51 ideas
| 501 | Reason is a more powerful persuader than gold [Democritus (attr)] |
| 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] |
| 514 | Beauty is merely animal without intelligence [Democritus (attr)] |
| 525 | Behave well when alone, and feel shame in you own eyes [Democritus (attr)] |
| 502 | Good breeding in men means having a good character [Democritus (attr)] |
| 507 | Virtuous love consists of decorous desire for the beautiful [Democritus (attr)] |
| 521 | We should only choose pleasures which are concerned with the beautiful [Democritus (attr)] |
| 505 | Good and true are the same for everyone, but pleasures differ [Democritus (attr)] |
| 508 | Only accept beneficial pleasures [Democritus (attr)] |
| 520 | The great pleasures come from the contemplation of noble works [Democritus (attr)] |
| 522 | Moderation brings more pleasures, and so increases pleasure [Democritus (attr)] |
| 506 | Immoderate desire is the mark of a child, not an adult [Democritus (attr)] |
| 523 | It is as brave to master pleasure as to overcome the enemy [Democritus (attr)] |
| 503 | Virtue doesn't just avoid evil, but also doesn't desire it [Democritus (attr)] |
| 518 | A bad life is just a drawn-out death [Democritus (attr)] |
| 497 | Be virtuous from duty, not from fear [Democritus (attr)] |
| 499 | Repentance of shameful deeds is salvation [Democritus (attr)] |
| 524 | Virtue comes more from practice than from nature [Democritus (attr)] |
| 519 | One must avoid even speaking of evil deeds [Democritus (attr)] |
| 500 | The wrongdoer is more unfortunate than the person wronged [Democritus (attr)] |
| 1539 | The endless desire for money is a crueller slavery than poverty [Democritus (attr)] |
| 526 | Small appetite makes poverty equal to wealth [Democritus (attr)] |
| 511 | It is better to have one intelligent friend than many unintelligent [Democritus (attr)] |
| 498 | It is a great thing, when one is in adversity, to think of duty [Democritus (attr)] |
| 1541 | It is better to be poor in a democracy than be rich without freedom [Democritus (attr)] |
| 20575 | Socialist economics needs a very strong central power, virtually leading to slavery [Hayek, by Oksala] |
| 22599 | Hayek was a liberal, but mainly concerned with market freedom [Hayek, by Dunt] |
| 22600 | Impeding the market is likely to lead to extensive state control [Hayek] |