25 ideas
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
18928 | If maximalism is necessary, then that nothing exists has a truthmaker, which it can't have [Cameron] |
18931 | Determinate truths don't need extra truthmakers, just truthmakers that are themselves determinate [Cameron] |
18932 | The facts about the existence of truthmakers can't have a further explanation [Cameron] |
18923 | The present property 'having been F' says nothing about a thing's intrinsic nature [Cameron] |
18926 | One temporal distibution property grounds our present and past truths [Cameron] |
18929 | We don't want present truthmakers for the past, if they are about to cease to exist! [Cameron] |
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] |
18924 | Being polka-dotted is a 'spatial distribution' property [Cameron] |
18930 | Change is instantiation of a non-uniform distributional property, like 'being red-then-orange' [Cameron] |
9100 | Our intellect only assents to what we believe to be true [William of Ockham] |
9101 | Abstractive cognition knows universals abstracted from many singulars [William of Ockham] |
18927 | Surely if things extend over time, then time itself must be extended? [Cameron] |