22 ideas
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] |
23548 | Indeterminacy is in conflict with classical logic [Fine,K] |
13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
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] |
23539 | Classical semantics has referents for names, extensions for predicates, and T or F for sentences [Fine,K] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
23544 | Local indeterminacy concerns a single object, and global indeterminacy covers a range [Fine,K] |
23540 | Conjoining two indefinites by related sentences seems to produce a contradiction [Fine,K] |
23546 | Standardly vagueness involves borderline cases, and a higher standpoint from which they can be seen [Fine,K] |
23542 | Identifying vagueness with ignorance is the common mistake of confusing symptoms with cause [Fine,K] |
23541 | Supervaluation can give no answer to 'who is the last bald man' [Fine,K] |
23545 | We do not have an intelligible concept of a borderline case [Fine,K] |
23547 | It seems absurd that there is no identity of any kind between two objects which involve survival [Fine,K] |
11968 | The intension of a sentence is the set of all possible worlds in which it is true [Carnap, by Kaplan] |
23543 | We identify laws with regularities because we mistakenly identify causes with their symptoms [Fine,K] |