34 ideas
17651 | Without words or other symbols, we have no world [Goodman] |
17652 | Truth is irrelevant if no statements are involved [Goodman] |
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] |
9944 | We understand some statements about all sets [Putnam] |
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] |
9937 | I do not believe mathematics either has or needs 'foundations' [Putnam] |
9939 | It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam] |
9940 | Maybe mathematics is empirical in that we could try to change it [Putnam] |
9941 | Science requires more than consistency of mathematics [Putnam] |
17656 | Being primitive or prior always depends on a constructional system [Goodman] |
17661 | We don't recognise patterns - we invent them [Goodman] |
17659 | Reality is largely a matter of habit [Goodman] |
17657 | We build our world, and ignore anything that won't fit [Goodman] |
9943 | You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam] |
17654 | A world can be full of variety or not, depending on how we sort it [Goodman] |
17653 | Things can only be judged the 'same' by citing some respect of sameness [Goodman] |
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] |
17660 | Discovery is often just finding a fit, like a jigsaw puzzle [Goodman] |
17658 | Users of digital thermometers recognise no temperatures in the gaps [Goodman] |
17650 | We lack frames of reference to transform physics, biology and psychology into one another [Goodman] |
17655 | Grue and green won't be in the same world, as that would block induction entirely [Goodman] |
17649 | If the world is one it has many aspects, and if there are many worlds they will collect into one [Goodman] |