematical practice and of the applicability of mathematics without reference to abstract objects.|
|Key works||In the twentieth century early serious attempts at constructing nominalistic foundations of mathematics are due to S.Leśniewski (see Simons 2008 for a survey, Leśniewski et al 1991 and Urbaniak 2013 for details). The second major attempt is Goodman & Quine 1947. Nominalistic literature started flourishing in 1980s. The main proposals include: Chihara 1990 (see also a later book S. Chihara 2003), Field 1980, Gottlieb 1980, Hellman 1989 and Azzouni 2004. See Burgess & Rosen 1997 for further references.|
|Introductions||A well-written, although somewhat hostile, survey of nominalistic options is Burgess & Rosen 1997. A reasoned overview of philosophical motivations of nominalism can be found in Chihara 1990 and S. Chihara 2003.|
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David Bourget (Western Ontario)
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