40 ideas
| 10528 | Definitions concern how we should speak, not how things are [Fine,K] |
| 12619 | We have no successful definitions, because they all use indefinable words [Fodor] |
| 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] |
| 10529 | If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K] |
| 10530 | Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K] |
| 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] |
| 12620 | If 'exist' is ambiguous in 'chairs and numbers exist', that mirrors the difference between chairs and numbers [Fodor] |
| 12613 | Empiricists use dispositions reductively, as 'possibility of sensation' or 'possibility of experimental result' [Fodor] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 12617 | Associationism can't explain how truth is preserved [Fodor] |
| 12615 | Mental representations are the old 'Ideas', but without images [Fodor] |
| 6650 | Fodor is now less keen on the innateness of concepts [Fodor, by Lowe] |
| 12618 | It is essential to the concept CAT that it be satisfied by cats [Fodor] |
| 12614 | I prefer psychological atomism - that concepts are independent of epistemic capacities [Fodor] |
| 12621 | Definable concepts have constituents, which are necessary, individuate them, and demonstrate possession [Fodor] |
| 12622 | Many concepts lack prototypes, and complex prototypes aren't built from simple ones [Fodor] |
| 12623 | The theory theory can't actually tell us what concepts are [Fodor] |
| 10527 | An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K] |
| 12616 | English has no semantic theory, just associations between sentences and thoughts [Fodor] |