3 ideas
| 23367 | Even pointing a finger should only be done for a reason [Epictetus] |
| Full Idea: Philosophy says it is not right even to stretch out a finger without some reason. | |
| From: Epictetus (fragments/reports [c.57], 15) | |
| A reaction: The key point here is that philosophy concerns action, an idea on which Epictetus is very keen. He rather despise theory. This idea perfectly sums up the concept of the wholly rational life (which no rational person would actually want to live!). |
| 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). |
| 16697 | Time is independent of motion, because God could stop everything for a short or long time [Crathorn, by Pasnau] |
| Full Idea: Suppose God annihilates everything, and then creates something new. The vacant interval could last a shorter or longer time, so there are facts about time independent of facts about motion. | |
| From: report of William Crathorn (Sentences [1335], I.16, concl.2) by Robert Pasnau - Metaphysical Themes 1274-1671 18.2 | |
| A reaction: Not very persuasive if God is in some way 'timeless'. Crathorn would have loved Shoemaker's argument, where motionless time is the best explanation, rather than a possible explanation. |