40 ideas
| 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] |
| 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] |
| 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] |
| 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] |
| 12056 | An ancestral relation is either direct or transitively indirect [Wiggins] |
| 12050 | Substances contain a source of change or principle of activity [Wiggins] |
| 12055 | Sortal predications are answers to the question 'what is x?' [Wiggins] |
| 12059 | A river may change constantly, but not in respect of being a river [Wiggins] |
| 12052 | We never single out just 'this', but always 'this something-or-other' [Wiggins] |
| 12063 | Sortal classification becomes science, with cross reference clarifying individuals [Wiggins] |
| 12051 | If the kinds are divided realistically, they fall into substances [Wiggins] |
| 12053 | 'Human being' is a better answer to 'what is it?' than 'poet', as the latter comes in degrees [Wiggins] |
| 12054 | Secondary substances correctly divide primary substances by activity-principles and relations [Wiggins] |
| 12047 | We refer to persisting substances, in perception and in thought, and they aid understanding [Wiggins] |
| 12057 | Matter underlies things, composes things, and brings them to be [Wiggins] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 12064 | The category of substance is more important for epistemology than for ontology [Wiggins] |
| 12049 | Naming the secondary substance provides a mass of general information [Wiggins] |
| 12065 | Seeing a group of soldiers as an army is irresistible, in ontology and explanation [Wiggins] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |