4 ideas
| 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). |
| 490 | Everything happens by reason and necessity [Leucippus] |
| Full Idea: Nothing happens at random; everything happens out of reason and by necessity. | |
| From: Leucippus (fragments/reports [c.435 BCE], B002), quoted by (who?) - where? |
| 6027 | From the fact that some men die, we cannot infer that they all do [Philodemus] |
| Full Idea: There is no necessary inference, from the fact that men familiar to us die when pierced through the heart, that all men do. | |
| From: Philodemus (On Signs (damaged) [c.50 BCE], 1.3) | |
| A reaction: This is scepticism about the logic of induction, long before David Hume. This is said to be a Stoic argument against Epicureans - though on the whole Stoics are not keen on scepticism. |
| 22241 | Don't fear god or worry about death; the good is easily got and the terrible easily cured [Philodemus] |
| Full Idea: Don't fear god, Don't worry about death; What is good is easy to get, What is terrible is easy to cure. | |
| From: Philodemus (Herculaneum Papyrus [c.50 BCE], 1005,4.9-14) | |
| A reaction: This is known as the Four-Part Cure, and is an epicurean prayer, probably formulated by Epicurus. |