49 ideas
14255 | We understand things through their dependency relations [Fine,K] |
9593 | Progress in philosophy is incremental, not an immature seeking after drama [Williamson] |
14250 | Metaphysics deals with the existence of things and with the nature of things [Fine,K] |
14259 | Maybe two objects might require simultaneous real definitions, as with two simultaneous terms [Fine,K] |
9594 | Correspondence to the facts is a bad account of analytic truth [Williamson] |
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] |
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] |
14253 | An object's 'being' isn't existence; there's more to an object than existence, and its nature doesn't include existence [Fine,K] |
14261 | There is 'weak' dependence in one definition, and 'strong' dependence in all the definitions [Fine,K] |
14251 | A natural modal account of dependence says x depends on y if y must exist when x does [Fine,K] |
14257 | An object depends on another if the second cannot be eliminated from the first's definition [Fine,K] |
14254 | Dependency is the real counterpart of one term defining another [Fine,K] |
9601 | The realist/anti-realist debate is notoriously obscure and fruitless [Williamson] |
9599 | There cannot be vague objects, so there may be no such thing as a mountain [Williamson] |
14252 | We should understand identity in terms of the propositions it renders true [Fine,K] |
9602 | Common sense and classical logic are often simultaneously abandoned in debates on vagueness [Williamson] |
14256 | How do we distinguish basic from derived esssences? [Fine,K] |
14258 | Maybe some things have essential relationships as well as essential properties [Fine,K] |
14260 | An object only essentially has a property if that property follows from every definition of the object [Fine,K] |
9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
9598 | Modal thinking isn't a special intuition; it is part of ordinary counterfactual thinking [Williamson] |
16536 | Williamson can't base metaphysical necessity on the psychology of causal counterfactuals [Lowe on Williamson] |
9596 | We scorn imagination as a test of possibility, forgetting its role in counterfactuals [Williamson] |
9597 | There are 'armchair' truths which are not a priori, because experience was involved [Williamson] |
9592 | Intuition is neither powerful nor vacuous, but reveals linguistic or conceptual competence [Williamson] |
20181 | When analytic philosophers run out of arguments, they present intuitions as their evidence [Williamson] |
9595 | You might know that the word 'gob' meant 'mouth', but not be competent to use it [Williamson] |
9600 | If languages are intertranslatable, and cognition is innate, then cultures are all similar [Williamson] |