33 ideas
20744 | Phenomenologists say all experience is about something and is directed [Aho] |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
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] |
3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
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] |
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] |
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] |
5998 | From the necessity of the past we can infer the impossibility of what never happens [Diod.Cronus, by White,MJ] |
20832 | The Master Argument seems to prove that only what will happen is possible [Diod.Cronus, by Epictetus] |
14304 | Conditionals are true when the antecedent is true, and the consequent has to be true [Diod.Cronus] |
20736 | Science has to abstract out the subjective attributes of things, focusing on what is objective [Aho] |
17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
6024 | Thought is unambiguous, and you should stick to what the speaker thinks they are saying [Diod.Cronus, by Gellius] |
20734 | Anxiety, nausea, guilt and absurdity shake us up, revealing our freedom and limits [Aho] |
20733 | Our 'existence' is how we create ourselves, unconstrained by any prior 'essence' [Aho] |
20753 | The self is constituted by its choices made within a social context [Aho] |
20738 | Social contracts and markets have made society seem disconnected and artificial [Aho] |
20737 | Protestantism brought the modern emphasis on inner states of the soul [Aho] |
20766 | Four Noble Truths: life is suffering, caused by attachment, it is avoidable, there is a path [Aho] |