35 ideas
23277 | Modern pragmatism sees objectivity as possible, despite its gradual evolution [Misak] |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
19108 | Truth is proper assertion, but that has varying standards [Misak] |
19094 | For pragmatists the loftiest idea of truth is just a feature of what remains forever assertible [Misak] |
19105 | Truth isn't a grand elusive property, if it is just the aim of our assertions and inquiries [Misak] |
19100 | Truth makes disagreements matter, or worth settling [Misak] |
19099 | 'True' is used for emphasis, clarity, assertion, comparison, objectivity, meaning, negation, consequence... [Misak] |
19103 | 'That's true' doesn't just refer back to a sentence, but implies sustained evidence for it [Misak] |
19101 | Disquotation is bivalent [Misak] |
19096 | Disquotationalism resembles a telephone directory [Misak] |
19106 | Disquotations says truth is assertion, and assertion proclaims truth - but what is 'assertion'? [Misak] |
19098 | Deflating the correspondence theory doesn't entail deflating all the other theories [Misak] |
19104 | Deflationism isn't a theory of truth, but an account of its role in natural language [Misak] |
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] |
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] |
17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
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] |
19109 | The anti-realism debate concerns whether indefeasibility is a plausible aim of inquiry [Misak] |
17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |