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). |
| 1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
| Full Idea: I regard you all as relatives - by nature, not by convention. By nature like is akin to like, but convention is a tyrant over humankind and often constrains people to act contrary to nature. | |
| From: Hippias (fragments/reports [c.430 BCE]), quoted by Plato - Protagoras 337c8 |
| 20575 | Socialist economics needs a very strong central power, virtually leading to slavery [Hayek, by Oksala] |
| Full Idea: Hayek argues that socialist economic equality can only be effectively put into practice by a strong, dictatorial government. Planning has to be imposed by force, and centralised economic power creates a dependency scarcely distingishable from slavery. | |
| From: report of F.A. Hayek (The Road to Serfdom [1944]) by Johanna Oksala - Political Philosophy: all that matters Ch.7 | |
| A reaction: I don't see much sign of the post-war British Labour government being anything like this, even though they nationalised the railways and introduce a national health service. Hayek was mesmerised by Russia. |
| 22599 | Hayek was a liberal, but mainly concerned with market freedom [Hayek, by Dunt] |
| Full Idea: Hayek was a liberal (rather than a conservative), …but the individual liberty he cared about was not diversity or freedom of thought. It was freedom to operate in the market. | |
| From: report of F.A. Hayek (The Road to Serfdom [1944]) by Ian Dunt - How to be a Liberal 7 | |
| A reaction: There seems to have been a drift from obsession with freedom to participate in the market, towards the less plausible idea that market forces can solve everything. I once met someone who was convinced the market could solve environmental problems. |
| 22600 | Impeding the market is likely to lead to extensive state control [Hayek] |
| Full Idea: Once the free working of the market is impeded beyond a certain degree, the planner will be forced to extend his controls until they become all comprehensive. | |
| From: F.A. Hayek (The Road to Serfdom [1944]), quoted by Ian Dunt - How to be a Liberal 7 | |
| A reaction: Hayek was terrified of totalitarianism (quite reasonably), but fascism and communism don't seem to have arisen in the way he describes. I'm not clear why sensible intervention in the market should slide down into nightmare. |