3 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. |
| 19413 | If we know what is good or rational, our knowledge is extended, and our free will restricted [Leibniz] |
| Full Idea: The more perfect one is, the more one is determined to the good, and so is more free at the same time. ...Our power and knowledge are more extended, and our will much the more limited within the bounds of perfect reason. | |
| From: Gottfried Leibniz (Letters to Pierre Bayle [1702], 1702) | |
| A reaction: I like this idea, which seems to me to derive from Aquinas. When I choose to eat and drink each day, or agree that 7+5 is 12, I don't complain about my lack of freedom in the choices. Goodness and reason are constraints I welcome. |
| 4422 | The end need not be the goal, as in the playing of a melody (and yet it must be completed) [Nietzsche] |
| Full Idea: Not every end is the goal; the end of a melody is not its goal; and yet: as long as the melody has not reached its end, it also hasn't reached its goal. A parable. | |
| From: Friedrich Nietzsche (The Wanderer and his Shadow [1880], §204) | |
| A reaction: A nice message for Aristotle, that there is no simple separation of ends and means. |