29 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] |
| 12582 | The function of beliefs is to produce beliefs-that-p when p [Millikan] |
| 4058 | Is someone's right to life diminished if they were conceived by a rape? [Thomson] |
| 4060 | The right to life does not bestow the right to use someone else's body to support that life [Thomson] |
| 4062 | No one is morally required to make huge sacrifices to keep someone else alive for nine months [Thomson] |
| 4061 | The right to life is not a right not to be killed, but not to be killed unjustly [Thomson] |
| 4057 | A newly fertilized ovum is no more a person than an acorn is an oak tree [Thomson] |
| 4695 | Maybe abortion can be justified despite the foetus having full human rights [Thomson, by Foot] |
| 4059 | It can't be murder for a mother to perform an abortion on herself to save her own life [Thomson] |
| 4696 | The foetus is safe in the womb, so abortion initiates its death, with the mother as the agent. [Foot on Thomson] |