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Single Idea 13417
[filed under theme 7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
]
Full Idea
If experience shows that some aspect of the physical world fails to instantiate a certain mathematical structure, one will modify the theory by sustituting a different structure, while the original structure doesn't lose its status as part of mathematics.
Gist of Idea
If a mathematical structure is rejected from a physical theory, it retains its mathematical status
Source
Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2)
Book Ref
-: 'Philosophia Mathematica' [-], p.224
A Reaction
This seems to be a beautifully simple and powerful objection to the Quinean idea that mathematics somehow only gets its authority from physics. It looked like a daft view to begin with, of course.
The
17 ideas
with the same theme
[troubles with theories of commitment]:
19446
|
To our consciousness it is language which looks unreal
[Feuerbach]
|
18775
|
Russell showed that descriptions may not have ontological commitment
[Russell, by Linsky,B]
|
14490
|
You can be implicitly committed to something without quantifying over it
[Thomasson on Quine]
|
16261
|
If commitment rests on first-order logic, we obviously lose the ontology concerning predication
[Maudlin on Quine]
|
7698
|
If to be is to be the value of a variable, we must already know the values available
[Jacquette on Quine]
|
19492
|
Quine is hopeless circular, deriving ontology from what is literal, and 'literal' from good ontology
[Yablo on Quine]
|
13417
|
If a mathematical structure is rejected from a physical theory, it retains its mathematical status
[Parsons,C]
|
13409
|
Our best theories may commit us to mathematical abstracta, but that doesn't justify the commitment
[Papineau]
|
9558
|
All scientific tests will verify mathematics, so it is a background, not something being tested
[Sober]
|
18499
|
Our quantifications only reveal the truths we accept; the ontology and truthmakers are another matter
[Heil]
|
18205
|
The theoretical indispensability of atoms did not at first convince scientists that they were real
[Maddy]
|
9559
|
If a successful theory confirms mathematics, presumably a failed theory disconfirms it?
[Chihara]
|
9566
|
No scientific explanation would collapse if mathematical objects were shown not to exist
[Chihara]
|
16259
|
Naïve translation from natural to formal language can hide or multiply the ontology
[Maudlin]
|
12438
|
In the vernacular there is no unequivocal ontological commitment
[Azzouni]
|
12441
|
We only get ontology from semantics if we have already smuggled it in
[Azzouni]
|
10637
|
Ordinary speakers posit objects without concern for ontology
[Linnebo]
|