29 ideas
| 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] |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| 7789 | Necessary implication is called 'strict implication'; if successful, it is called 'entailment' [Girle] |
| 9175 | We may fix the reference of 'Cicero' by a description, but thereafter the name is rigid [Kripke] |
| 9171 | The function of names is simply to refer [Kripke] |
| 7790 | If an argument is invalid, a truth tree will indicate a counter-example [Girle] |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| 7800 | Analytic truths are divided into logically and conceptually necessary [Girle] |
| 7801 | Possibilities can be logical, theoretical, physical, economic or human [Girle] |
| 9174 | It is necessary that this table is not made of ice, but we don't know it a priori [Kripke] |
| 7792 | A world has 'access' to a world it generates, which is important in possible worlds semantics [Girle] |
| 9172 | A 'rigid designator' designates the same object in all possible worlds [Kripke] |
| 9173 | We cannot say that Nixon might have been a different man from the one he actually was [Kripke] |
| 9176 | Modal statements about this table never refer to counterparts; that confuses epistemology and metaphysics [Kripke] |
| 9177 | Identity theorists must deny that pains can be imagined without brain states [Kripke] |
| 9178 | Pain, unlike heat, is picked out by an essential property [Kripke] |