29 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] |
| 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] |
| 9175 | We may fix the reference of 'Cicero' by a description, but thereafter the name is rigid [Kripke] |
| 9171 | The function of names is simply to refer [Kripke] |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| 7508 | Good reductionism connects fields of knowledge, but doesn't replace one with another [Pinker] |
| 9174 | It is necessary that this table is not made of ice, but we don't know it a priori [Kripke] |
| 9172 | A 'rigid designator' designates the same object in all possible worlds [Kripke] |
| 9173 | We cannot say that Nixon might have been a different man from the one he actually was [Kripke] |
| 9176 | Modal statements about this table never refer to counterparts; that confuses epistemology and metaphysics [Kripke] |
| 7510 | Connectionists say the mind is a general purpose learning device [Pinker] |
| 7513 | Is memory stored in protein sequences, neurons, synapses, or synapse-strengths? [Pinker] |
| 7509 | Roundworms live successfully with 302 neurons, so human freedom comes from our trillions [Pinker] |
| 9177 | Identity theorists must deny that pains can be imagined without brain states [Kripke] |
| 7511 | Neural networks can generalise their training, e.g. truths about tigers apply mostly to lions [Pinker] |
| 7512 | There are five types of reasoning that seem beyond connectionist systems [Pinker, by PG] |
| 9178 | Pain, unlike heat, is picked out by an essential property [Kripke] |
| 7505 | Many think that accepting human nature is to accept innumerable evils [Pinker] |
| 7516 | In 1828, the stuff of life was shown to be ordinary chemistry, not a magic gel [Pinker] |
| 7515 | All the evidence says evolution is cruel and wasteful, not intelligent [Pinker] |
| 7514 | Intelligent Design says that every unexplained phenomenon must be design, by default [Pinker] |