44 ideas
| 9912 | There are no such things as numbers [Benacerraf] |
| 9901 | Numbers can't be sets if there is no agreement on which sets they are [Benacerraf] |
| 9151 | Benacerraf says numbers are defined by their natural ordering [Benacerraf, by Fine,K] |
| 13891 | To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C] |
| 17904 | A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf] |
| 17906 | To explain numbers you must also explain cardinality, the counting of things [Benacerraf] |
| 9898 | We can count intransitively (reciting numbers) without understanding transitive counting of items [Benacerraf] |
| 17903 | Someone can recite numbers but not know how to count things; but not vice versa [Benacerraf] |
| 9897 | The application of a system of numbers is counting and measurement [Benacerraf] |
| 9900 | For Zermelo 3 belongs to 17, but for Von Neumann it does not [Benacerraf] |
| 9899 | The successor of x is either x and all its members, or just the unit set of x [Benacerraf] |
| 8697 | Disputes about mathematical objects seem irrelevant, and mathematicians cannot resolve them [Benacerraf, by Friend] |
| 8304 | No particular pair of sets can tell us what 'two' is, just by one-to-one correlation [Benacerraf, by Lowe] |
| 9906 | If ordinal numbers are 'reducible to' some set-theory, then which is which? [Benacerraf] |
| 9907 | If any recursive sequence will explain ordinals, then it seems to be the structure which matters [Benacerraf] |
| 9908 | The job is done by the whole system of numbers, so numbers are not objects [Benacerraf] |
| 9909 | The number 3 defines the role of being third in a progression [Benacerraf] |
| 9911 | Number words no more have referents than do the parts of a ruler [Benacerraf] |
| 8925 | Mathematical objects only have properties relating them to other 'elements' of the same structure [Benacerraf] |
| 9938 | How can numbers be objects if order is their only property? [Benacerraf, by Putnam] |
| 9910 | Number-as-objects works wholesale, but fails utterly object by object [Benacerraf] |
| 9903 | Number words are not predicates, as they function very differently from adjectives [Benacerraf] |
| 9904 | The set-theory paradoxes mean that 17 can't be the class of all classes with 17 members [Benacerraf] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| 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] |