41 ideas
20981 | What justifies reliance on reason? Is it just a tool? Why is it better than blind belief? [Sen] |
20982 | In politics and ethics, scrutiny from different perspectives is essential for objectivity [Sen] |
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] |
20990 | Rationality is conformity to reasons that can be sustained even after scrutiny [Sen] |
21005 | A human right is not plausible if public scrutiny might reject it [Sen] |
20983 | The original position insures that the agreements reached are fair [Sen] |
20987 | The veil of ignorance encourages neutral interests, but not a wider view of values [Sen] |
20984 | A social contract limits the pursuit of justice to members of a single society [Sen] |
20986 | A person's voice may count because of their interests, or because of their good sense [Sen] |
21001 | Famines tend to be caused by authoritarian rule [Sen] |
21002 | Effective democracy needs tolerant values [Sen] |
20999 | Democracy as 'government by discussion' now has wide support [Sen] |
20979 | Democracy needs more than some institutions; diverse sections of the people must be heard [Sen] |
20993 | Eradicating smallpox does not impoverish nature [Sen] |
20995 | Capabilities are part of freedom, involving real opportunities [Sen] |
20998 | Freedom can involve capabilities, independence and non-interference [Sen] |
20997 | The need for equality among people arises from impartiality and objectivity [Sen] |
20996 | All modern theories of justice demand equality of something [Sen] |
20988 | Freedom from torture or terrorist attacks is independent of citizenship [Sen] |
20980 | You don't need a complete theory of justice to see that slavery is wrong [Sen] |
20978 | Practical justice concerns not only ideals, but ways to achieve them [Sen] |
20985 | Our institutions should promote justice, rather than embodying it [Sen] |
20994 | We must focus on removing manifest injustice, not just try to design a perfect society [Sen] |
21000 | If justice needs public reasoning, which needs democracy, then justice and democracy are linked [Sen] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |