48 ideas
19275 | You cannot understand what exists without understanding possibility and necessity [Hale] |
19291 | A canonical defintion specifies the type of thing, and what distinguish this specimen [Hale] |
19297 | The two Barcan principles are easily proved in fairly basic modal logic [Hale] |
19301 | With a negative free logic, we can dispense with the Barcan formulae [Hale] |
19296 | If second-order variables range over sets, those are just objects; properties and relations aren't sets [Hale] |
19289 | Maybe conventionalism applies to meaning, but not to the truth of propositions expressed [Hale] |
19298 | Unlike axiom proofs, natural deduction proofs needn't focus on logical truths and theorems [Hale] |
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] |
19295 | Add Hume's principle to logic, to get numbers; arithmetic truths rest on the nature of the numbers [Hale] |
9904 | The set-theory paradoxes mean that 17 can't be the class of all classes with 17 members [Benacerraf] |
19281 | Interesting supervenience must characterise the base quite differently from what supervenes on it [Hale] |
19278 | There is no gap between a fact that p, and it is true that p; so we only have the truth-condtions for p [Hale] |
19302 | If a chair could be made of slightly different material, that could lead to big changes [Hale] |
9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
19290 | Absolute necessities are necessarily necessary [Hale] |
19286 | 'Absolute necessity' is when there is no restriction on the things which necessitate p [Hale] |
19288 | Logical and metaphysical necessities differ in their vocabulary, and their underlying entities [Hale] |
19285 | Logical necessity is something which is true, no matter what else is the case [Hale] |
19287 | Maybe each type of logic has its own necessity, gradually becoming broader [Hale] |
19282 | It seems that we cannot show that modal facts depend on non-modal facts [Hale] |
19276 | The big challenge for essentialist views of modality is things having necessary existence [Hale] |
19293 | Essentialism doesn't explain necessity reductively; it explains all necessities in terms of a few basic natures [Hale] |
19294 | If necessity derives from essences, how do we explain the necessary existence of essences? [Hale] |
19279 | What are these worlds, that being true in all of them makes something necessary? [Hale] |
19299 | Possible worlds make every proposition true or false, which endorses classical logic [Hale] |
19300 | The molecules may explain the water, but they are not what 'water' means [Hale] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |