48 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] |
15509 | Some say qualities are parts of things - as repeatable universals, or as particulars [Lewis] |
20712 | God is 'eternal' either by being non-temporal, or by enduring forever [Davies,B] |
20701 | Can God be good, if he has not maximised goodness? [Davies,B] |
20702 | The goodness of God may be a higher form than the goodness of moral agents [Davies,B] |
20703 | How could God have obligations? What law could possibly impose them? [Davies,B] |
20694 | 'Natural theology' aims to prove God to anyone (not just believers) by reason or argument [Davies,B] |
20706 | A distinct cause of the universe can't be material (which would be part of the universe) [Davies,B] |
20707 | The universe exhibits design either in its sense of purpose, or in its regularity [Davies,B] |
20708 | If God is an orderly being, he cannot be the explanation of order [Davies,B] |
20710 | Maybe an abnormal state of mind is needed to experience God? [Davies,B] |
20711 | A believer can experience the world as infused with God [Davies,B] |
20709 | The experiences of God are inconsistent, not universal, and untestable [Davies,B] |
20697 | One does not need a full understanding of God in order to speak of God [Davies,B] |
20699 | Paradise would not contain some virtues, such as courage [Davies,B] |