21 ideas
8378 | Philosophers usually learn science from each other, not from science [Russell] |
13838 | A decent modern definition should always imply a semantics [Hacking] |
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] |
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] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
17809 | Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel] |
17810 | The study of mathematical foundations needs new non-mathematical concepts [Kreisel] |
8375 | 'Necessary' is a predicate of a propositional function, saying it is true for all values of its argument [Russell] |
4396 | The law of causality is a source of confusion, and should be dropped from philosophy [Russell] |
8376 | If causes are contiguous with events, only the last bit is relevant, or the event's timing is baffling [Russell] |
8380 | Striking a match causes its igniting, even if it sometimes doesn't work [Russell] |
8379 | In causal laws, 'events' must recur, so they have to be universals, not particulars [Russell] |
8381 | The constancy of scientific laws rests on differential equations, not on cause and effect [Russell] |
17811 | The natural conception of points ducks the problem of naming or constructing each point [Kreisel] |