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Full Idea
Points in abstract Euclidean space are abstract objects, and yet are not objects of abstraction, since they are not introduced through a principle of abstraction of the sort envisaged by Frege.
Gist of Idea
Points in Euclidean space are abstract objects, but not introduced by abstraction
Source
Kit Fine (The Limits of Abstraction [2002], I.1)
Book Ref
Fine,Kit: 'The Limits of Abstraction' [OUP 2008], p.9
A Reaction
The point seems to be that they are not abstracted 'from' anything, but are simpy posited as basic constituents. I suggest that points are idealisations (of smallness) rather than abstractions. They are idealised 'from' substances.
| 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] |