49 ideas
| 21474 | Metaphysics studies the inexplicable ends of explanation [Schopenhauer] |
| 23277 | Modern pragmatism sees objectivity as possible, despite its gradual evolution [Misak] |
| 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] |
| 21470 | For me the objective thing-in-itself is the will [Schopenhauer] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 21479 | Knowledge is not power! Ignorant people possess supreme authority [Schopenhauer] |
| 21476 | A priori propositions are those we could never be seriously motivated to challenge [Schopenhauer] |
| 21473 | All knowledge and explanation rests on the inexplicable [Schopenhauer] |
| 21478 | Half our thinking is unconscious, and we reach conclusions while unaware of premises [Schopenhauer] |
| 21477 | We don't control our own thinking [Schopenhauer] |
| 21475 | All of our concepts are borrowed from perceptual knowledge [Schopenhauer] |
| 21372 | Aesthetics concerns how we can take pleasure in an object, with no reference to the will [Schopenhauer] |
| 21488 | The beautiful is a perception of Plato's Forms, which eliminates the will [Schopenhauer] |
| 21483 | Man is essentially a dreadful wild animal [Schopenhauer] |
| 21466 | Pleasure is weaker, and pain stronger, than we expect [Schopenhauer] |
| 21484 | A man's character can be learned from a single characteristic action [Schopenhauer] |
| 21482 | The five Chinese virtues: pity, justice, politeness, wisdom, honesty [Schopenhauer] |
| 21481 | Buddhists wisely start with the cardinal vices [Schopenhauer] |
| 21480 | Boredom is only felt by those clever enough to need activity [Schopenhauer] |
| 21469 | Human life is a mistake, shown by boredom, which is direct awareness of the fact [Schopenhauer] |
| 21485 | The state only exists to defend citizens, from exterior threats, and from one another [Schopenhauer] |
| 21486 | Poverty and slavery are virtually two words for the same thing [Schopenhauer] |
| 21487 | The freedom of the press to sell poison outweighs its usefulness [Schopenhauer] |
| 21471 | If suicide was quick and easy, most people would have done it by now [Schopenhauer] |
| 21467 | Would humanity still exist if sex wasn't both desired and pleasurable? [Schopenhauer] |
| 21472 | Only religion introduces serious issues to uneducated people [Schopenhauer] |
| 21468 | The Creator created the possibilities for worlds, so should have made a better one than this possible [Schopenhauer] |