29 ideas
16415 | Esoteric metaphysics aims to be top science, investigating ultimate reality [Hofweber] |
16413 | Science has discovered properties of things, so there are properties - so who needs metaphysics? [Hofweber] |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
6334 | The function of the truth predicate? Understanding 'true'? Meaning of 'true'? The concept of truth? A theory of truth? [Horwich] |
6342 | Some correspondence theories concern facts; others are built up through reference and satisfaction [Horwich] |
6332 | The common-sense theory of correspondence has never been worked out satisfactorily [Horwich] |
6335 | The redundancy theory cannot explain inferences from 'what x said is true' and 'x said p', to p [Horwich] |
6344 | Truth is a useful concept for unarticulated propositions and generalisations about them [Horwich] |
6336 | No deflationary conception of truth does justice to the fact that we aim for truth [Horwich] |
23299 | Horwich's deflationary view is novel, because it relies on propositions rather than sentences [Horwich, by Davidson] |
6337 | The deflationary picture says believing a theory true is a trivial step after believing the theory [Horwich] |
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] |
6339 | Logical form is the aspects of meaning that determine logical entailments [Horwich] |
16416 | The quantifier in logic is not like the ordinary English one (which has empty names, non-denoting terms etc) [Hofweber] |
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] |
6338 | We could know the truth-conditions of a foreign sentence without knowing its meaning [Horwich] |
6340 | There are Fregean de dicto propositions, and Russellian de re propositions, or a mixture [Horwich] |
6341 | Right translation is a mapping of languages which preserves basic patterns of usage [Horwich] |