30 ideas
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] |
7949 | Varied descriptions of an event will explain varied behaviour relating to it [Davidson, by Macdonald,C] |
16458 | Semantic vagueness involves alternative and equal precisifications of the language [Lewis] |
20020 | If one action leads directly to another, they are all one action [Davidson, by Wilson/Schpall] |
20072 | We explain an intention by giving an account of acting with an intention [Davidson, by Stout,R] |
20045 | Acting for a reason is a combination of a pro attitude, and a belief that the action is appropriate [Davidson] |
23734 | The best explanation of reasons as purposes for actions is that they are causal [Davidson, by Smith,M] |
23737 | Reasons can give purposes to actions, without actually causing them [Smith,M on Davidson] |
20075 | Early Davidson says intentional action is caused by reasons [Davidson, by Stout,R] |
6664 | Reasons must be causes when agents act 'for' reasons [Davidson, by Lowe] |
3395 | Davidson claims that what causes an action is the reason for doing it [Davidson, by Kim] |