more from this thinker
|
more from this text
Single Idea 8857
[filed under theme 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
]
Full Idea
Quantification over mathematical entities is indispensable for science..., therefore we should accept such quantification; but this commits us to accepting the existence of the mathematical entities in question.
Gist of Idea
We must quantify over numbers for science; but that commits us to their existence
Source
Hilary Putnam (The Philosophy of Logic [1971], p.57), quoted by Stephen Yablo - Apriority and Existence
Book Ref
'New Essays on the A Priori', ed/tr. Boghossian,P /Peacocke,C [OUP 2000], p.197
A Reaction
I'm not surprised that Hartry Field launched his Fictionalist view of mathematics in response to such a counterintuitive claim. I take it we use numbers to slice up reality the way we use latitude to slice up the globe. No commitment to lines!
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]
|