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| 16279 | General causal theories of knowledge are refuted by mathematics [Lewis] |
| Full Idea: Causal accounts of knowledge are all very well in their place, but if they are put forward as general theories, then mathematics refutes them. | |
| From: David Lewis (On the Plurality of Worlds [1986], 2.4) | |
| A reaction: You might have some sort of notion of an abstraction from causation which mimicked it in the mathematics case. Lots of things seem to be 'forced' in mathematics. Call it 'ersatz causation'. Necessities are enforcers. |
| 12417 | Mathematicians only accept their own proofs when everyone confims them [Hume] |
| Full Idea: There is no Mathematician so expert as to place entire confidence in any truth upon his discovery of it. ..Every time he runs over his proofs his confidence encreases, ..and is rais'd to perfection by the applause of the learned world. | |
| From: David Hume (Treatise of Human Nature [1739], IV.1.4) | |
| A reaction: [compressed] Quoted by Kitcher, and a nice example of the social nature of 'warrants', even in mathematics. It was illustrated well in the 1990s by the story of the proof of Fermat's Last Theorem by Andrew Wiles. |