23 ideas
8092 | Logic was merely a branch of rhetoric until the scientific 17th century [Devlin] |
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] |
13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
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] |
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] |
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] |
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] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |