, Volume 21, Issue 2, pp 301-304

Nominalism and the application of mathematics

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A significant feature of contemporary science is the widespread use of mathematics in several of its subfields. In many instances, the content of scientific theories cannot be formulated without reference to mathematical objects (such as functions, numbers, or sets). In the hands of W. V. Quine and Hilary Putnam, this feature of scientific practice was invoked in support of platonism (the view according to which mathematical objects exist). Quine and Putnam insisted that one ought to be ontologically committed to mathematical entities since they are indispensable to our best theories of the world. This is the indispensability argument.

This argument posed a formidable challenge to nominalists, who now needed to show either (i) that mathematical entities are not indispensable to mathematics or (ii) that quantification over these entities does not require ontological commitment. Since Hartry Field’s Science without Numbers (Princeton, NJ: Princeton University Press, 1980), most nominalisa