25 ideas
9766 | Study vagueness first by its logic, then by its truth-conditions, and then its metaphysics [Fine,K] |
13838 | A decent modern definition should always imply a semantics [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] |
13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [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] |
9775 | Excluded Middle, and classical logic, may fail for vague predicates [Fine,K] |
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] |
9771 | Logic holding between indefinite sentences is the core of all language [Fine,K] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
9768 | Vagueness is semantic, a deficiency of meaning [Fine,K] |
9776 | A thing might be vaguely vague, giving us higher-order vagueness [Fine,K] |
9767 | A vague sentence is only true for all ways of making it completely precise [Fine,K] |
9770 | Logical connectives cease to be truth-functional if vagueness is treated with three values [Fine,K] |
9772 | Meaning is both actual (determining instances) and potential (possibility of greater precision) [Fine,K] |
9773 | With the super-truth approach, the classical connectives continue to work [Fine,K] |
9774 | Borderline cases must be under our control, as capable of greater precision [Fine,K] |
9769 | Vagueness can be in predicates, names or quantifiers [Fine,K] |
9074 | Abstraction cannot produce the concept of a 'game', as there is no one common feature [Barnes,J] |
9073 | Abstraction from an ambiguous concept like 'mole' will define them as the same [Barnes,J] |
9072 | Defining concepts by abstractions will collect together far too many attributes from entities [Barnes,J] |