49 ideas
9593 | Progress in philosophy is incremental, not an immature seeking after drama [Williamson] |
9594 | Correspondence to the facts is a bad account of analytic truth [Williamson] |
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] |
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] |
9601 | The realist/anti-realist debate is notoriously obscure and fruitless [Williamson] |
9599 | There cannot be vague objects, so there may be no such thing as a mountain [Williamson] |
15516 | A property is any class of possibilia [Lewis] |
9602 | Common sense and classical logic are often simultaneously abandoned in debates on vagueness [Williamson] |
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] |
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] |
15512 | In mereology no two things consist of the same atoms [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] |
9598 | Modal thinking isn't a special intuition; it is part of ordinary counterfactual thinking [Williamson] |
16536 | Williamson can't base metaphysical necessity on the psychology of causal counterfactuals [Lowe on Williamson] |
9596 | We scorn imagination as a test of possibility, forgetting its role in counterfactuals [Williamson] |
9597 | There are 'armchair' truths which are not a priori, because experience was involved [Williamson] |
15509 | Some say qualities are parts of things - as repeatable universals, or as particulars [Lewis] |
9592 | Intuition is neither powerful nor vacuous, but reveals linguistic or conceptual competence [Williamson] |
20181 | When analytic philosophers run out of arguments, they present intuitions as their evidence [Williamson] |
9595 | You might know that the word 'gob' meant 'mouth', but not be competent to use it [Williamson] |
9600 | If languages are intertranslatable, and cognition is innate, then cultures are all similar [Williamson] |
20698 | Irenaeus says evil is necessary for perfect human development [Irenaeus, by Davies,B] |