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Full Idea
Arguments such as the dispensability argument are attempting to show something about the essentially non-numerical character of physical reality, rather than something about the nature or non-existence of the numbers themselves.
Gist of Idea
The indispensability argument shows that nature is non-numerical, not the denial of numbers
Source
Kit Fine (The Question of Ontology [2009], p.160)
Book Ref
'Metametaphysics', ed/tr. Chalmers/Manley/Wasserman [OUP 2009], p.160
A Reaction
This is aimed at Hartry Field. If Quine was right, and we only believe in numbers because of our science, and then Field shows our science doesn't need it, then Fine would be wrong. Quine must be wrong, as well as Field.
| 12211 | It is plausible that x^2 = -1 had no solutions before complex numbers were 'introduced' [Fine,K] |
| 12209 | The indispensability argument shows that nature is non-numerical, not the denial of numbers [Fine,K] |
| 12212 | Just as we introduced complex numbers, so we introduced sums and temporal parts [Fine,K] |
| 12214 | 'Exists' is a predicate, not a quantifier; 'electrons exist' is like 'electrons spin' [Fine,K] |
| 12213 | Ontological claims are often universal, and not a matter of existential quantification [Fine,K] |
| 12215 | The existence of numbers is not a matter of identities, but of constituents of the world [Fine,K] |
| 12216 | Real objects are those which figure in the facts that constitute reality [Fine,K] |
| 12218 | Being real and being fundamental are separate; Thales's water might be real and divisible [Fine,K] |
| 12217 | For ontology we need, not internal or external views, but a view from outside reality [Fine,K] |