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. |
| 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. |
| 14665 | We can call the quality of Plato 'Platonity', and say it is a quality which only he possesses [Boethius] |
| Full Idea: Let the incommunicable property of Plato be called 'Platonity'. For we can call this quality 'Platonity' by a fabricated word, in the way in which we call the quality of man 'humanity'. Therefore this Platonity is one man's alone - Plato's. | |
| From: Boethius (Librium de interpretatione editio secunda [c.516], PL64 462d), quoted by Alvin Plantinga - Actualism and Possible Worlds 5 | |
| A reaction: Plantinga uses this idea to reinstate the old notion of a haecceity, to bestow unshakable identity on things. My interest in the quotation is that the most shocking confusions about properties arose long before the invention of set theory. |