37 ideas
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| 10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| 10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
| 10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
| 10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
| 10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
| 10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
| 10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
| 10763 | Completeness and compactness together give axiomatizability [Tharp] |
| 10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
| 10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
| 10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
| 10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
| 10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
| 23125 | Most good social changes are incremental, rather than revolutionary [Gopnik] |
| 23126 | Conservatives often want peace, prosperity and tolerance, but not social fairness [Gopnik] |
| 23132 | Conservatives believe obedience and rank are essential to social order [Gopnik] |
| 23128 | The opposite of liberalism is dogmatism [Gopnik] |
| 23142 | People are fallible, so liberalism tries to distribute power [Gopnik] |
| 23143 | Liberals have tried very hard to build a conscience into their institutions [Gopnik] |
| 23141 | Left-wingers are inconsistent in their essentialist descriptions of social groups [Gopnik] |
| 23124 | Liberal community is not blood ties or tradition, but shared choices, and sympathy for the losers [Gopnik] |
| 23127 | Liberal community includes flight from the family, into energetic reforming groups [Gopnik] |
| 23129 | Right-wingers attack liberal faith in reason, left-wingers attack its faith in reform [Gopnik] |
| 23133 | Cosmopolitan liberals lack national loyalty, and welcome excessive immigration [Gopnik] |
| 23138 | Modern left-wingers criticise liberalism's control of culture [Gopnik] |
| 23139 | Liberalism's attempt to be neutral and colour-blind erases cultural identities [Gopnik] |
| 23135 | Classic Marxists see liberalism as the ideology of the bourgeoisie [Gopnik] |
| 23140 | Environmental disasters result not from capitalism, but from a general drive for growth [Gopnik] |
| 23130 | Popular imperialism gives the poor the belief that their acts have world historical meaning [Gopnik] |
| 23131 | Patriots love their place, but nationalists have a paranoid ethnic hostility [Gopnik] |
| 23136 | Liberal free speech is actually paid speech [Gopnik] |
| 23134 | A 'free' society implies a free market, which always produces predatory capitalism and inequalities [Gopnik] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |