44 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] |
| 18933 | Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius] |
| 16185 | Causality indicates which properties are real [Cartwright,N] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 16182 | Two main types of explanation are by causes, or by citing a theoretical framework [Cartwright,N] |
| 16184 | An explanation is a model that fits a theory and predicts the phenomenological laws [Cartwright,N] |
| 16167 | Laws get the facts wrong, and explanation rests on improvements and qualifications of laws [Cartwright,N] |
| 16169 | Laws apply to separate domains, but real explanations apply to intersecting domains [Cartwright,N] |
| 16171 | The covering law view assumes that each phenomenon has a 'right' explanation [Cartwright,N] |
| 16176 | Covering-law explanation lets us explain storms by falling barometers [Cartwright,N] |
| 16177 | I disagree with the covering-law view that there is a law to cover every single case [Cartwright,N] |
| 16180 | You can't explain one quail's behaviour by just saying that all quails do it [Cartwright,N] |
| 16183 | In science, best explanations have regularly turned out to be false [Cartwright,N] |
| 9866 | Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato] |
| 5864 | Destroy seriousness with laughter, and laughter with seriousness [Gorgias] |
| 16175 | A cause won't increase the effect frequency if other causes keep interfering [Cartwright,N] |
| 6781 | There are fundamental explanatory laws (false!), and phenomenological laws (regularities) [Cartwright,N, by Bird] |
| 16166 | Laws of appearances are 'phenomenological'; laws of reality are 'theoretical' [Cartwright,N] |
| 16179 | Good organisation may not be true, and the truth may not organise very much [Cartwright,N] |
| 16178 | There are few laws for when one theory meets another [Cartwright,N] |
| 16170 | To get from facts to equations, we need a prepared descriptions suited to mathematics [Cartwright,N] |
| 16181 | Simple laws have quite different outcomes when they act in combinations [Cartwright,N] |