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Single Idea 14604
[filed under theme 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
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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
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If it can't be expressed mathematically, it can't occur in nature?
[Heisenberg]
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18198
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Mathematics is part of science; transfinite mathematics I take as mostly uninterpreted
[Quine]
|
9556
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Nearly all of mathematics has to quantify over abstract objects
[Quine]
|
9941
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Science requires more than consistency of mathematics
[Putnam]
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18199
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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]
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9623
|
Field needs a semantical notion of second-order consequence, and that needs sets
[Brown,JR on Field,H]
|
8863
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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]
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8712
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Mathematics should be treated as true whenever it is indispensable to our best physical theory
[Friend]
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