28 ideas
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| 10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| 10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
| 10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
| 10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
| 10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
| 10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
| 10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
| 10763 | Completeness and compactness together give axiomatizability [Tharp] |
| 10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
| 10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
| 10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
| 10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
| 10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
| 7508 | Good reductionism connects fields of knowledge, but doesn't replace one with another [Pinker] |
| 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] |
| 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] |
| 7505 | Many think that accepting human nature is to accept innumerable evils [Pinker] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 7516 | In 1828, the stuff of life was shown to be ordinary chemistry, not a magic gel [Pinker] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| 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] |