33 ideas
8092 | Logic was merely a branch of rhetoric until the scientific 17th century [Devlin] |
13838 | A decent modern definition should always imply a semantics [Hacking] |
19079 | For idealists reality is like a collection of beliefs, so truths and truthmakers are not distinct [Young,JO] |
19076 | Coherence theories differ over the coherence relation, and over the set of proposition with which to cohere [Young,JO] |
19077 | Two propositions could be consistent with your set, but inconsistent with one another [Young,JO] |
19078 | Coherence with actual beliefs, or our best beliefs, or ultimate ideal beliefs? [Young,JO] |
19084 | Coherent truth is not with an arbitrary set of beliefs, but with a set which people actually do believe [Young,JO] |
19083 | How do you identify the best coherence set; and aren't there truths which don't cohere? [Young,JO] |
19075 | Deflationary theories reject analysis of truth in terms of truth-conditions [Young,JO] |
8081 | 'No councillors are bankers' and 'All bankers are athletes' implies 'Some athletes are not councillors' [Devlin] |
8085 | Modern propositional inference replaces Aristotle's 19 syllogisms with modus ponens [Devlin] |
13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
8086 | Predicate logic retains the axioms of propositional logic [Devlin] |
8091 | Situation theory is logic that takes account of context [Devlin] |
8087 | Golden ages: 1900-1960 for pure logic, and 1950-1985 for applied logic [Devlin] |
8089 | Montague's intensional logic incorporated the notion of meaning [Devlin] |
13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
8082 | Where a conditional is purely formal, an implication implies a link between premise and conclusion [Devlin] |
8072 | Sentences of apparent identical form can have different contextual meanings [Devlin] |
13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
8075 | Space and time are atomic in the arrow, and divisible in the tortoise [Devlin] |
8088 | People still say the Hopi have no time concepts, despite Whorf's later denial [Devlin] |
19074 | Are truth-condtions other propositions (coherence) or features of the world (correspondence)? [Young,JO] |
19082 | Coherence truth suggests truth-condtions are assertion-conditions, which need knowledge of justification [Young,JO] |
8073 | How do we parse 'time flies like an arrow' and 'fruit flies like an apple'? [Devlin] |
8076 | The distinction between sentences and abstract propositions is crucial in logic [Devlin] |