Van Inwagen and the Quine-Putnam indispensability argument

Erkenntnis 67 (3):439 - 453 (2007)
In this paper I do two things: (1) I support the claim that there is still some confusion about just what the Quine-Putnam indispensability argument is and the way it employs Quinean meta-ontology and (2) I try to dispel some of this confusion by presenting the argument in a way which reveals its important meta-ontological features, and include these features explicitly as premises. As a means to these ends, I compare Peter van Inwagen’s argument for the existence of properties with Putnam’s presentation of the indispensability argument. Van Inwagen’s argument is a classic exercise in Quinean meta-ontology and yet he claims – despite his argument’s conspicuous similarities to the Quine-Putnam argument – that his own has a substantially different form. I argue, however, that there is no such difference between these two arguments even at a very high level of specificity; I show that there is a detailed generic indispensability argument that captures the single form of both. The arguments are identical in every way except for the kind of objects they argue for – an irrelevant difference for my purposes. Furthermore, Putnam’s and van Inwagen’s presentations make an assumption that is often mistakenly taken to be an important feature of the Quine-Putnam argument. Yet this assumption is only the implicit backdrop against which the argument is typically presented. This last point is brought into sharper relief by the fact that van Inwagen’s list of the four nominalistic responses to his argument is too short. His list is missing an important – and historically popular – fifth option.
Keywords Indispensability  Quine  Putnam  Van Inwagen  Ontology  Meta-ontology  Mathematics  Properties
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DOI 10.1007/s10670-007-9052-3
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Science Without Numbers.Hartry Field - 1980 - Princeton University Press.
Realism in Mathematics.Penelope Maddy - 1990 - Oxford University Prress.
The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford University Press.
On What There's Not.Joseph Melia - 1995 - Analysis 55 (4):223 - 229.

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