11 ideas
| 17879 | Axiomatising set theory makes it all relative [Skolem] |
| Full Idea: Axiomatising set theory leads to a relativity of set-theoretic notions, and this relativity is inseparably bound up with every thoroughgoing axiomatisation. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.296) |
| 13536 | Skolem did not believe in the existence of uncountable sets [Skolem] |
| Full Idea: Skolem did not believe in the existence of uncountable sets. | |
| From: Thoralf Skolem (works [1920], 5.3) | |
| A reaction: Kit Fine refers somewhere to 'unrepentent Skolemites' who still hold this view. |
| 20100 | Classical liberalism seeks freedom of opinion, of private life, of expression, and of property [Micklethwait/Wooldridge] |
| Full Idea: The classical liberals agreed on a basic list of freedoms: of opinion (including religion), of private life, of expression, and of property | |
| From: Micklethwait,J/Wooldridge,A (The Fourth Revolution [2014], 9) | |
| A reaction: Mill is main articulator of this. Modern neo-liberals focus on economic freedom. Neither of them seem to make freedom of opportunity central, though I suspect our modern Liberal Party would. |
| 17878 | If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem] |
| Full Idea: Löwenheim's theorem reads as follows: If a first-order proposition is satisfied in any domain at all, it is already satisfied in a denumerably infinite domain. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.293) |
| 17880 | Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem] |
| Full Idea: The initial foundations should be immediately clear, natural and not open to question. This is satisfied by the notion of integer and by inductive inference, by it is not satisfied by the axioms of Zermelo, or anything else of that kind. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.299) | |
| A reaction: This is a plea (endorsed by Almog) that the integers themselves should be taken as primitive and foundational. I would say that the idea of successor is more primitive than the integers. |
| 17881 | Mathematician want performable operations, not propositions about objects [Skolem] |
| Full Idea: Most mathematicians want mathematics to deal, ultimately, with performable computing operations, and not to consist of formal propositions about objects called this or that. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.300) |
| 20097 | The welfare state aims at freedom from want, and equality of opportunity [Micklethwait/Wooldridge] |
| Full Idea: In the classical liberal tradition freedom meant freedom from external control, and equality meant equality before the law. In the welfare state (of Beatrice Webb) freedom was reinterpreted as freedom from want, and equality as equality of opportunity. | |
| From: Micklethwait,J/Wooldridge,A (The Fourth Revolution [2014], 3) | |
| A reaction: The authors call this the 'third revolution' in government, after 17th century centralisation and early 19th century accountability. Tawney 1931 is the key text. |
| 20099 | For communists history is driven by the proletariat [Micklethwait/Wooldridge] |
| Full Idea: For the communists the proletariat rather than the state was the locomotive of history. | |
| From: Micklethwait,J/Wooldridge,A (The Fourth Revolution [2014], 3) | |
| A reaction: I feel increasingly reluctant to support any party which appears to mainly represent the interests of a single social class, no matter how large that class may be. An attraction of liberalism is that it makes no reference to class. |
| 20098 | Fans of economic freedom claim that capitalism is self-correcting [Micklethwait/Wooldridge] |
| Full Idea: The central laissez-faire conceit is that capitalism is a self-correcting mechanism. | |
| From: Micklethwait,J/Wooldridge,A (The Fourth Revolution [2014], 3) | |
| A reaction: This was Keynes's rather left-wing criticism of standard capitalist views. These resurfaced in the 1980s with mantras about the virtues of 'market forces'. |
| 20096 | Roman law entrenched property rights [Micklethwait/Wooldridge] |
| Full Idea: Roman law entrenched property rights. | |
| From: Micklethwait,J/Wooldridge,A (The Fourth Revolution [2014], 1 Intro) | |
| A reaction: Normally attributed to Locke, so this is a good corrective. Was the principle gradually forgotten before Locke? |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| Full Idea: Hermarchus said that animal killing is justified by considerations of human safety and nourishment and by animals' inability to form contractual relations of justice with us. | |
| From: report of Hermarchus (fragments/reports [c.270 BCE]) by David A. Sedley - Hermarchus | |
| A reaction: Could the last argument be used to justify torturing animals? Or could we eat a human who was too brain-damaged to form contracts? |