5 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). |
| 7777 | We accept a metaphor when we see the sentence is false [Davidson] |
| Full Idea: It is only when a sentence is taken to be false that we accept it as a metaphor. | |
| From: Donald Davidson (What Metaphors Mean [1978], p.40) | |
| A reaction: This strikes me as a very nice and true generalisation, even though Davidson mentions "no man is an island" as a counterexample. We thirst for meaning, and switch to a second meaning when the first one looks peculiar. |
| 7775 | Understanding a metaphor is a creative act, with no rules [Davidson] |
| Full Idea: Understanding a metaphor is as much a creative endeavour as making a metaphor, and as little guided by rules. | |
| From: Donald Davidson (What Metaphors Mean [1978], p.29) | |
| A reaction: This is good news for literature studies courses. Davidson's point is that the metaphor itself only gives you a literal meaning, so it doesn't tell you how to interpret it. It seems an attractive proposal. |
| 7776 | Metaphors just mean what their words literally mean [Davidson] |
| Full Idea: Metaphors mean what the words, in their most literal interpretation, mean, and nothing more. | |
| From: Donald Davidson (What Metaphors Mean [1978], p.30) | |
| A reaction: This pronouncement must be the result of Davidson anguishing over the truth conditions for metaphors, which are usually either taken to have a 'metaphorical meaning', or to be abbreviated similes. He solved his problem at a stroke! Plausible. |
| 9425 | Lewis later proposed the axioms at the intersection of the best theories (which may be few) [Mumford on Lewis] |
| Full Idea: Later Lewis said we must choose between the intersection of the axioms of the tied best systems. He chose for laws the axioms that are in all the tied systems (but then there may be few or no axioms in the intersection). | |
| From: comment on David Lewis (Subjectivist's Guide to Objective Chance [1980], p.124) by Stephen Mumford - Laws in Nature |