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Full Idea
The incommensurability of the diagonal always exists, and so it is not in time.
Clarification
A diagonal cannot be expressed as a fraction of whole numbers (e.g. square root of 2)
Gist of Idea
The incommensurability of the diagonal always exists, and so it is not in time
Source
Aristotle (Physics [c.337 BCE], 221b36)
Book Ref
Aristotle: 'Physics', ed/tr. Waterfield,Robin [OUP 1996], p.112
A Reaction
This must make Aristotle sympathetic to Platonism in mathematics, even though he rejects the full theory of Forms. Such a view is not uncommon among modern philosophers. Presumably the incommensurability is true in all possible worlds? 'In'?
| 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] |