display all the ideas for this combination of philosophers
3 ideas
| 24030 | 3+4=7 is necessary because we cannot conceive of seven without including three and four [Descartes] |
| Full Idea: When I say that four and three make seven, this connection is necessary, because one cannot conceive the number seven distinctly without including in it in a confused way the number four and the number three. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 12) | |
| A reaction: This seems to make the truths of arithmetic conceptual, and hence analytic. |
| 2301 | We know by thought that what is done cannot be undone [Descartes] |
| Full Idea: Some ideas belong exclusively to the mind, such as perceiving that what has been done cannot be undone, and everything else that is known by the light of nature. | |
| From: René Descartes (Meditations [1641], §6.82) |
| 3642 | Pythagoras' Theorem doesn't cease to be part of the essence of triangles just because we doubt it [Arnauld on Descartes] |
| 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'. | |
| From: comment on René Descartes (Meditations [1641], §6.78) by Antoine Arnauld - Objections to 'Meditations' (Fourth) 202 |