11044 | One is prior to two, because its existence is implied by two [Aristotle] |
10091 | God made the integers, all the rest is the work of man [Kronecker] |
7524 | Order, not quantity, is central to defining numbers [Dedekind] |
10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [George/Velleman on Dedekind] |
18256 | Quantity is inconceivable without the idea of addition [Frege] |
13510 | Could a number just be something which occurs in a progression? [Hart,WD on Russell] |
14128 | Some claim priority for the ordinals over cardinals, but there is no logical priority between them [Russell] |
14129 | Ordinals presuppose two relations, where cardinals only presuppose one [Russell] |
14132 | Properties of numbers don't rely on progressions, so cardinals may be more basic [Russell] |
18255 | Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett] |
9191 | Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett] |
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 [Fine,K on Benacerraf] |
18102 | A cardinal is the earliest ordinal that has that number of predecessors [Bostock] |
13892 | One could grasp numbers, and name sizes with them, without grasping ordering [Wright,C] |
13489 | Von Neumann treated cardinals as a special sort of ordinal [Hart,WD] |
9983 | Cantor took the ordinal numbers to be primary [Tait] |
17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Heck] |
8661 | The natural numbers are primitive, and the ordinals are up one level of abstraction [Friend] |