44 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] |
| 10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| 10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
| 10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| 10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
| 10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
| 10871 | Axiom of Existence: there exists at least one set [Clegg] |
| 10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| 10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
| 10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
| 10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
| 10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
| 10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
| 12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
| 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] |