Spelling Out the Quine-Putnam Indispensability Argument The Quine-Putnam indispensability argument has attracted a great deal of attention, in part because many see it as the best argument for mathematical realism or platonism. Thus anti-realists about mathematical entities or nominalists need to identify where the Quine-Putnam argument goes wrong. Many platonists, on the other hand, rely very heavily on this argument to justify their belief in mathematical entities.
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A weak indispensability argument is distinguished from a strong indispensability thesis. The weak argument is the combination of the criterion of ontological commitment, holism and a mild naturalism.
It is used to refute nominalism. Putnam defends Quine’s argument, in places. 2 One can find elements of Quine’s indispensability argument in Quines , , , , , , , and b. En este trabajo rechazo los alegatos de Psillos () contra el nominalismo moderado (NM).
El NM es una variante del realismo que recomienda restringir la creencia racional a los contenidos puramente nominalistas de las teorías científicas.
The indispensability argument in the philosophy of mathematics transfers evidence from natural science to mathematics. Thus, this argument is an inter-theoretic indispensability argument.
One might apply inter-theoretic indispensability arguments in other areas. In particular, Quine (; a; b; a; c) and Putnam (a; b) have argued that the indispensability of mathematics to empirical science gives us good reason to believe in the existence of mathematical entities.
The Indispensability of Mathematics, New York, NY: Oxford University Press. This book offers an excellent, systematic exploration of the Quine-Putnam Indispensability Argument and some of the most important challenges that have been leveled against it.