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Full Idea
Frege's identification of the abstract with the realm of non-mental things entails that unobservables such as quarks are abstract. The abstract nature of chess, and the possibility of abstracta in the mind of God, show they can be mind-dependent.
Gist of Idea
If abstracta are non-mental, quarks are abstracta, and yet chess and God's thoughts are mental
Source
comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Gideon Rosen - Abstract Objects 'Way of Neg'
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.3
A Reaction
I like the robust question 'if a is said to 'exist', what is it said to be made of?' I consider the views of Frege to have had too much influence in this area, and recognising the role of the mind (psychology!) in abstraction is a start.
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] |