27 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] |
| 7658 | Obviously there can't be a functional anaylsis of qualia if they are defined by intrinsic properties [Dennett] |
| 5952 | Rather than being the whole soul, maybe I am its chief part? [Plutarch] |
| 7655 | The work done by the 'homunculus in the theatre' must be spread amongst non-conscious agencies [Dennett] |
| 7657 | Intelligent agents are composed of nested homunculi, of decreasing intelligence, ending in machines [Dennett] |
| 7656 | I don't deny consciousness; it just isn't what people think it is [Dennett] |
| 5951 | If atoms have no qualities, they cannot possibly produce a mind [Plutarch] |
| 7654 | What matters about neuro-science is the discovery of the functional role of the chemistry [Dennett] |
| 20796 | Action needs an affinity for a presentation, and an impulse toward the affinity [Plutarch] |
| 5948 | The good life involves social participation, loyalty, temperance and honesty [Plutarch] |
| 5950 | If only atoms exist, how do qualities arise when the atoms come together? [Plutarch] |
| 5955 | No one will ever find a city that lacks religious practices [Plutarch] |