36 ideas
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
18365 | If truths are just identical with facts, then truths will make themselves true [David] |
18362 | Examples show that truth-making is just non-symmetric, not asymmetric [David] |
18360 | It is assumed that a proposition is necessarily true if its truth-maker exists [David] |
18358 | Two different propositions can have the same fact as truth-maker [David] |
18355 | What matters is truth-making (not truth-makers) [David] |
18354 | Correspondence is symmetric, while truth-making is taken to be asymmetric [David] |
18356 | Correspondence is an over-ambitious attempt to explain truth-making [David] |
18363 | Correspondence theorists see facts as the only truth-makers [David] |
18364 | Correspondence theory likes ideal languages, that reveal the structure of propositions [David] |
18359 | One proposition can be made true by many different facts [David] |
18357 | What makes a disjunction true is simpler than the disjunctive fact it names [David] |
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] |
9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
6007 | If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R] |
17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
6008 | Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
15897 | Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine] |
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] |
18361 | A reflexive relation entails that the relation can't be asymmetric [David] |
17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |