51 ideas
| 5331 | You can't infer that because you have a hidden birth-mark, everybody else does [Ayer] |
| 13134 | We negate predicates but do not negate names [Westerhoff] |
| 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] |
| 2611 | It is currently held that quantifying over something implies belief in its existence [Ayer] |
| 13124 | Categories can be ordered by both containment and generality [Westerhoff] |
| 13117 | How far down before we are too specialised to have a category? [Westerhoff] |
| 13116 | Maybe objects in the same category have the same criteria of identity [Westerhoff] |
| 13118 | Categories are base-sets which are used to construct states of affairs [Westerhoff] |
| 13125 | Categories are held to explain why some substitutions give falsehood, and others meaninglessness [Westerhoff] |
| 13126 | Categories systematize our intuitions about generality, substitutability, and identity [Westerhoff] |
| 13130 | Categories as generalities don't give a criterion for a low-level cut-off point [Westerhoff] |
| 13131 | The aim is that everything should belong in some ontological category or other [Westerhoff] |
| 13123 | All systems have properties and relations, and most have individuals, abstracta, sets and events [Westerhoff] |
| 13115 | Ontological categories are like formal axioms, not unique and with necessary membership [Westerhoff] |
| 13119 | Categories merely systematise, and are not intrinsic to objects [Westerhoff] |
| 13135 | A thing's ontological category depends on what else exists, so it is contingent [Westerhoff] |
| 16520 | We see properties necessary for a kind (in the definition), but not for an individual [Ayer] |
| 13129 | Essential kinds may be too specific to provide ontological categories [Westerhoff] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 2613 | The theory of other minds has no rival [Ayer] |
| 5328 | Originally I combined a mentalistic view of introspection with a behaviouristic view of other minds [Ayer] |
| 5330 | Physicalism undercuts the other mind problem, by equating experience with 'public' brain events [Ayer] |
| 5326 | Qualia must be united by a subject, because they lead to concepts and judgements [Ayer] |
| 5325 | Is something an 'experience' because it relates to other experiences, or because it relates to a subject? [Ayer] |
| 5324 | Bodily identity and memory work together to establish personal identity [Ayer] |
| 5322 | Self-consciousness is not basic, because experiences are not instrinsically marked with ownership [Ayer] |
| 5327 | Temporal gaps in the consciousness of a spirit could not be bridged by memories [Ayer] |
| 5329 | Why shouldn't we say brain depends on mind? Better explanation! [Ayer] |
| 2610 | Talk of propositions is just shorthand for talking about equivalent sentences [Ayer] |