34 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] |
16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
6685 | 'Subjectivism' is an extension of relativism from the social group to the individual [Graham] |
6699 | The chain of consequences may not be the same as the chain of responsibility [Graham] |
6698 | Negative consequences are very hard (and possibly impossible) to assess [Graham] |
6700 | We can't criticise people because of unforeseeable consequences [Graham] |
6704 | Egoism submits to desires, but cannot help form them [Graham] |
6701 | Rescue operations need spontaneous benevolence, not careful thought [Graham] |
6693 | 'What if everybody did that?' rather misses the point as an objection to cheating [Graham] |
6691 | It is more plausible to say people can choose between values, than that they can create them [Graham] |
6688 | Life is only absurd if you expected an explanation and none turns up [Graham] |
6705 | Existentialism may transcend our nature, unlike eudaimonism [Graham] |
6690 | A standard problem for existentialism is the 'sincere Nazi' [Graham] |
6689 | The key to existentialism: the way you make choices is more important than what you choose [Graham] |
6706 | The great religions are much more concerned with the religious life than with ethics [Graham] |
6709 | Western religion saves us from death; Eastern religion saves us from immortality [Graham] |