36 ideas
| 15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
| 7786 | Propositional logic handles negation, disjunction, conjunction; predicate logic adds quantifiers, predicates, relations [Girle] |
| 7798 | There are three axiom schemas for propositional logic [Girle] |
| 7799 | Proposition logic has definitions for its three operators: or, and, and identical [Girle] |
| 7797 | Axiom systems of logic contain axioms, inference rules, and definitions of proof and theorems [Girle] |
| 7794 | There are seven modalities in S4, each with its negation [Girle] |
| 7793 | ◊p → □◊p is the hallmark of S5 [Girle] |
| 7795 | S5 has just six modalities, and all strings can be reduced to those [Girle] |
| 7787 | Possible worlds logics use true-in-a-world rather than true [Girle] |
| 7788 | Modal logic has four basic modal negation equivalences [Girle] |
| 7796 | Modal logics were studied in terms of axioms, but now possible worlds semantics is added [Girle] |
| 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] |
| 7789 | Necessary implication is called 'strict implication'; if successful, it is called 'entailment' [Girle] |
| 7790 | If an argument is invalid, a truth tree will indicate a counter-example [Girle] |
| 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] |
| 11976 | Aristotelian essentialism says essences are not relative to specification [Lewis] |
| 7800 | Analytic truths are divided into logically and conceptually necessary [Girle] |
| 11978 | Causal necessities hold in all worlds compatible with the laws of nature [Lewis] |
| 7801 | Possibilities can be logical, theoretical, physical, economic or human [Girle] |
| 7792 | A world has 'access' to a world it generates, which is important in possible worlds semantics [Girle] |
| 11979 | It doesn't take the whole of a possible Humphrey to win the election [Lewis] |
| 16994 | Counterpart theory is bizarre, as no one cares what happens to a mere counterpart [Kripke on Lewis] |
| 11974 | Counterparts are not the original thing, but resemble it more than other things do [Lewis] |
| 11975 | If the closest resembler to you is in fact quite unlike you, then you have no counterpart [Lewis] |
| 11977 | Essential attributes are those shared with all the counterparts [Lewis] |