9 ideas
| 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. |
| 21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
| Full Idea: Cantor proved that the number of sets in a collection of terms is larger than the number of terms. Hence Cantor's Paradox says the number of sets in the collection of all sets must be larger than the number of sets in the collection of all sets. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: The sets must count as terms in the next iteration, but that is a normal application of the Power Set axiom. |
| 21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
| Full Idea: The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: Formulated by Burali-Forti in 1897. |
| 18086 | Weierstrass eliminated talk of infinitesimals [Weierstrass, by Kitcher] |
| Full Idea: Weierstrass effectively eliminated the infinitesimalist language of his predecessors. | |
| From: report of Karl Weierstrass (works [1855]) by Philip Kitcher - The Nature of Mathematical Knowledge 10.6 |
| 18092 | Weierstrass made limits central, but the existence of limits still needed to be proved [Weierstrass, by Bostock] |
| Full Idea: After Weierstrass had stressed the importance of limits, one now needed to be able to prove the existence of such limits. | |
| From: report of Karl Weierstrass (works [1855]) by David Bostock - Philosophy of Mathematics 4.4 | |
| A reaction: The solution to this is found in work on series (going back to Cauchy), and on Dedekind's cuts. |
| 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? |