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Full Idea
Just as one can extend the domain of discourse to include solutions to the equation 'x^2=-1' so one can extend the domain of discourse to include objects that satisfy the condition 'x is the sum of the G's' or 'x is a temporal part of the object b at t'.
Gist of Idea
Just as we introduced complex numbers, so we introduced sums and temporal parts
Source
Kit Fine (The Question of Ontology [2009], p.164)
Book Ref
'Metametaphysics', ed/tr. Chalmers/Manley/Wasserman [OUP 2009], p.164
A Reaction
This thought lies behind Fine's 'Proceduralism'. I take it that our collection of abstracta consists entirely of items we have either deliberately or unthinkingly 'introduced' into our discourse when they seemed useful. They then submit to certain laws.
| 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] |