40 ideas
| 22338 | An unexamined life can be virtuous [Murdoch] |
| 22337 | Philosophy must keep returning to the beginning [Murdoch] |
| 23563 | Philosophy moves continually between elaborate theories and the obvious facts [Murdoch] |
| 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] |
| 22341 | Literature is the most important aspect of culture, because it teaches understanding of living [Murdoch] |
| 22347 | Appreciating beauty in art or nature opens up the good life, by restricting selfishness [Murdoch] |
| 22339 | Love is a central concept in morals [Murdoch] |
| 22348 | Ordinary human love is good evidence of transcendent goodness [Murdoch] |
| 22343 | If I attend properly I will have no choices [Murdoch] |
| 22349 | Art trains us in the love of virtue [Murdoch] |
| 22340 | It is hard to learn goodness from others, because their virtues are part of their personal history [Murdoch] |
| 22350 | Only trivial virtues can be possessed on their own [Murdoch] |
| 22346 | Moral reflection and experience gradually reveals unity in the moral world [Murdoch] |
| 22342 | Kantian existentialists care greatly for reasons for action, whereas Surrealists care nothing [Murdoch] |
| 22351 | Only a philosopher might think choices create values [Murdoch] |
| 22345 | Moral philosophy needs a central concept with all the traditional attributes of God [Murdoch] |
| 16712 | Atheism is an atrocious and intolerable crime in any country [Descartes] |