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Single Idea 10261

[filed under theme 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics ]

Full Idea

Field argues that to account for the applicability of mathematics, we need to assume little more than the possibility of the mathematics, not its truth.

Gist of Idea

The application of mathematics only needs its possibility, not its truth

Source

report of Hartry Field (Science without Numbers [1980]) by Stewart Shapiro - Philosophy of Mathematics 7.2

Book Ref

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.223

A Reaction

Very persuasive. We can apply chess to real military situations, provided that chess isn't self-contradictory (or even naturally impossible?).

The 17 ideas with the same theme [maths as a necessity for empirical investigation]:

17536 If it can't be expressed mathematically, it can't occur in nature? [Heisenberg]
18198 Mathematics is part of science; transfinite mathematics I take as mostly uninterpreted [Quine]
9556 Nearly all of mathematics has to quantify over abstract objects [Quine]
9941 Science requires more than consistency of mathematics [Putnam]
18199 Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam]
8857 We must quantify over numbers for science; but that commits us to their existence [Putnam]
8732 It is spooky the way mathematics anticipates physics [Weinberg]
18150 Actual measurement could never require the precision of the real numbers [Bostock]
3143 Physics requires the existence of properties, and also the abstract objects of arithmetic [Rey]
10261 The application of mathematics only needs its possibility, not its truth [Field,H, by Shapiro]
18218 Hilbert explains geometry, by non-numerical facts about space [Field,H]
9623 Field needs a semantical notion of second-order consequence, and that needs sets [Brown,JR on Field,H]
8863 We must treat numbers as existing in order to express ourselves about the arrangement of planets [Yablo]
18204 Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy]
18207 Maybe applications of continuum mathematics are all idealisations [Maddy]
14604 If a notion is ontologically basic, it should be needed in our best attempt at science [Schaffer,J]
8712 Mathematics should be treated as true whenever it is indispensable to our best physical theory [Friend]