Argument
Quine–Putnam indispensability argument
Overview
The Quine–Putnam 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. It was named after the philosophers Willard Van Orman Quine and Hilary Putnam, and is one of the most important arguments in the philosophy of mathematics.
Although elements of the indispensability argument may have originated with 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 naturalism, confirmational holism, and the criterion of ontological commitment. Putnam gave Quine's argument its first detailed formulation in his 1971 book Philosophy of Logic. He later came to disagree with various aspects of Quine's thinking, however, and formulated 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 differs in important ways from their formulations. It is presented in the Stanford Encyclopedia of Philosophy:
We ought to have ontological commitment to all and only the entities that are indispensable to our best scientific theories.
Mathematical entities are indispensable to our best scientific theories.
Therefore, we ought to have ontological commitment to mathematical entities.
Nominalists, philosophers who reject the existence of abstract objects, have argued against both premises of this argument. An influential argument by Hartry Field claims that mathematical entities are dispensable to science. This argument has been supported by attempts to demonstrate that scientific and mathematical theories can be reformulated to remove all references to mathematical entities. Other philosophers, including Penelope Maddy, Elliott Sober, and Joseph Melia, have argued that we do not need to believe in all of the entities that are indispensable to science. The arguments of these writers inspired a new explanatory version of the argument, which Alan Baker and Mark Colyvan support, that argues mathematics is indispensable to specific scientific explanations as well as whole theories.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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XLIX. That the eternal truths cannot be thus enumerated, but that this is not necessary. What I have already enumerated we are to regard as things, or the qualities or modes of things. We now come to speak of eternal truths. When we apprehend that it is impossible a thing can arise from nothing, this proposition, EX NIHILO NIHIL FIT, is not considered as somewhat existing, or as the mode of a thing, but as an…
René Descartes, Selections from the Principles of Philosophy
States what Quine–Putnam indispensability argument is; the author is tied to Quine–Putnam indispensability argument in the knowledge graph.
Eleventh Proposition. “The existence of the infinite is in every respect impossible.” The following is an explanation of this proposition. The impossibility of the existence of an infinite body has been clearly demonstrated; the same can be said of an infinite number of bodies, though each of them be finite, if these beings, infinite in number, exist at…
Moses Maimonides, The guide for the perplexed
States what Quine–Putnam indispensability argument is.
The logical basis of the theory alone belongs to philosophy, and alone will occupy us to-night. The way the problem of continuity enters into philosophy is, broadly speaking, the following: Space and time are treated by mathematicians as consisting of points and instants, but they also have a property, easier to feel than to define, which is called continuity, and is thought by many philosophers to be destroyed when…
Bertrand Russell, Our Knowledge of the External World as a Field for Scientific Method in Philosophy
States what Quine–Putnam indispensability argument is.
Philosophers who discussed Quine–Putnam indispensability argument
Related ideas
- First-order logic
- Nelson Goodman
- Paul Benacerraf
- Classical physics
- Zermelo–Fraenkel set theory
- Hartry Field
- Modal realism
- Formalism (philosophy of mathematics)
- Cartesian doubt
- Kurt Gödel
- Contingency (philosophy)
- Logical positivism
- Metaphysics
- Mathematical object
- Internet Encyclopedia of Philosophy
- Constructivism (philosophy of mathematics)
- David Malet Armstrong
- Nominalism
- Number theory
- Explanatory power
- Ontology
- Plato
- Word and Object
- Simplicity
Place in the tradition
Part of Analytic philosophy.
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