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7. Existence / A. Nature of Existence / 4. Abstract Existence

[existing non-causally and outside space-time]

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