37 ideas
| 22115 | Wise people should contemplate and discuss the truth, and fight against falsehood [Aquinas] |
| 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] |
| 17000 | We might fix identities for small particulars, but it is utopian to hope for such things [Kripke] |
| 11868 | A different piece of wood could have been used for that table; constitution isn't identity [Wiggins on Kripke] |
| 17044 | A relation can clearly be reflexive, and identity is the smallest reflexive relation [Kripke] |
| 16999 | A vague identity may seem intransitive, and we might want to talk of 'counterparts' [Kripke] |
| 17058 | What many people consider merely physically necessary I consider completely necessary [Kripke] |
| 4970 | What is often held to be mere physical necessity is actually metaphysical necessity [Kripke] |
| 17059 | Unicorns are vague, so no actual or possible creature could count as a unicorn [Kripke] |
| 4950 | Possible worlds are useful in set theory, but can be very misleading elsewhere [Kripke] |
| 17003 | Kaplan's 'Dthat' is a useful operator for transforming a description into a rigid designation [Kripke] |
| 9221 | The best known objection to counterparts is Kripke's, that Humphrey doesn't care if his counterpart wins [Kripke, by Sider] |
| 17052 | The a priori analytic truths involving fixing of reference are contingent [Kripke] |
| 4969 | I regard the mind-body problem as wide open, and extremely confusing [Kripke] |
| 20700 | Without God's influence every operation would stop, so God causes everything [Aquinas] |
| 4956 | A description may fix a reference even when it is not true of its object [Kripke] |
| 17032 | Even if Gödel didn't produce his theorems, he's still called 'Gödel' [Kripke] |
| 15202 | Eternity coexists with passing time, as the centre of a circle coexists with its circumference [Aquinas] |