9987 | An aggregate in which order does not matter I call a 'set' [Bolzano] |
15946 | Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Lavine on Cantor] |
9616 | A set is a collection into a whole of distinct objects of our intuition or thought [Cantor] |
15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Lavine on Cantor] |
13455 | Frege did not think of himself as working with sets [Hart,WD on Frege] |
17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
3302 | Set theory is full of Platonist metaphysics, so Quine aimed to keep it separate from logic [Benardete,JA on Quine] |
18396 | The set theory brackets { } assert that the member is a unit [Armstrong] |
10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
18114 | There is no single agreed structure for set theory [Bostock] |
10807 | Mathematics reduces to set theory, which reduces, with some mereology, to the singleton function [Lewis] |
18395 | Sets are mereological sums of the singletons of their members [Armstrong on Lewis] |
15496 | We can build set theory on singletons: classes are then fusions of subclasses, membership is the singleton [Lewis] |
3326 | Set theory attempts to reduce the 'is' of predication to mathematics [Benardete,JA] |
3327 | The set of Greeks is included in the set of men, but isn't a member of it [Benardete,JA] |
9967 | 'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien] |
13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
8309 | A set is a 'number of things', not a 'collection', because nothing actually collects the members [Lowe] |
10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
8474 | Unlike elementary logic, set theory is not complete [Orenstein] |
10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
13451 | The two best understood conceptions of set are the Iterative and the Limitation of Size [Rayo/Uzquiano] |
17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
16309 | Every attempt at formal rigour uses some set theory [Halbach] |
15657 | To prove the consistency of set theory, we must go beyond set theory [Halbach] |
18830 | Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic [Rumfitt] |