48 ideas
| 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] |
| 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] |
| 13076 | Scholastics treat relations as two separate predicates of the relata [Cover/O'Leary-Hawthorne] |
| 23708 | Humeans see properties as having no more essential features and relations than their distinctness [Friend/Kimpton-Nye, by PG] |
| 23709 | Dispositions are what individuate properties, and they constitute their essence [Friend/Kimpton-Nye] |
| 23707 | Powers are properties which necessitate dispositions [Friend/Kimpton-Nye] |
| 23714 | Dispositional essentialism (unlike the grounding view) says only fundamental properties are powers [Friend/Kimpton-Nye] |
| 23711 | A power is a property which consists entirely of dispositions [Friend/Kimpton-Nye] |
| 23712 | Powers are qualitative properties which fully ground dispositions [Friend/Kimpton-Nye] |
| 23698 | Dispositions have directed behaviour which occurs if triggered [Friend/Kimpton-Nye] |
| 23699 | 'Masked' dispositions fail to react because something intervenes [Friend/Kimpton-Nye] |
| 23700 | A disposition is 'altered' when the stimulus reverses the disposition [Friend/Kimpton-Nye] |
| 23701 | A disposition is 'mimicked' if a different cause produces that effect from that stimulus [Friend/Kimpton-Nye] |
| 23702 | A 'trick' can look like a stimulus for a disposition which will happen without it [Friend/Kimpton-Nye] |
| 23703 | Some dispositions manifest themselves without a stimulus [Friend/Kimpton-Nye] |
| 23704 | We could analyse dispositions as 'possibilities', with no mention of a stimulus [Friend/Kimpton-Nye] |
| 13102 | If you individuate things by their origin, you still have to individuate the origins themselves [Cover/O'Leary-Hawthorne] |
| 13103 | Numerical difference is a symmetrical notion, unlike proper individuation [Cover/O'Leary-Hawthorne] |
| 13104 | Haecceity as property, or as colourless thisness, or as singleton set [Cover/O'Leary-Hawthorne] |
| 13100 | Maybe 'substance' is more of a mass-noun than a count-noun [Cover/O'Leary-Hawthorne] |
| 13068 | We can ask for the nature of substance, about type of substance, and about individual substances [Cover/O'Leary-Hawthorne] |
| 13069 | The general assumption is that substances cannot possibly be non-substances [Cover/O'Leary-Hawthorne] |
| 13072 | Modern essences are sets of essential predicate-functions [Cover/O'Leary-Hawthorne] |
| 17080 | Modern essentialists express essence as functions from worlds to extensions for predicates [Cover/O'Leary-Hawthorne] |
| 13101 | Necessity-of-origin won't distinguish ex nihilo creations, or things sharing an origin [Cover/O'Leary-Hawthorne] |
| 23710 | Dispositionalism says modality is in the powers of this world, not outsourced to possible worlds [Friend/Kimpton-Nye] |
| 13081 | Even extreme modal realists might allow transworld identity for abstract objects [Cover/O'Leary-Hawthorne] |
| 13071 | We can go beyond mere causal explanations if we believe in an 'order of being' [Cover/O'Leary-Hawthorne] |
| 17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
| 23706 | Hume's Dictum says no connections are necessary - so mass and spacetime warping could separate [Friend/Kimpton-Nye] |