43 ideas
9331 | How do we determine which of the sentences containing a term comprise its definition? [Horwich] |
3993 | Arguments are nearly always open to challenge, but they help to explain a position rather than force people to believe [Lewis] |
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] |
3990 | The whole truth supervenes on the physical truth [Lewis] |
3991 | Where pixels make up a picture, supervenience is reduction [Lewis] |
9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
9333 | A priori belief is not necessarily a priori justification, or a priori knowledge [Horwich] |
9342 | Understanding needs a priori commitment [Horwich] |
9332 | Meaning is generated by a priori commitment to truth, not the other way around [Horwich] |
9341 | Meanings and concepts cannot give a priori knowledge, because they may be unacceptable [Horwich] |
9334 | If we stipulate the meaning of 'number' to make Hume's Principle true, we first need Hume's Principle [Horwich] |
9339 | A priori knowledge (e.g. classical logic) may derive from the innate structure of our minds [Horwich] |
3995 | A mind is an organ of representation [Lewis] |
3994 | Human pain might be one thing; Martian pain might be something else [Lewis] |
3989 | I am a reductionist about mind because I am an a priori reductionist about everything [Lewis] |
3992 | Folk psychology makes good predictions, by associating mental states with causal roles [Lewis] |
3996 | Folk psychology doesn't say that there is a language of thought [Lewis] |
3998 | If you don't share an external world with a brain-in-a-vat, then externalism says you don't share any beliefs [Lewis] |
3997 | Nothing shows that all content is 'wide', or that wide content has logical priority [Lewis] |
3999 | A spontaneous duplicate of you would have your brain states but no experience, so externalism would deny him any beliefs [Lewis] |
4000 | Wide content derives from narrow content and relationships with external things [Lewis] |