52 ideas
14684 | A world is 'accessible' to another iff the first is possible according to the second [Salmon,N] |
14669 | For metaphysics, T may be the only correct system of modal logic [Salmon,N] |
14667 | System B has not been justified as fallacy-free for reasoning on what might have been [Salmon,N] |
14668 | In B it seems logically possible to have both p true and p is necessarily possibly false [Salmon,N] |
14692 | System B implies that possibly-being-realized is an essential property of the world [Salmon,N] |
14671 | What is necessary is not always necessarily necessary, so S4 is fallacious [Salmon,N] |
14686 | S5 modal logic ignores accessibility altogether [Salmon,N] |
14691 | S5 believers say that-things-might-have-been-that-way is essential to ways things might have been [Salmon,N] |
14693 | The unsatisfactory counterpart-theory allows the retention of S5 [Salmon,N] |
14670 | Metaphysical (alethic) modal logic concerns simple necessity and possibility (not physical, epistemic..) [Salmon,N] |
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] |
14678 | Any property is attached to anything in some possible world, so I am a radical anti-essentialist [Salmon,N] |
9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
14680 | Logical possibility contains metaphysical possibility, which contains nomological possibility [Salmon,N] |
14690 | In the S5 account, nested modalities may be unseen, but they are still there [Salmon,N] |
14677 | Metaphysical necessity is said to be unrestricted necessity, true in every world whatsoever [Salmon,N] |
14679 | Bizarre identities are logically but not metaphysically possible, so metaphysical modality is restricted [Salmon,N] |
14688 | Without impossible worlds, the unrestricted modality that is metaphysical has S5 logic [Salmon,N] |
14685 | Metaphysical necessity is NOT truth in all (unrestricted) worlds; necessity comes first, and is restricted [Salmon,N] |
14681 | Logical necessity is free of constraints, and may accommodate all of S5 logic [Salmon,N] |
14676 | Nomological necessity is expressed with intransitive relations in modal semantics [Salmon,N] |
14689 | Necessity and possibility are not just necessity and possibility according to the actual world [Salmon,N] |
14674 | Impossible worlds are also ways for things to be [Salmon,N] |
14682 | Denial of impossible worlds involves two different confusions [Salmon,N] |
14687 | Without impossible worlds, how things might have been is the only way for things to be [Salmon,N] |
14683 | Possible worlds rely on what might have been, so they can' be used to define or analyse modality [Salmon,N] |
14672 | Possible worlds are maximal abstract ways that things might have been [Salmon,N] |
14675 | Possible worlds just have to be 'maximal', but they don't have to be consistent [Salmon,N] |
14673 | You can't define worlds as sets of propositions, and then define propositions using worlds [Salmon,N] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |