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] |
| 6472 | Continuity is a sufficient criterion for the identity of a rock, but not for part of a smooth fluid [Russell] |
| 6473 | Physical things are series of appearances whose matter obeys physical laws [Russell] |
| 6465 | We need not deny substance, but there seems no reason to assert it [Russell] |
| 6471 | The assumption by physicists of permanent substance is not metaphysically legitimate [Russell] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 6466 | Where possible, logical constructions are to be substituted for inferred entities [Russell] |
| 6467 | No sensibile is ever a datum to two people at once [Russell] |
| 6483 | Russell held that we are aware of states of our own brain [Russell, by Robinson,H] |
| 8244 | Sense-data are qualities devoid of subjectivity, which are the basis of science [Russell, by Deleuze/Guattari] |
| 6462 | Sense-data are not mental, but are part of the subject-matter of physics [Russell] |
| 6463 | Sense-data are objects, and do not contain the subject as part, the way beliefs do [Russell] |
| 6464 | Sense-data are usually objects within the body, but are not part of the subject [Russell] |
| 6459 | We do not know whether sense-data exist as objects when they are not data [Russell] |
| 6460 | 'Sensibilia' are identical to sense-data, without actually being data for any mind [Russell] |
| 6461 | Ungiven sense-data can no more exist than unmarried husbands [Russell] |
| 6458 | Individuating sense-data is difficult, because they divide when closely attended to [Russell] |
| 6469 | Sense-data may be subjective, if closing our eyes can change them [Russell] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 6470 | Matter is the limit of appearances as distance from the object diminishes [Russell] |
| 6468 | There is 'private space', and there is also the 'space of perspectives' [Russell] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |