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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.
| 5105 | The incommensurability of the diagonal always exists, and so it is not in time [Aristotle] |
| 8910 | General and universal are not real entities, but useful inventions of the mind, concerning words or ideas [Locke] |
| 6717 | Abstract ideas are impossible [Berkeley] |
| 7700 | We can't think about the abstract idea of triangles, but only of particular triangles [Hume] |
| 8911 | If abstracta are non-mental, quarks are abstracta, and yet chess and God's thoughts are mental [Rosen on Frege] |
| 8634 | The equator is imaginary, but not fictitious; thought is needed to recognise it [Frege] |
| 8960 | Internal questions about abstractions are trivial, and external ones deeply problematic [Carnap, by Szabó] |
| 10136 | Points in Euclidean space are abstract objects, but not introduced by abstraction [Fine,K] |
| 10144 | Postulationism says avoid abstract objects by giving procedures that produce truth [Fine,K] |
| 10145 | Abstracts cannot be identified with sets [Fine,K] |
| 12212 | Just as we introduced complex numbers, so we introduced sums and temporal parts [Fine,K] |
| 4239 | Nominalists deny abstract objects, because we can have no reason to believe in their existence [Lowe] |
| 14592 | Some abstract things have a beginning and end, so may exist in time (though not space) [Swoyer] |