25 ideas
7893 | Our life is the creation of our mind [Anon (Dham)] |
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] |
9216 | Each area of enquiry, and its source, has its own distinctive type of necessity [Fine,K] |
7898 | The world is just the illusion of an appearance [Anon (Dham)] |
9214 | Unsupported testimony may still be believable [Fine,K] |
7894 | Hate is conquered by love [Anon (Dham)] |
7899 | Even divine pleasure will not satisfy the wise, as it is insatiable, and leads to pain [Anon (Dham)] |
7896 | The foolish gradually fill with evil, like a slowly-filled water-jar [Anon (Dham)] |
7897 | The wise gradually fill with good, like a slowly-filled water-jar [Anon (Dham)] |
7895 | Don't befriend fools; either find superior friends, or travel alone [Anon (Dham)] |
9215 | Causation is easier to disrupt than logic, so metaphysics is part of nature, not vice versa [Fine,K] |
7900 | Speak the truth, yield not to anger, give what you can to him who asks [Anon (Dham)] |