35 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] |
| 8228 | Being is revealed at the point between waking and sleep [Anon (Cent)] |
| 5163 | Basic propositions refer to a single experience, are incorrigible, and conclusively verifiable [Ayer] |
| 8232 | Neglect your self, and feel the consciousness of each other being [Anon (Cent)] |
| 5167 | The argument from analogy fails, so the best account of other minds is behaviouristic [Ayer] |
| 5164 | A statement is meaningful if observation statements can be deduced from it [Ayer] |
| 5165 | Directly verifiable statements must entail at least one new observation statement [Ayer] |
| 5166 | The principle of verification is not an empirical hypothesis, but a definition [Ayer] |
| 5162 | Sentences only express propositions if they are meaningful; otherwise they are 'statements' [Ayer] |
| 8230 | Just as you have the impulse to do something, stop [Anon (Cent)] |
| 5168 | Moral approval and disapproval concerns classes of actions, rather than particular actions [Ayer] |
| 8234 | Bondage and liberation are relative terms, which only frighten those already terrified of the universe [Anon (Cent)] |
| 8227 | Feel your whole body saturated with cosmic essence [Anon (Cent)] |
| 8231 | Abandon attachment to body, and feel the joy of being everywhere [Anon (Cent)] |
| 8229 | The serenity in blue sky beyond clouds [Anon (Cent)] |
| 8233 | Imagine fire burning up your whole body, but not you [Anon (Cent)] |