35 ideas
19048 | Contextual definition shifted the emphasis from words to whole sentences [Quine] |
19047 | Bentham's contextual definitions preserved terms after their denotation became doubtful [Quine] |
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] |
18529 | Relations are expressed either as absolute facts, or by a relational concept [William of Ockham] |
16779 | Cut wood doesn't make a new substance, but seems to make separate subjects [William of Ockham] |
16757 | Hot water naturally cools down, which is due to the substantial form of the water [William of Ockham] |
9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
19049 | In scientific theories sentences are too brief to be independent vehicles of empirical meaning [Quine] |
19046 | Empiricism improvements: words for ideas, then sentences, then systems, then no analytic, then naturalism [Quine] |
9102 | If an animal approached from a distance, we might abstract 'animal' from one instance [William of Ockham] |
9114 | There are no secure foundations to prove the separate existence of mind, in reason or experience [William of Ockham] |
19050 | Holism in language blurs empirical synthetic and empty analytic sentences [Quine] |
9115 | To love God means to love whatever God wills to be loved [William of Ockham] |