38 ideas
| 17651 | Without words or other symbols, we have no world [Goodman] |
| 17652 | Truth is irrelevant if no statements are involved [Goodman] |
| 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] |
| 17656 | Being primitive or prior always depends on a constructional system [Goodman] |
| 17661 | We don't recognise patterns - we invent them [Goodman] |
| 17659 | Reality is largely a matter of habit [Goodman] |
| 17657 | We build our world, and ignore anything that won't fit [Goodman] |
| 17654 | A world can be full of variety or not, depending on how we sort it [Goodman] |
| 17653 | Things can only be judged the 'same' by citing some respect of sameness [Goodman] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 17660 | Discovery is often just finding a fit, like a jigsaw puzzle [Goodman] |
| 17658 | Users of digital thermometers recognise no temperatures in the gaps [Goodman] |
| 17650 | We lack frames of reference to transform physics, biology and psychology into one another [Goodman] |
| 17655 | Grue and green won't be in the same world, as that would block induction entirely [Goodman] |
| 17649 | If the world is one it has many aspects, and if there are many worlds they will collect into one [Goodman] |
| 1422 | God's existence is either necessary or impossible, and no one has shown that the concept of God is contradictory [Malcolm] |