39 ideas
| 4036 | What matters is not how many entities we postulate, but how many kinds of entities [Armstrong, by Mellor/Oliver] |
| 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] |
| 15754 | Without properties we would be unable to express the laws of nature [Armstrong] |
| 4034 | Whether we apply 'cold' or 'hot' to an object is quite separate from its change of temperature [Armstrong] |
| 8535 | To the claim that every predicate has a property, start by eliminating failure of application of predicate [Armstrong] |
| 8537 | Tropes fall into classes, because exact similarity is symmetrical and transitive [Armstrong] |
| 8538 | Trope theory needs extra commitments, to symmetry and non-transitivity, unless resemblance is exact [Armstrong] |
| 8539 | Universals are required to give a satisfactory account of the laws of nature [Armstrong] |
| 8529 | Deniers of properties and relations rely on either predicates or on classes [Armstrong] |
| 8532 | Resemblances must be in certain 'respects', and they seem awfully like properties [Armstrong] |
| 8530 | Change of temperature in objects is quite independent of the predicates 'hot' and 'cold' [Armstrong] |
| 8536 | We want to know what constituents of objects are grounds for the application of predicates [Armstrong] |
| 8531 | In most sets there is no property common to all the members [Armstrong] |
| 15753 | Essences might support Resemblance Nominalism, but they are too coarse and ill-defined [Armstrong] |
| 8533 | Predicates need ontological correlates to ensure that they apply [Armstrong] |
| 4035 | There must be some explanation of why certain predicates are applicable to certain objects [Armstrong] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 8541 | Regularities theories are poor on causal connections, counterfactuals and probability [Armstrong] |
| 8540 | The introduction of sparse properties avoids the regularity theory's problem with 'grue' [Armstrong] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |