41 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] |
| 10405 | In the iterative conception of sets, they form a natural hierarchy [Swoyer] |
| 10407 | Logical Form explains differing logical behaviour of similar sentences [Swoyer] |
| 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] |
| 10421 | Supervenience is nowadays seen as between properties, rather than linguistic [Swoyer] |
| 10410 | Anti-realists can't explain different methods to measure distance [Swoyer] |
| 10416 | Can properties have parts? [Swoyer] |
| 10399 | If a property such as self-identity can only be in one thing, it can't be a universal [Swoyer] |
| 10417 | There are only first-order properties ('red'), and none of higher-order ('coloured') [Swoyer] |
| 10413 | The best-known candidate for an identity condition for properties is necessary coextensiveness [Swoyer] |
| 10402 | Various attempts are made to evade universals being wholly present in different places [Swoyer] |
| 10400 | Conceptualism says words like 'honesty' refer to concepts, not to properties [Swoyer] |
| 10403 | If properties are abstract objects, then their being abstract exemplifies being abstract [Swoyer] |
| 10406 | One might hope to reduce possible worlds to properties [Swoyer] |
| 10404 | Extreme empiricists can hardly explain anything [Swoyer] |
| 10408 | Intensions are functions which map possible worlds to sets of things denoted by an expression [Swoyer] |
| 10409 | Research suggests that concepts rely on typical examples [Swoyer] |
| 10401 | The F and G of logic cover a huge range of natural language combinations [Swoyer] |
| 10420 | Maybe a proposition is just a property with all its places filled [Swoyer] |
| 21995 | Must production determine superstructure, or could it be the other way round? [Singer on Marx] |
| 20577 | Even decently paid workers still have their produce bought with money stolen from them [Marx] |
| 10412 | If laws are mere regularities, they give no grounds for future prediction [Swoyer] |
| 10411 | Two properties can have one power, and one property can have two powers [Swoyer] |