21 ideas
13838 | A decent modern definition should always imply a semantics [Hacking] |
18901 | Truthmakers are facts 'of' a domain, not something 'in' the domain [Sommers] |
18904 | 'Predicable' terms come in charged pairs, with one the negation of the other [Sommers, by Engelbretsen] |
18895 | Logic which maps ordinary reasoning must be transparent, and free of variables [Sommers] |
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] |
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] |
18897 | Predicate logic has to spell out that its identity relation '=' is an equivalent relation [Sommers] |
18893 | Translating into quantificational idiom offers no clues as to how ordinary thinkers reason [Sommers] |
13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
18903 | Sommers promotes the old idea that negation basically refers to terms [Sommers, by Engelbretsen] |
13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
18894 | Predicates form a hierarchy, from the most general, down to names at the bottom [Sommers] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
18900 | Unfortunately for realists, modern logic cannot say that some fact exists [Sommers] |
10494 | Several words may label a category; one word can name several categories; some categories lack words [Ellen] |
18898 | In standard logic, names are the only way to refer [Sommers] |