Indispensability Arguments in Mathematics
Edited by Rafal Urbaniak (Uniwersytetu Gdanskiego, Uniwersytetu Gdanskiego)
Assistant editors: Pawel Pawlowski, Sam Roberts
About this topic
Summary | One of the lines of reasoning in support of mathematical platonism employs the fact that mathematical theories find applications in sciences which, at least prima facie, concern themselves with the physical world. From the indispensability of mathematics in science the argument moves to the indispensability of reference to mathematical objects in science. Further on, since we, supposedly, have good reasons to accept the existence of objects our best scientific theories have to refer to, we should accept the existence of such mathematical objects, on a par with the existence of electrons and other invisible entities postulated by such scientific theories. Accordingly, the argument has been attacked on different grounds. Some deny the indispensability of mathematics in science, some claim that indispensability of mathematical theories is not the same as the indispensability of reference to mathematical objects, some insist that this approach doesn't make justice to the difference between a priori mathematical knowledge and a posteriori scientific knowledge, some worry that applied mathematics is only a part of theoretical mathematics and some suggest that best scientific theories don't have to be our guide to metaphysics. |
Key works | Loci classici are Quine 1953, Quine 1981, Putnam 1975 and Putnam 1971. Further considerations can be found for instance in Parsons 1980, Chihara 1973 and Maddy 1992. Field 1980 is directed at showing the dispensability of mathematics in science. An extensive defence of the indispensability argument have been mounted by Colyvan 2001. |
Introductions | Start with Colyvan 2008 (and references therein). |
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Related categories
Siblings:
- Mathematical Fictionalism (93)
- Mathematical Nominalism (220)
- Mathematical Platonism (443)
- Mathematical Psychologism (25)
- Mathematical Structuralism (325)
- Mathematical Neo-Fregeanism (375)
- Indeterminacy in Mathematics (28)
- Debunking Arguments about Mathematics (17)
- Numbers (372)
- The Nature of Sets (259 | 99)
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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 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 Lynne Tirrell Aness Kim Webster Other editors Contact us Learn more about PhilPapers |