62 ideas
| 22317 | Truth does not admit of more and less [Frege] |
| 13455 | Frege did not think of himself as working with sets [Frege, by Hart,WD] |
| 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] |
| 16895 | The null set is indefensible, because it collects nothing [Frege, by Burge] |
| 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] |
| 21717 | Reducibility undermines type ramification, and is committed to the existence of functions [Quine, by Linsky,B] |
| 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] |
| 3328 | Frege proposed a realist concept of a set, as the extension of a predicate or concept or function [Frege, by Benardete,JA] |
| 9179 | Frege frequently expressed a contempt for language [Frege, by Dummett] |
| 13473 | Frege thinks there is an independent logical order of the truths, which we must try to discover [Frege, by Hart,WD] |
| 6076 | For Frege, predicates are names of functions that map objects onto the True and False [Frege, by McGinn] |
| 3319 | Frege gives a functional account of predication so that we can dispense with predicates [Frege, by Benardete,JA] |
| 9871 | Frege always, and fatally, neglected the domain of quantification [Dummett on Frege] |
| 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] |
| 16884 | Basic truths of logic are not proved, but seen as true when they are understood [Frege, by Burge] |
| 3331 | If '5' is the set of all sets with five members, that may be circular, and you can know a priori if the set has content [Benardete,JA on Frege] |
| 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] |
| 16880 | Frege aimed to discover the logical foundations which justify arithmetical judgements [Frege, by Burge] |
| 8689 | Eventually Frege tried to found arithmetic in geometry instead of in logic [Frege, by Friend] |
| 15520 | Existence doesn't come in degrees; once asserted, it can't then be qualified [Lewis] |
| 5657 | Frege's logic showed that there is no concept of being [Frege, by Scruton] |
| 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] |
| 3318 | Frege made identity a logical notion, enshrined above all in the formula 'for all x, x=x' [Frege, by Benardete,JA] |
| 16885 | To understand a thought, understand its inferential connections to other thoughts [Frege, by Burge] |
| 16887 | Frege's concept of 'self-evident' makes no reference to minds [Frege, by Burge] |
| 16894 | An apriori truth is grounded in generality, which is universal quantification [Frege, by Burge] |
| 15509 | Some say qualities are parts of things - as repeatable universals, or as particulars [Lewis] |
| 16882 | The building blocks contain the whole contents of a discipline [Frege] |
| 5816 | Frege said concepts were abstract entities, not mental entities [Frege, by Putnam] |
| 7307 | A thought is not psychological, but a condition of the world that makes a sentence true [Frege, by Miller,A] |
| 7309 | Frege's 'sense' is the strict and literal meaning, stripped of tone [Frege, by Miller,A] |
| 7312 | 'Sense' solves the problems of bearerless names, substitution in beliefs, and informativeness [Frege, by Miller,A] |
| 7725 | 'P or not-p' seems to be analytic, but does not fit Kant's account, lacking clear subject or predicate [Frege, by Weiner] |
| 7316 | Analytic truths are those that can be demonstrated using only logic and definitions [Frege, by Miller,A] |
| 3307 | Frege put forward an ontological argument for the existence of numbers [Frege, by Benardete,JA] |