32 ideas
18005 | Philosophy aims to become more disciplined about categories [Ryle] |
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] |
14297 | A dispositional property is not a state, but a liability to be in some state, given a condition [Ryle] |
14300 | No physical scientist now believes in an occult force-exerting agency [Ryle] |
19440 | How do you know you have conceived a thing deeply enough to assess its possibility? [Vaidya] |
2622 | Can one movement have a mental and physical cause? [Ryle] |
1353 | Reporting on myself has the same problems as reporting on you [Ryle] |
1354 | We cannot introspect states of anger or panic [Ryle] |
2624 | I cannot prepare myself for the next thought I am going to think [Ryle] |
2620 | Dualism is a category mistake [Ryle] |
2388 | Behaviour depends on desires as well as beliefs [Chalmers on Ryle] |
3354 | You can't explain mind as dispositions, if they aren't real [Benardete,JA on Ryle] |
2387 | How can behaviour be the cause of behaviour? [Chalmers on Ryle] |