29 ideas
19336 | Wisdom involves the desire to achieve perfection [Leibniz] |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
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] |
10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
7696 | Leibniz first asked 'why is there something rather than nothing?' [Leibniz, by Jacquette] |
19341 | There must be a straining towards existence in the essence of all possible things [Leibniz] |
19428 | Because something does exist, there must be a drive in possible things towards existence [Leibniz] |
16235 | Persistence conditions cannot contradict, so there must be a 'dominant sortal' [Burke,M, by Hawley] |
14753 | The 'dominant' of two coinciding sortals is the one that entails the widest range of properties [Burke,M, by Sider] |
16072 | 'The rock' either refers to an object, or to a collection of parts, or to some stuff [Burke,M, by Wasserman] |
14751 | Tib goes out of existence when the tail is lost, because Tib was never the 'cat' [Burke,M, by Sider] |
16071 | Sculpting a lump of clay destroys one object, and replaces it with another one [Burke,M, by Wasserman] |
16234 | Burke says when two object coincide, one of them is destroyed in the process [Burke,M, by Hawley] |
13278 | Maybe the clay becomes a different lump when it becomes a statue [Burke,M, by Koslicki] |
14750 | Two entities can coincide as one, but only one of them (the dominant sortal) fixes persistence conditions [Burke,M, by Sider] |
5047 | The world is physically necessary, as its contrary would imply imperfection or moral absurdity [Leibniz] |
19343 | We follow the practical rule which always seeks maximum effect for minimum cost [Leibniz] |
19429 | The principle of determination in things obtains the greatest effect with the least effort [Leibniz] |