4 ideas
| 16676 | Why use more things when fewer will do? [William of Ockham] |
| Full Idea: It is pointless to do through more things something that can be done through fewer. | |
| From: William of Ockham (Tractatus de corpore Christi [1323], Ch. 29), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 14.3 | |
| A reaction: The more famous formulation isn't found in his works, so I'm delighted to find an authentic quotation from the man. |
| 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. |
| 16675 | Every extended material substance is composed of parts distant from one another [William of Ockham] |
| Full Idea: Every extended material substance is composed of substantial parts distant from one another in place or location. | |
| From: William of Ockham (Tractatus de corpore Christi [1323], Ch. 12) | |
| A reaction: Pasnau glosses this as that 'bodies have corpuscular structure', meaning that they are made up of parts of matter (rather than just enformed matter, I think). |