42 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] |
| 1350 | Continuity is needed for existence, otherwise we would say a thing existed after it ceased to exist [Reid] |
| 21322 | We treat slowly changing things as identical for the sake of economy in language [Reid] |
| 21320 | Identity is familiar to common sense, but very hard to define [Reid] |
| 1367 | Identity can only be affirmed of things which have a continued existence [Reid] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 23644 | Without memory we could have no concept of duration [Reid] |
| 23643 | We all trust our distinct memories (but not our distinct imaginings) [Reid] |
| 1356 | A person is a unity, and doesn't come in degrees [Reid] |
| 1359 | Personal identity is the basis of all rights, obligations and responsibility [Reid] |
| 21319 | I can hardly care about rational consequence if it wasn't me conceiving the antecedent [Reid] |
| 21323 | The identity of a thief is only known by similarity, but memory gives certainty in our own case [Reid] |
| 21321 | Memory reveals my past identity - but so does testimony of other witnesses [Reid] |
| 21324 | If consciousness is transferable 20 persons can be 1; forgetting implies 1 can be 20 [Reid] |
| 21325 | Boy same as young man, young man same as old man, old man not boy, if forgotten! [Reid] |
| 21327 | If a stolen horse is identified by similitude, its identity is not therefore merely similitude [Reid] |
| 1366 | If consciousness is personal identity, it is continually changing [Reid] |
| 1352 | Thoughts change continually, but the self doesn't [Reid] |
| 22745 | Pherecydes said the first principle and element is earth [Pherecydes, by Sext.Empiricus] |
| 5883 | Pherecydes was the first to say that the soul is eternal [Pherecydes, by Cicero] |