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Single Idea 14604

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

Full Idea

Science represents our best systematic understanding of the world, and if a certain notion proves unneeded in our best attempt at that, this provides strong evidence that what this notion concerns is not ontologically basic.

Gist of Idea

If a notion is ontologically basic, it should be needed in our best attempt at science

Source

Jonathan Schaffer (Causation and Laws of Nature [2008], 3.2)

Book Ref

'Contemporary Debates in Metaphysics', ed/tr. Sider/Hawthorne/Zimmerman [Blackwell 2008], p.92

A Reaction

But is the objective of science to find out what is 'ontologically basic'? If scientists can't get a purchase on a question, they have no interest in it. What are electrons made of?

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]