39 ideas
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
18915 | If facts are the truthmakers, they are not in the world [Engelbretsen] |
18919 | There are no 'falsifying' facts, only an absence of truthmakers [Engelbretsen] |
18913 | Traditional term logic struggled to express relations [Engelbretsen] |
18907 | Term logic rests on negated terms or denial, and that propositions are tied pairs [Engelbretsen] |
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] |
18912 | Was logic a branch of mathematics, or mathematics a branch of logic? [Engelbretsen] |
18905 | Propositions can be analysed as pairs of terms glued together by predication [Engelbretsen] |
18922 | Logical syntax is actually close to surface linguistic form [Engelbretsen] |
18908 | Standard logic only negates sentences, even via negated general terms or predicates [Engelbretsen] |
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] |
18917 | Existence and nonexistence are characteristics of the world, not of objects [Engelbretsen] |
16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
18916 | Facts are not in the world - they are properties of the world [Engelbretsen] |
18921 | Individuals are arranged in inclusion categories that match our semantics [Engelbretsen] |
17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
18918 | Terms denote objects with properties, and statements denote the world with that property [Engelbretsen] |
18920 | 'Socrates is wise' denotes a sentence; 'that Socrates is wise' denotes a proposition [Engelbretsen] |
18906 | Negating a predicate term and denying its unnegated version are quite different [Engelbretsen] |