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Single Idea 9558

[filed under theme 7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems ]

Full Idea

If mathematical statements are part of every competing hypothesis, then no matter which hypothesis comes out best in the light of observations, they will be part of the best hypothesis. They are not tested, but are a background assumption.

Gist of Idea

All scientific tests will verify mathematics, so it is a background, not something being tested

Source

Elliott Sober (Mathematics and Indispensibility [1993], 45), quoted by Charles Chihara - A Structural Account of Mathematics

Book Ref

Chihara,Charles: 'A Structural Account of Mathematics' [OUP 2004], p.128

A Reaction

This is a very nice objection to the Quine-Putnam thesis that mathematics is confirmed by the ongoing successes of science.

The 17 ideas with the same theme [troubles with theories of commitment]:

19446 To our consciousness it is language which looks unreal [Feuerbach]
18775 Russell showed that descriptions may not have ontological commitment [Russell, by Linsky,B]
14490 You can be implicitly committed to something without quantifying over it [Thomasson on Quine]
16261 If commitment rests on first-order logic, we obviously lose the ontology concerning predication [Maudlin on Quine]
7698 If to be is to be the value of a variable, we must already know the values available [Jacquette on Quine]
19492 Quine is hopeless circular, deriving ontology from what is literal, and 'literal' from good ontology [Yablo on Quine]
13417 If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C]
13409 Our best theories may commit us to mathematical abstracta, but that doesn't justify the commitment [Papineau]
9558 All scientific tests will verify mathematics, so it is a background, not something being tested [Sober]
18499 Our quantifications only reveal the truths we accept; the ontology and truthmakers are another matter [Heil]
18205 The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy]
9559 If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara]
9566 No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara]
16259 Naïve translation from natural to formal language can hide or multiply the ontology [Maudlin]
12438 In the vernacular there is no unequivocal ontological commitment [Azzouni]
12441 We only get ontology from semantics if we have already smuggled it in [Azzouni]
10637 Ordinary speakers posit objects without concern for ontology [Linnebo]