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. |
| 8800 | If you would deny a truth if you know the full evidence, then knowledge has social aspects [Harman, by Sosa] |
| Full Idea: If one reads of a genuine assassination, but then fails to read the reports next day which untruthfully deny the event, one probably does not know of the event. But we must conclude that knowledge has a further 'social aspect'. | |
| From: report of Gilbert Harman (Induction [1970], §IV) by Ernest Sosa - The Raft and the Pyramid Appx | |
| A reaction: I doubt if this is enough to support an externalist account of defeasibility. Wise people don't 'know' of an event after one report. For 24 hours the Royalists thought they had won Marston Moor! You know he's dead when you see the Zapruder film. |