4 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. |
| 9159 | You can't simply convert geometry into algebra, as some spatial content is lost [Burge] |
| Full Idea: Although one can translate geometrical propositions into algebraic ones and produce equivalent models, the meaning of geometrical propositions seems to me to be thereby lost. Pure geometry involves spatial content, even if abstracted from physical space. | |
| From: Tyler Burge (Frege on Apriority [2000], IV) | |
| A reaction: This supports Frege's view (against Quine) that geometry won't easily fit into the programme of logicism. I agree with Burge. You would be focusing on the syntax of geometry, and leaving out the semantics. |
| 7829 | God no more has human perfections than we have animal perfections [Spinoza] |
| Full Idea: To ascribe to God those attributes which make a man perfect would be as wrong as to ascribe to a man the attributes that make perfect an elephant or an ass. | |
| From: Baruch de Spinoza (Letters to Blijenburgh [1665], 1665), quoted by Matthew Stewart - The Courtier and the Heretic Ch.10 | |
| A reaction: This would be a difficulty for Aquinas's Fourth Way (Idea 1432), and one which I think Aquinas might acknowledge, given his desire that we should be humble when trying to comprehend God (Idea 1410). It leaves us struggling to grasp the concept of God. |
| 7830 | A talking triangle would say God is triangular [Spinoza] |
| Full Idea: If a triangle could speak it would say that God is eminently triangular. | |
| From: Baruch de Spinoza (Letters to Blijenburgh [1665], 1665), quoted by Matthew Stewart - The Courtier and the Heretic Ch.10 | |
| A reaction: Spinoza had a rather appealing waspish wit. This nicely dramatises an ancient idea (Idea 407). You can, of course, if you believe in God, infer some of His characteristics from His creation. But then see Hume: Ideas 1439, 6960, 6967, 1440. |