51 ideas
| 9065 | S5 collapses iterated modalities (◊□P→□P, and ◊◊P→◊P) [Keefe/Smith] |
| 6007 | If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R] |
| 6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
| 6008 | Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R] |
| 9935 | Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf] |
| 9912 | There are no such things as numbers [Benacerraf] |
| 13412 | Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf] |
| 13413 | We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf] |
| 9901 | Numbers can't be sets if there is no agreement on which sets they are [Benacerraf] |
| 13411 | If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [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] |
| 9899 | The successor of x is either x and all its members, or just the unit set of x [Benacerraf] |
| 9900 | For Zermelo 3 belongs to 17, but for Von Neumann it does not [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] |
| 13415 | An adequate account of a number must relate it to its series [Benacerraf] |
| 9908 | The job is done by the whole system of numbers, so numbers are not objects [Benacerraf] |
| 9907 | If any recursive sequence will explain ordinals, then it seems to be the structure which matters [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] |
| 17927 | Realists have semantics without epistemology, anti-realists epistemology but bad semantics [Benacerraf, by Colyvan] |
| 9936 | The platonist view of mathematics doesn't fit our epistemology very well [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] |
| 9064 | Objects such as a cloud or Mount Everest seem to have fuzzy boundaries in nature [Keefe/Smith] |
| 9044 | If someone is borderline tall, no further information is likely to resolve the question [Keefe/Smith] |
| 9048 | The simplest approach, that vagueness is just ignorance, retains classical logic and semantics [Keefe/Smith] |
| 9055 | The epistemic view of vagueness must explain why we don't know the predicate boundary [Keefe/Smith] |
| 9049 | Supervaluationism keeps true-or-false where precision can be produced, but not otherwise [Keefe/Smith] |
| 9056 | Vague statements lack truth value if attempts to make them precise fail [Keefe/Smith] |
| 9058 | Some of the principles of classical logic still fail with supervaluationism [Keefe/Smith] |
| 9059 | The semantics of supervaluation (e.g. disjunction and quantification) is not classical [Keefe/Smith] |
| 9060 | Supervaluation misunderstands vagueness, treating it as a failure to make things precise [Keefe/Smith] |
| 9050 | A third truth-value at borderlines might be 'indeterminate', or a value somewhere between 0 and 1 [Keefe/Smith] |
| 9061 | People can't be placed in a precise order according to how 'nice' they are [Keefe/Smith] |
| 9062 | If truth-values for vagueness range from 0 to 1, there must be someone who is 'completely tall' [Keefe/Smith] |
| 9063 | How do we decide if my coat is red to degree 0.322 or 0.321? [Keefe/Smith] |
| 9045 | Vague predicates involve uncertain properties, uncertain objects, and paradoxes of gradual change [Keefe/Smith] |
| 9047 | Many vague predicates are multi-dimensional; 'big' involves height and volume; heaps include arrangement [Keefe/Smith] |
| 9053 | If there is a precise borderline area, that is not a case of vagueness [Keefe/Smith] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |