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Single Idea 18150
[filed under theme 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
]
Full Idea
We all know that in practice no physical measurement can be 100 per cent accurate, and so it cannot require the existence of a genuinely irrational number, rather than some of the rational numbers close to it.
Gist of Idea
Actual measurement could never require the precision of the real numbers
Source
David Bostock (Philosophy of Mathematics [2009], 9.A.3)
Book Ref
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.280
Related Ideas
Idea 18156
Modern axioms of geometry do not need the real numbers [Bostock]
Idea 18207
Maybe applications of continuum mathematics are all idealisations [Maddy]
The
17 ideas
with the same theme
[maths as a necessity for empirical investigation]:
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17536
|
If it can't be expressed mathematically, it can't occur in nature?
[Heisenberg]
|
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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]
|
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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]
|
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18150
|
Actual measurement could never require the precision of the real numbers
[Bostock]
|
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3143
|
Physics requires the existence of properties, and also the abstract objects of arithmetic
[Rey]
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10261
|
The application of mathematics only needs its possibility, not its truth
[Field,H, by Shapiro]
|
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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]
|
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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]
|
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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
|
Mathematics should be treated as true whenever it is indispensable to our best physical theory
[Friend]
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