24 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] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
7789 | Necessary implication is called 'strict implication'; if successful, it is called 'entailment' [Girle] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
7790 | If an argument is invalid, a truth tree will indicate a counter-example [Girle] |
17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
7800 | Analytic truths are divided into logically and conceptually necessary [Girle] |
7801 | Possibilities can be logical, theoretical, physical, economic or human [Girle] |
13766 | 'If' is the same as 'given that', so the degrees of belief should conform to probability theory [Ramsey, by Ramsey] |
7792 | A world has 'access' to a world it generates, which is important in possible worlds semantics [Girle] |
19143 | Ramsey gave axioms for an uncertain agent to decide their preferences [Ramsey, by Davidson] |