Mathematical Nominalism
Edited by Rafal Urbaniak (Uniwersytetu Gdanskiego, Uniwersytetu Gdanskiego)
Assistant editors: Sam Roberts, Pawel Pawlowski
About this topic
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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Related categories
Siblings:
- Mathematical Fictionalism (96)
- Mathematical Platonism (455)
- Mathematical Aristotelianism (105)
- Mathematical Psychologism (25)
- Mathematical Structuralism (326)
- Mathematical Neo-Fregeanism (379)
- Indeterminacy in Mathematics (33)
- Debunking Arguments about Mathematics (20)
- Indispensability Arguments in Mathematics (248)
- Numbers (370)
- The Nature of Sets (286 | 111)
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Editorial team
General Editors:
David Bourget (Western Ontario) David Chalmers (ANU, NYU) Area Editors: David Bourget Gwen Bradford Berit Brogaard Margaret Cameron David Chalmers James Chase Rafael De Clercq Ezio Di Nucci Esa Diaz-Leon Barry Hallen Hans Halvorson Jonathan Ichikawa Michelle Kosch Øystein Linnebo JeeLoo Liu Paul Livingston Brandon Look Manolo Martínez Matthew McGrath Michiru Nagatsu Susana Nuccetelli Giuseppe Primiero Jack Alan Reynolds Darrell P. Rowbottom Aleksandra Samonek Constantine Sandis Howard Sankey Jonathan Schaffer Thomas Senor Robin Smith Daniel Star Jussi Suikkanen Aness Kim Webster Other editors Contact us Learn more about PhilPapers |