33 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] |
10397 | Abelard's mereology involves privileged and natural divisions, and principal parts [Abelard, by King,P] |
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] |
10395 | Abelard was an irrealist about virtually everything apart from concrete individuals [Abelard, by King,P] |
10396 | If 'animal' is wholly present in Socrates and an ass, then 'animal' is rational and irrational [Abelard, by King,P] |
15384 | Only words can be 'predicated of many'; the universality is just in its mode of signifying [Abelard, by Panaccio] |
8481 | The de dicto-de re modality distinction dates back to Abelard [Abelard, by Orenstein] |
15385 | Abelard's problem is the purely singular aspects of things won't account for abstraction [Panaccio on Abelard] |
6387 | A minimum requirement for a theory of meaning is that it include an account of truth [Davidson] |
6391 | A theory of truth tells us how communication by language is possible [Davidson] |
6388 | Is reference the key place where language and the world meet? [Davidson] |
6390 | With a holistic approach, we can give up reference in empirical theories of language [Davidson] |
6389 | To explain the reference of a name, you must explain its sentence-role, so reference can't be defined nonlinguistically [Davidson] |
15383 | Nothing external can truly be predicated of an object [Abelard, by Panaccio] |
10398 | Natural kinds are not special; they are just well-defined resemblance collections [Abelard, by King,P] |