51 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] |
| 17518 | Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers] |
| 17516 | If counting needs a sortal, what of things which fall under two sortals? [Ayers] |
| 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] |
| 17520 | Events do not have natural boundaries, and we have to set them [Ayers] |
| 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] |
| 17519 | To express borderline cases of objects, you need the concept of an 'object' [Ayers] |
| 17510 | Speakers need the very general category of a thing, if they are to think about it [Ayers] |
| 17522 | We use sortals to classify physical objects by the nature and origin of their unity [Ayers] |
| 17515 | Seeing caterpillar and moth as the same needs continuity, not identity of sortal concepts [Ayers] |
| 17511 | Recognising continuity is separate from sortals, and must precede their use [Ayers] |
| 17517 | Could the same matter have more than one form or principle of unity? [Ayers] |
| 12716 | The concept of forces or powers best reveals the true concept of substance [Leibniz] |
| 17513 | If there are two objects, then 'that marble, man-shaped object' is ambiguous [Ayers] |
| 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] |
| 17523 | Sortals basically apply to individuals [Ayers] |
| 17521 | You can't have the concept of a 'stage' if you lack the concept of an object [Ayers] |
| 17514 | Temporal 'parts' cannot be separated or rearranged [Ayers] |
| 17509 | Some say a 'covering concept' completes identity; others place the concept in the reference [Ayers] |
| 17512 | If diachronic identities need covering concepts, why not synchronic identities too? [Ayers] |
| 15509 | Some say qualities are parts of things - as repeatable universals, or as particulars [Lewis] |