58 ideas
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] |
15506 | If we don't understand the singleton, then we don't understand classes [Lewis] |
15497 | We can replace the membership relation with the member-singleton relation (plus mereology) [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] |
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] |
15523 | Set theory isn't innocent; it generates infinities from a single thing; but mathematics needs it [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] |
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] |
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] |
10566 | Lewis prefers giving up singletons to giving up sums [Lewis, by Fine,K] |
23647 | Objects have an essential constitution, producing its qualities, which we are too ignorant to define [Reid] |
11958 | Impossibilites are easily conceived in mathematics and geometry [Reid, by Molnar] |
15509 | Some say qualities are parts of things - as repeatable universals, or as particulars [Lewis] |
23646 | Reference is by name, or a term-plus-circumstance, or ostensively, or by description [Reid] |
23645 | A word's meaning is the thing conceived, as fixed by linguistic experts [Reid] |
23125 | Most good social changes are incremental, rather than revolutionary [Gopnik] |
23126 | Conservatives often want peace, prosperity and tolerance, but not social fairness [Gopnik] |
23132 | Conservatives believe obedience and rank are essential to social order [Gopnik] |
23128 | The opposite of liberalism is dogmatism [Gopnik] |
23142 | People are fallible, so liberalism tries to distribute power [Gopnik] |
23143 | Liberals have tried very hard to build a conscience into their institutions [Gopnik] |
23141 | Left-wingers are inconsistent in their essentialist descriptions of social groups [Gopnik] |
23124 | Liberal community is not blood ties or tradition, but shared choices, and sympathy for the losers [Gopnik] |
23127 | Liberal community includes flight from the family, into energetic reforming groups [Gopnik] |
23129 | Right-wingers attack liberal faith in reason, left-wingers attack its faith in reform [Gopnik] |
23133 | Cosmopolitan liberals lack national loyalty, and welcome excessive immigration [Gopnik] |
23138 | Modern left-wingers criticise liberalism's control of culture [Gopnik] |
23139 | Liberalism's attempt to be neutral and colour-blind erases cultural identities [Gopnik] |
23135 | Classic Marxists see liberalism as the ideology of the bourgeoisie [Gopnik] |
23140 | Environmental disasters result not from capitalism, but from a general drive for growth [Gopnik] |
23130 | Popular imperialism gives the poor the belief that their acts have world historical meaning [Gopnik] |
23131 | Patriots love their place, but nationalists have a paranoid ethnic hostility [Gopnik] |
23136 | Liberal free speech is actually paid speech [Gopnik] |
23134 | A 'free' society implies a free market, which always produces predatory capitalism and inequalities [Gopnik] |