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Full Idea
You can't reason 'I know the triangle is right-angled, but I doubt Pythagoras' Theorem, therefore it does not belong to the essence of right-angled triangles that the square on the hypotenuse is equal to the sum of the squares on the other two sides'.
Gist of Idea
Pythagoras' Theorem doesn't cease to be part of the essence of triangles just because we doubt it
Source
comment on René Descartes (Meditations [1641], §6.78) by Antoine Arnauld - Objections to 'Meditations' (Fourth) 202
Book Ref
Descartes,René: 'Meditations on First Philosophy etc.', ed/tr. Cottingham,John [CUP 1986], p.109
| 3642 | Pythagoras' Theorem doesn't cease to be part of the essence of triangles just because we doubt it [Arnauld on Descartes] |
| 16582 | We can imagine a point swelling and contracting - but not how this could be done [Hobbes] |
| 11958 | Impossibilites are easily conceived in mathematics and geometry [Reid, by Molnar] |
| 8562 | It is possible to conceive what is not possible [Shoemaker] |
| 15252 | If Goldbach's Conjecture is true (and logically necessary), we may be able to conceive its opposite [Harré/Madden] |
| 9660 | The impossible can be imagined as long as it is a bit vague [Lewis] |
| 2407 | One can wrongly imagine two things being non-identical even though they are the same (morning/evening star) [Chalmers] |
| 3106 | If claims of metaphysical necessity are based on conceivability, we should be cautious [Segal] |
| 10652 | Conceivability may indicate possibility, but literary fantasy does not [Varzi] |
| 14714 | Contradictory claims about a necessary god both seem apriori coherent [Schroeter] |