31 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] |
| 7789 | Necessary implication is called 'strict implication'; if successful, it is called 'entailment' [Girle] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 7790 | If an argument is invalid, a truth tree will indicate a counter-example [Girle] |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| 7800 | Analytic truths are divided into logically and conceptually necessary [Girle] |
| 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] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 7902 | The Buddha made flowers float in the air, to impress people, and make them listen [Mahavastu] |