Edited by Rafal Urbaniak (University of Ghent, University of Gdansk, University of Calgary)
|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 1961, Quine 1981, Putnam 1975 and Putnam 1971. Further considerations can be found for instance in Parsons 1979, 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 2003.|
|Introductions||Start with Colyvan 2008 (and references therein).|
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