40 ideas
| 8092 | Logic was merely a branch of rhetoric until the scientific 17th century [Devlin] |
| 21962 | Metaphysics is the roots of the tree of science [Descartes] |
| 3659 | I know the truth that God exists and is the author of truth [Descartes] |
| 13252 | Some truths have true negations [Beall/Restall] |
| 13247 | A truthmaker is an object which entails a sentence [Beall/Restall] |
| 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] |
| 8086 | Predicate logic retains the axioms of propositional logic [Devlin] |
| 13249 | (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall] |
| 13243 | Excluded middle must be true for some situation, not for all situations [Beall/Restall] |
| 13242 | It's 'relevantly' valid if all those situations make it true [Beall/Restall] |
| 13245 | Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall] |
| 13246 | Relevant logic does not abandon classical logic [Beall/Restall] |
| 13254 | A doesn't imply A - that would be circular [Beall/Restall] |
| 13255 | Relevant logic may reject transitivity [Beall/Restall] |
| 13250 | Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall] |
| 8091 | Situation theory is logic that takes account of context [Devlin] |
| 13235 | Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall] |
| 13238 | Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall] |
| 8089 | Montague's intensional logic incorporated the notion of meaning [Devlin] |
| 8087 | Golden ages: 1900-1960 for pure logic, and 1950-1985 for applied logic [Devlin] |
| 13234 | The view of logic as knowing a body of truths looks out-of-date [Beall/Restall] |
| 13232 | Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall] |
| 13241 | The model theory of classical predicate logic is mathematics [Beall/Restall] |
| 13253 | There are several different consequence relations [Beall/Restall] |
| 13240 | A sentence follows from others if they always model it [Beall/Restall] |
| 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] |
| 13236 | Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall] |
| 8075 | Space and time are atomic in the arrow, and divisible in the tortoise [Devlin] |
| 13237 | Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall] |
| 13244 | Relevant necessity is always true for some situation (not all situations) [Beall/Restall] |
| 3657 | Understanding, not the senses, gives certainty [Descartes] |
| 8088 | People still say the Hopi have no time concepts, despite Whorf's later denial [Devlin] |
| 13239 | Judgement is always predicating a property of a subject [Beall/Restall] |
| 8073 | How do we parse 'time flies like an arrow' and 'fruit flies like an apple'? [Devlin] |
| 13248 | We can rest truth-conditions on situations, rather than on possible worlds [Beall/Restall] |
| 13233 | Propositions commit to content, and not to any way of spelling it out [Beall/Restall] |
| 8076 | The distinction between sentences and abstract propositions is crucial in logic [Devlin] |
| 3660 | Atheism arises from empiricism, because God is intangible [Descartes] |