The Quine-Putnam indispensability argument, developed from the work of Willard Van Orman Quine and Hilary Putnam, argues for mathematical Platonism, the view that abstract mathematical objects such as numbers and sets genuinely exist, on the grounds that reference to such objects is indispensable to formulating our best scientific theories. The argument holds that a person who accepts a scientific theory should accept as real all and only the entities that theory quantifies over or otherwise requires, that our best scientific theories cannot be stated without quantifying over mathematical objects, and that therefore anyone who accepts those theories should accept the existence of mathematical objects on the same footing as unobservable physical entities such as electrons. Quine himself limited the argument's force to whatever mathematics science actually requires, explicitly excluding more abstract regions of set theory he described as mathematical recreation without ontological rights, and the argument remains one of the central considerations weighed in debates between mathematical realists and nominalists.
Facts
Origin Year1976 is the earliest year the cited SEP article attaches to Quine on this argument; Quines underlying naturalism dates to his 1948 On What There Is and Putnams own contribution to his 1971 Philosophy of Logic. Classification
Position Kind Sources
1. Indispensability Arguments in the Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)
Stanford Encyclopedia of PhilosophyIndispensability Arguments in the Philosophy of Mathematics (SEP), introduction
One of the most intriguing features of mathematics is its applicability to empirical science.
Indispensability Arguments in the Philosophy of Mathematics (SEP), on Quine and Putnam
Quine (1976; 1980a; 1980b; 1981a; 1981c) and Putnam (1979a; 1979b) have argued that the indispensability of mathematics to empirical science gives us good reason to believe in the existence of mathematical entities.
View the Source Frequently Asked Questions
Did Quine think the indispensability argument justified belief in all of mathematics, including advanced set theory?
No. Quine limited the argument's force to whatever mathematics science actually requires, explicitly excluding more abstract regions of set theory he described as mathematical recreation without ontological rights.
The Quine-Putnam indispensability argument, developed from the work of Willard Van Orman Quine and Hilary Putnam, argues for mathematical Platonism on the grounds that reference to mathematical objects is indispensable to formulating our best scientific theories: a person who accepts a scientific theory should accept as real all and only the entities that theory quantifies over, our best theories cannot be stated without quantifying over mathematical objects, so anyone who accepts those theories should accept mathematical objects on the same footing as unobservable physical entities such as electrons. Quine himself limited the argument's force to whatever mathematics science actually requires, explicitly excluding more abstract regions of set theory he described as mathematical recreation without ontological rights, so the argument on his own view does not extend to every part of mathematics, only the portion empirical science genuinely uses.
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