63 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] |
| 18395 | Sets are mereological sums of the singletons of their members [Lewis, by Armstrong] |
| 15496 | We can build set theory on singletons: classes are then fusions of subclasses, membership is the singleton [Lewis] |
| 15500 | Classes divide into subclasses in many ways, but into members in only one way [Lewis] |
| 15499 | A subclass of a subclass is itself a subclass; a member of a member is not in general a member [Lewis] |
| 15503 | We needn't accept this speck of nothingness, this black hole in the fabric of Reality! [Lewis] |
| 15498 | We can accept the null set, but there is no null class of anything [Lewis] |
| 15502 | There are four main reasons for asserting that there is an empty set [Lewis] |
| 15497 | We can replace the membership relation with the member-singleton relation (plus mereology) [Lewis] |
| 15506 | If we don't understand the singleton, then we don't understand classes [Lewis] |
| 15511 | If singleton membership is external, why is an object a member of one rather than another? [Lewis] |
| 15513 | Maybe singletons have a structure, of a thing and a lasso? [Lewis] |
| 15507 | Set theory has some unofficial axioms, generalisations about how to understand it [Lewis] |
| 10191 | Set theory reduces to a mereological theory with singletons as the only atoms [Lewis, by MacBride] |
| 15523 | Set theory isn't innocent; it generates infinities from a single thing; but mathematics needs it [Lewis] |
| 15508 | If singletons are where their members are, then so are all sets [Lewis] |
| 15514 | A huge part of Reality is only accepted as existing if you have accepted set theory [Lewis] |
| 15525 | Plural quantification lacks a complete axiom system [Lewis] |
| 15518 | I like plural quantification, but am not convinced of its connection with second-order logic [Lewis] |
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| 15524 | Zermelo's model of arithmetic is distinctive because it rests on a primitive of set theory [Lewis] |
| 15517 | Giving up classes means giving up successful mathematics because of dubious philosophy [Lewis] |
| 15515 | To be a structuralist, you quantify over relations [Lewis] |
| 15520 | Existence doesn't come in degrees; once asserted, it can't then be qualified [Lewis] |
| 15501 | We have no idea of a third sort of thing, that isn't an individual, a class, or their mixture [Lewis] |
| 15504 | Atomless gunk is an individual whose parts all have further proper parts [Lewis] |
| 15516 | A property is any class of possibilia [Lewis] |
| 14748 | The many are many and the one is one, so they can't be identical [Lewis] |
| 6129 | Lewis affirms 'composition as identity' - that an object is no more than its parts [Lewis, by Merricks] |
| 15512 | In mereology no two things consist of the same atoms [Lewis] |
| 15519 | Trout-turkeys exist, despite lacking cohesion, natural joints and united causal power [Lewis] |
| 15521 | Given cats, a fusion of cats adds nothing further to reality [Lewis] |
| 15522 | The one has different truths from the many; it is one rather than many, one rather than six [Lewis] |
| 10566 | Lewis prefers giving up singletons to giving up sums [Lewis, by Fine,K] |
| 14244 | Lewis only uses fusions to create unities, but fusions notoriously flatten our distinctions [Oliver/Smiley on Lewis] |
| 10660 | A commitment to cat-fusions is not a further commitment; it is them and they are it [Lewis] |
| 14678 | Any property is attached to anything in some possible world, so I am a radical anti-essentialist [Salmon,N] |
| 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] |
| 15509 | Some say qualities are parts of things - as repeatable universals, or as particulars [Lewis] |