37 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] |
12295 | 3-D says things are stretched in space but not in time, and entire at a time but not at a location [Fine,K] |
12298 | Genuine motion, rather than variation of position, requires the 'entire presence' of the object [Fine,K] |
12296 | 4-D says things are stretched in space and in time, and not entire at a time or at a location [Fine,K] |
18882 | You can ask when the wedding was, but not (usually) when the bride was [Fine,K, by Simons] |
12297 | Three-dimensionalist can accept temporal parts, as things enduring only for an instant [Fine,K] |
23805 | Some explanations offer to explain a mystery by a greater mystery [Schulte] |
23806 | Naturalist accounts of representation must match the views of cognitive science [Schulte] |
23793 | On the whole, referential content is seen as broad, and sense content as narrow [Schulte] |
23796 | Naturalists must explain both representation, and what is represented [Schulte] |
23792 | Phenomenal and representational character may have links, or even be united [Schulte] |
23795 | Naturalistic accounts of content cannot rely on primitive mental or normative notions [Schulte] |
23804 | Maybe we can explain mental content in terms of phenomenal properties [Schulte] |
23802 | Conceptual role semantics says content is determined by cognitive role [Schulte] |
23797 | Cause won't explain content, because one cause can produce several contents [Schulte] |
23799 | Teleosemantics explains content in terms of successful and unsuccessful functioning [Schulte] |
23800 | Teleosemantic explanations say content is the causal result of naturally selected functions [Schulte] |
23798 | Information theories say content is information, such as smoke making fire probable [Schulte] |