39 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] |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| 10861 | Beyond infinity cardinals and ordinals can come apart [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] |
| 6472 | Continuity is a sufficient criterion for the identity of a rock, but not for part of a smooth fluid [Russell] |
| 6473 | Physical things are series of appearances whose matter obeys physical laws [Russell] |
| 6465 | We need not deny substance, but there seems no reason to assert it [Russell] |
| 6471 | The assumption by physicists of permanent substance is not metaphysically legitimate [Russell] |
| 6466 | Where possible, logical constructions are to be substituted for inferred entities [Russell] |
| 6483 | Russell held that we are aware of states of our own brain [Russell, by Robinson,H] |
| 8244 | Sense-data are qualities devoid of subjectivity, which are the basis of science [Russell, by Deleuze/Guattari] |
| 6462 | Sense-data are not mental, but are part of the subject-matter of physics [Russell] |
| 6463 | Sense-data are objects, and do not contain the subject as part, the way beliefs do [Russell] |
| 6464 | Sense-data are usually objects within the body, but are not part of the subject [Russell] |
| 6467 | No sensibile is ever a datum to two people at once [Russell] |
| 6459 | We do not know whether sense-data exist as objects when they are not data [Russell] |
| 6460 | 'Sensibilia' are identical to sense-data, without actually being data for any mind [Russell] |
| 6461 | Ungiven sense-data can no more exist than unmarried husbands [Russell] |
| 6458 | Individuating sense-data is difficult, because they divide when closely attended to [Russell] |
| 6469 | Sense-data may be subjective, if closing our eyes can change them [Russell] |
| 5996 | Critolaus redefined Aristotle's moral aim as fulfilment instead of happiness [Critolaus, by White,SA] |
| 6470 | Matter is the limit of appearances as distance from the object diminishes [Russell] |
| 6468 | There is 'private space', and there is also the 'space of perspectives' [Russell] |