3 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). |
| 20436 | Art leads to mental health, and mental clarity [Beardsley,M, by Carroll,N] |
| Full Idea: Beardsley says aesthetic experience relieves tensions and quiet destructive emotions. It also aids us in sorting out the jumble in the flow of consciousness, by virtue of its tendencies toward heightened clarity and coherence. | |
| From: report of Monroe Beardsley (Aesthetics: problems in the philosophy of criticism [1958]) by Noël Carroll - Monroe Beardsley p.162-3 | |
| A reaction: I find this claim highly implausible. I like art, but I feel neither healthier nor clearer after experiencing it. |
| 1497 | For Anaximenes nature is air, which takes different forms by rarefaction and condensation [Anaximenes, by Simplicius] |
| Full Idea: Unlike Anaximander, Anaximenes' underlying nature is not boundless, but specific, since he says that it is air, and claims that it is thanks to rarefaction and condensation that it manifests in different forms in different things. | |
| From: report of Anaximenes (fragments/reports [c.546 BCE], A5) by Simplicius - On Aristotle's 'Physics' 9.24.26- |