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- The Quine–Putnam indispensability argument, also known simply as the indispensability argument, is an argument in the philosophy of mathematics for the existence of abstract mathematical objects such as numbers and sets, a position known as mathematical platonism. Named after the philosophers Willard Quine and Hilary Putnam, it is one of the most important arguments in the philosophy of mathematics and is widely considered to be one of the best arguments for platonism. Although elements of the indispensability argument can be dated back to thinkers such as Gottlob Frege and Kurt Gödel, Quine's development of the argument was unique for introducing to it a number of his philosophical positions such as his naturalism, confirmational holism, and criterion of ontological commitment. Putnam gave Quine's argument its first detailed formulation in his 1971 book Philosophy of Logic. However, he later came to disagree with various aspects of Quine's thinking, formulating his own indispensability argument based on the no miracles argument in the philosophy of science. A standard form of the argument in contemporary philosophy is credited to Mark Colyvan; whilst being influenced by both Quine and Putnam, it also differs in important ways from their own formulations. It is presented in the Stanford Encyclopedia of Philosophy as: 1.
* We ought to have ontological commitment to all and only the entities that are indispensable to our best scientific theories. 2.
* Mathematical entities are indispensable to our best scientific theories. 3.
* Therefore, we ought to have ontological commitment to mathematical entities. Philosophers that reject the existence of abstract objects (nominalists) have argued against both premises of this argument. The most influential argument against the indispensability argument, primarily advanced by Hartry Field, denies the indispensability of mathematical entities to science. This argument is supported by attempts to reformulate scientific and mathematical theories to remove reference to mathematical entities. The premise that we should believe in all the entities of science has also been subject to criticism by a variety of philosophers, including Penelope Maddy, Elliott Sober, and Joseph Melia. The arguments of these writers inspired a new explanatory version of the argument, supported by Alan Baker and Mark Colyvan, that argues that mathematics is indispensable not just to whole theories, but also to specific scientific explanations. (en)
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- Marcus (en)
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- Putnam (en)
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- §6.1 (en)
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- §2 (en)
- §4 (en)
- §2.1 (en)
- §2a (en)
- §3.2 (en)
- §5 (en)
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- Marcus (en)
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- §4 (en)
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- §7 (en)
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- §2 (en)
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- The Quine–Putnam indispensability argument, also known simply as the indispensability argument, is an argument in the philosophy of mathematics for the existence of abstract mathematical objects such as numbers and sets, a position known as mathematical platonism. Named after the philosophers Willard Quine and Hilary Putnam, it is one of the most important arguments in the philosophy of mathematics and is widely considered to be one of the best arguments for platonism. (en)
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- Quine–Putnam indispensability argument (en)
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