31 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] |
| 7621 | Special relativity, unlike general relativity, was operationalist in spirit [Putnam on Einstein] |
| 7658 | Obviously there can't be a functional anaylsis of qualia if they are defined by intrinsic properties [Dennett] |
| 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] |
| 7654 | What matters about neuro-science is the discovery of the functional role of the chemistry [Dennett] |
| 22955 | Einstein took causation to be the bedrock of physics [Einstein, by Coveney/Highfield] |
| 20638 | General relativity assumes laws of nature are the same in all frames of reference [Einstein, by Close] |
| 20636 | Newton is a special case of Einstein's general theory, with an infinite speed of light [Einstein, by Close] |
| 21230 | The theory is 'special' because it sticks to observers moving straight, at constant speeds [Einstein, by Farmelo] |
| 21231 | Assume the speed of light is constant for all observers, and the laws of physics are the same [Einstein, by Farmelo] |
| 20634 | General Relativity says there is no absolute force or acceleration [Einstein, by Close] |
| 20648 | Mass is a measure of energy content [Einstein] |
| 21232 | Space-time arises from the connection between measurements of space and of time [Einstein, by Farmelo] |
| 7626 | I do not believe in a personal God [Einstein] |