3 ideas
| 15382 | Paraconsistent reasoning can just mean responding sensibly to inconsistencies [Jago] |
| Full Idea: A practical application of paraconsistent reasoning is in large databases. It does not mean that contradictions could be true, but only that we sometimes need to draw sensible conclusions from inconsistent data. 'Dialethists' believe some contradictions. | |
| From: Mark Jago (Paraconsistent Logic [2010]) | |
| A reaction: Interesting as a more cautious and sensible attitude to the scandal of paraconsistency. |
| 18189 | ZFC could contain a contradiction, and it can never prove its own consistency [MacLane] |
| Full Idea: We have at hand no proof that the axioms of ZFC for set theory will never yield a contradiction, while Gödel's second theorem tells us that such a consistency proof cannot be conducted within ZFC. | |
| From: Saunders MacLane (Mathematics: Form and Function [1986], p.406), quoted by Penelope Maddy - Naturalism in Mathematics | |
| A reaction: Maddy quotes this, while defending set theory as the foundation of mathematics, but it clearly isn't the most secure foundation that could be devised. She says the benefits of set theory do not need guaranteed consistency (p.30). |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| Full Idea: Anaxarchus said that he was not even sure that he knew nothing. | |
| From: report of Anaxarchus (fragments/reports [c.340 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.10.1 |