7 ideas
| 10245 | One geometry cannot be more true than another [Poincaré] |
| Full Idea: One geometry cannot be more true than another; it can only be more convenient. | |
| From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics | |
| A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate. |
| 19406 | I strongly believe in the actual infinite, which indicates the perfections of its author [Leibniz] |
| Full Idea: I am so much for the actual infinite that instead of admitting that nature abhors it, as is commonly said, I hold that it affects nature everywhere in order to indicate the perfections of its author. | |
| From: Gottfried Leibniz (Reply to Foucher [1693], p.99) | |
| A reaction: I would have thought that, for Leibniz, while infinities indicate the perfections of their author, that is not the reason why they exist. God wasn't, presumably, showing off. Leibniz does not think we can actually know these infinities. |
| 3626 | Knowing the attributes is enough to reveal a substance [Descartes] |
| Full Idea: I have never thought that anything more is required to reveal a substance than its various attributes. | |
| From: René Descartes (Reply to Fifth Objections [1641], 360) |
| 3630 | Our thinking about external things doesn't disprove the existence of innate ideas [Descartes] |
| Full Idea: You can't prove that Praxiteles never made any statues on the grounds that he did not get from within himself the marble from which he sculpted them. | |
| From: René Descartes (Reply to Fifth Objections [1641], 362) |
| 3631 | A blind man may still contain the idea of colour [Descartes] |
| Full Idea: How do you know that there is no idea of colour in a man born blind? | |
| From: René Descartes (Reply to Fifth Objections [1641], 363) |
| 3640 | Possible existence is a perfection in the idea of a triangle [Descartes] |
| Full Idea: Possible existence is a perfection in the idea of a triangle, just as necessary existence is a perfection in the idea of God. | |
| From: René Descartes (Reply to Fifth Objections [1641], 383) |
| 3639 | Necessary existence is a property which is uniquely part of God's essence [Descartes] |
| Full Idea: In the case of God necessary existence is in fact a property in the strictest sense of the term, since it applies to him alone and forms a part of his essence as it does of no other thing | |
| From: René Descartes (Reply to Fifth Objections [1641], 383) |