34 ideas
15585 | Later Heidegger sees philosophy as more like poetry than like science [Heidegger, by Polt] |
4975 | A thought can be split in many ways, so that different parts appear as subject or predicate [Frege] |
9901 | Numbers can't be sets if there is no agreement on which sets they are [Benacerraf] |
9912 | There are no such things as numbers [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] |
9949 | There is the concept, the object falling under it, and the extension (a set, which is also an object) [Frege, by George/Velleman] |
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] |
18995 | Frege mistakenly takes existence to be a property of concepts, instead of being about things [Frege, by Yablo] |
10317 | It is unclear whether Frege included qualities among his abstract objects [Frege, by Hale] |
10535 | Frege's 'objects' are both the referents of proper names, and what predicates are true or false of [Frege, by Dummett] |
9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
9839 | Frege equated the concepts under which an object falls with its properties [Frege, by Dummett] |
4973 | As I understand it, a concept is the meaning of a grammatical predicate [Frege] |
9167 | Frege felt that meanings must be public, so they are abstractions rather than mental entities [Frege, by Putnam] |
4974 | For all the multiplicity of languages, mankind has a common stock of thoughts [Frege] |