66 ideas
| 12027 | There must be a plausible epistemological theory alongside any metaphysical theory [Forbes,G] |
| 12005 | The symbol 'ι' forms definite descriptions; (ιx)F(x) says 'the x which is such that F(x)' [Forbes,G] |
| 12010 | Is the meaning of 'and' given by its truth table, or by its introduction and elimination rules? [Forbes,G] |
| 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] |
| 12023 | Vagueness problems arise from applying sharp semantics to vague languages [Forbes,G] |
| 12017 | In all instances of identity, there must be some facts to ensure the identity [Forbes,G] |
| 12024 | If we combined two clocks, it seems that two clocks may have become one clock. [Forbes,G] |
| 11885 | Only individual essences will ground identities across worlds in other properties [Forbes,G, by Mackie,P] |
| 12014 | An individual essence is a set of essential properties which only that object can have [Forbes,G] |
| 12015 | Non-trivial individual essence is properties other than de dicto, or universal, or relational [Forbes,G] |
| 12013 | Essential properties depend on a category, and perhaps also on particular facts [Forbes,G] |
| 13804 | A property is essential iff the object would not exist if it lacked that property [Forbes,G] |
| 13805 | Properties are trivially essential if they are not grounded in a thing's specific nature [Forbes,G] |
| 12012 | Essential properties are those without which an object could not exist [Forbes,G] |
| 13808 | A relation is essential to two items if it holds in every world where they exist [Forbes,G] |
| 13806 | Trivially essential properties are existence, self-identity, and de dicto necessities [Forbes,G] |
| 13807 | A property is 'extraneously essential' if it is had only because of the properties of other objects [Forbes,G] |
| 12025 | Artefacts have fuzzy essences [Forbes,G] |
| 12022 | Same parts does not ensure same artefact, if those parts could constitute a different artefact [Forbes,G] |
| 13809 | One might be essentialist about the original bronze from which a statue was made [Forbes,G] |
| 12020 | An individual might change their sex in a world, but couldn't have differed in sex at origin [Forbes,G] |
| 11888 | Identities must hold because of other facts, which must be instrinsic [Forbes,G, by Mackie,P] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 12003 | De re modal formulae, unlike de dicto, are sensitive to transworld identities [Forbes,G] |
| 12028 | De re necessity is a form of conceptual necessity, just as de dicto necessity is [Forbes,G] |
| 13810 | The source of de dicto necessity is not concepts, but the actual properties of the thing [Forbes,G] |
| 12008 | Unlike places and times, we cannot separate possible worlds from what is true at them [Forbes,G] |
| 12009 | The problem with possible worlds realism is epistemological; we can't know properties of possible objects [Forbes,G] |
| 12007 | Possible worlds are points of logical space, rather like other times than our own [Forbes,G] |
| 12011 | Transworld identity concerns the limits of possibility for ordinary things [Forbes,G] |
| 12016 | The problem of transworld identity can be solved by individual essences [Forbes,G] |
| 12004 | Counterpart theory is not good at handling the logic of identity [Forbes,G] |
| 12021 | Haecceitism attributes to each individual a primitive identity or thisness [Forbes,G] |
| 12029 | We believe in thisnesses, because we reject bizarre possibilities as not being about that individual [Forbes,G] |
| 21513 | We can no more expect a precise definition of coherence than we can of the moral ideal [Ewing] |
| 21497 | If undetailed, 'coherence' is just a vague words that covers all possible arguments [Ewing] |
| 18671 | The ground for an attitude is not a thing's 'goodness', but its concrete characteristics [Ewing] |