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Full Idea
Let any man try to conceive a triangle in general, which is neither Isoceles nor Scalenum, nor has any particular length or proportion of sides; and he will perceive the absurdity of all the scholastic notions with regard to abstraction and general ideas.
Clarification
Isoceles and Scalene are particular shapes of triangle
Gist of Idea
We can't think about the abstract idea of triangles, but only of particular triangles
Source
David Hume (Enquiry Conc Human Understanding [1748], XII.II.122)
Book Ref
Hume,David: 'Enquiries Conc. Human Understanding, Morals', ed/tr. Selby-Bigge/Nidditch [OUP 1975], p.155
A Reaction
I think there is a basic error in this. I admit that I can only imagine a particular triangle, but it doesn't follow that I am thinking about one triangle. Ontology/epistemology confusion. I picture a shape while believing the shape to be irrelevant.
| 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] |