46 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] |
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] |
15503 | We needn't accept this speck of nothingness, this black hole in the fabric of Reality! [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] |
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] |
21563 | The 'no classes' theory says the propositions just refer to the members [Russell] |
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] |
21565 | Richard's puzzle uses the notion of 'definition' - but that cannot be defined [Russell] |
21564 | Vicious Circle: what involves ALL must not be one of those ALL [Russell] |
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] |
15504 | Atomless gunk is an individual whose parts all have further proper parts [Lewis] |
15501 | We have no idea of a third sort of thing, that isn't an individual, a class, or their mixture [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] |
6230 | If the soul were a tabula rasa, with no innate ideas, there could be no moral goodness or justice [Cudworth] |
15509 | Some say qualities are parts of things - as repeatable universals, or as particulars [Lewis] |
6228 | Senses cannot judge one another, so what judges senses cannot be a sense, but must be superior [Cudworth] |
6229 | Sense is fixed in the material form, and so can't grasp abstract universals [Cudworth] |
6227 | Keeping promises and contracts is an obligation of natural justice [Cudworth] |
6225 | Obligation to obey all positive laws is older than all laws [Cudworth] |
6224 | An omnipotent will cannot make two things equal or alike if they aren't [Cudworth] |
6223 | If the will and pleasure of God controls justice, then anything wicked or unjust would become good if God commanded it [Cudworth] |
6226 | The requirement that God must be obeyed must precede any authority of God's commands [Cudworth] |