62 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] |
| 12747 | Monads are not extended, but have a kind of situation in extension [Leibniz] |
| 12748 | Only monads are substances, and bodies are collections of them [Leibniz] |
| 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] |
| 13184 | The division of nature into matter makes distinct appearances, and that presupposes substances [Leibniz] |
| 13188 | The only indications of reality are agreement among phenomena, and their agreement with necessities [Leibniz] |
| 12752 | Only unities have any reality [Leibniz] |
| 13187 | In actual things nothing is indefinite [Leibniz] |
| 19383 | A man's distant wife dying is a real change in him [Leibniz] |
| 15516 | A property is any class of possibilia [Lewis] |
| 13179 | A complete monad is a substance with primitive active and passive power [Leibniz] |
| 12749 | Derivate forces are in phenomena, but primitive forces are in the internal strivings of substances [Leibniz] |
| 12722 | Thought terminates in force, rather than extension [Leibniz] |
| 19379 | The law of the series, which determines future states of a substance, is what individuates it [Leibniz] |
| 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] |
| 13182 | Changeable accidents are modifications of unchanging essences [Leibniz] |
| 13178 | Things in different locations are different because they 'express' those locations [Leibniz] |
| 19411 | In nature there aren't even two identical straight lines, so no two bodies are alike [Leibniz] |
| 19412 | If two bodies only seem to differ in their position, those different environments will matter [Leibniz] |
| 15509 | Some say qualities are parts of things - as repeatable universals, or as particulars [Lewis] |
| 19410 | Scientific truths are supported by mutual agreement, as well as agreement with the phenomena [Leibniz] |
| 13183 | Primitive forces are internal strivings of substances, acting according to their internal laws [Leibniz] |
| 20618 | Persons must be conscious, reasoning, motivated, communicative, self-aware [Warren, by Tuckness/Wolf] |
| 19409 | Soul represents body, but soul remains unchanged, while body continuously changes [Leibniz] |
| 11873 | Our notions may be formed from concepts, but concepts are formed from things [Leibniz] |
| 13186 | Universals are just abstractions by concealing some of the circumstances [Leibniz] |
| 13185 | Even if extension is impenetrable, this still offers no explanation for motion and its laws [Leibniz] |
| 13177 | An entelechy is a law of the series of its event within some entity [Leibniz] |
| 13093 | The only permanence in things, constituting their substance, is a law of continuity [Leibniz] |
| 13096 | The force behind motion is like a soul, with its own laws of continual change [Leibniz] |
| 13180 | Space is the order of coexisting possibles [Leibniz] |
| 13181 | Time is the order of inconsistent possibilities [Leibniz] |