64 ideas
| 6961 | An analogy begins to break down as soon as the two cases differ [Hume] |
| 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] |
| 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] |
| 15523 | Set theory isn't innocent; it generates infinities from a single thing; but mathematics needs it [Lewis] |
| 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] |
| 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] |
| 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] |
| 19553 | Commitment to 'I have a hand' only makes sense in a context where it has been doubted [Hawthorne] |
| 15509 | Some say qualities are parts of things - as repeatable universals, or as particulars [Lewis] |
| 21285 | Events are baffling before experience, and obvious after experience [Hume] |
| 19551 | How can we know the heavyweight implications of normal knowledge? Must we distort 'knowledge'? [Hawthorne] |
| 19552 | We wouldn't know the logical implications of our knowledge if small risks added up to big risks [Hawthorne] |
| 19554 | Denying closure is denying we know P when we know P and Q, which is absurd in simple cases [Hawthorne] |
| 6959 | We can't assume God's perfections are like our ideas or like human attributes [Hume] |
| 6957 | The objects of theological reasoning are too big for our minds [Hume] |
| 21255 | No being's non-existence can imply a contradiction, so its existence cannot be proved a priori [Hume] |
| 21254 | A chain of events requires a cause for the whole as well as the parts, yet the chain is just a sum of parts [Hume] |
| 1435 | If something must be necessary so that something exists rather than nothing, why can't the universe be necessary? [Hume] |
| 6962 | The thing which contains order must be God, so see God where you see order [Hume] |
| 6960 | Analogy suggests that God has a very great human mind [Hume] |
| 6958 | How can we pronounce on a whole after a brief look at a very small part? [Hume] |
| 21279 | If the divine cause is proportional to its effects, the effects are finite, so the Deity cannot be infinite [Hume] |
| 21282 | Design cannot prove a unified Deity. Many men make a city, so why not many gods for a world? [Hume] |
| 21280 | From a ship you would judge its creator a genius, not a mere humble workman [Hume] |
| 6966 | Creation is more like vegetation than human art, so it won't come from reason [Hume] |
| 21281 | This excellent world may be the result of a huge sequence of trial-and-error [Hume] |
| 21283 | Humans renew their species sexually. If there are many gods, would they not do the same? [Hume] |
| 21284 | This Creator god might be an infant or incompetent or senile [Hume] |
| 6967 | Order may come from an irrational source as well as a rational one [Hume] |
| 21286 | Motion often begins in matter, with no sign of a controlling agent [Hume] |
| 21287 | The universe could settle into superficial order, without a designer [Hume] |
| 21288 | Ideas arise from objects, not vice versa; ideas only influence matter if they are linked [Hume] |
| 21256 | A surprise feature of all products of 9 looks like design, but is actually a necessity [Hume] |
| 6965 | The universe may be the result of trial-and-error [Hume] |
| 6964 | From our limited view, we cannot tell if the universe is faulty [Hume] |
| 6963 | Why would we infer an infinite creator from a finite creation? [Hume] |