39 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] |
| 18680 | To avoid misunderstandings supervenience is often expressed negatively: no A-change without B-change [Orsi] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 18684 | Rather than requiring an action, a reason may 'entice' us, or be 'eligible', or 'justify' it [Orsi] |
| 18666 | Value-maker concepts (such as courageous or elegant) simultaneously describe and evaluate [Orsi] |
| 18685 | Final value is favoured for its own sake, and personal value for someone's sake [Orsi] |
| 18667 | The '-able' concepts (like enviable) say this thing deserves a particular response [Orsi] |
| 18679 | Things are only valuable if something makes it valuable, and we can ask for the reason [Orsi] |
| 18682 | A complex value is not just the sum of the values of the parts [Orsi] |
| 18683 | Trichotomy Thesis: comparable values must be better, worse or the same [Orsi] |
| 18686 | The Fitting Attitude view says values are fitting or reasonable, and values are just byproducts [Orsi] |
| 18672 | Values from reasons has the 'wrong kind of reason' problem - admiration arising from fear [Orsi] |
| 18677 | A thing may have final value, which is still derived from other values, or from relations [Orsi] |
| 18669 | Values can be normative in the Fitting Attitude account, where 'good' means fitting favouring [Orsi] |
| 18670 | The Buck-Passing view of normative values says other properties are reasons for the value [Orsi] |
| 18668 | Truths about value entail normative truths about actions or attitudes [Orsi] |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |