43 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] |
| 16588 | I prefer a lack of form to mean non-existence, than to think of some quasi-existence [Augustine] |
| 22979 | Three main questions seem to be whether a thing is, what it is, and what sort it is [Augustine] |
| 22977 | I can distinguish different smells even when I am not experiencing them [Augustine] |
| 22982 | Why does joy in my mind make me happy, but joy in my memory doesn't? [Augustine] |
| 22981 | Mind and memory are the same, as shown in 'bear it in mind' or 'it slipped from mind' [Augustine] |
| 22980 | Memory contains innumerable principles of maths, as well as past sense experiences [Augustine] |
| 22983 | We would avoid remembering sorrow or fear if that triggered the emotions afresh [Augustine] |
| 22978 | Memory is so vast that I cannot recognise it as part of my mind [Augustine] |
| 22984 | Without memory I could not even speak of myself [Augustine] |
| 5982 | If the future does not exist, how can prophets see it? [Augustine] |
| 22976 | Memories are preserved separately, according to category [Augustine] |
| 18678 | Maybe final value rests on the extrinsic property of being valued by a rational agent [Korsgaard, by Orsi] |
| 22985 | Everyone wants happiness [Augustine] |
| 5984 | Maybe time is an extension of the mind [Augustine] |
| 22888 | To be aware of time it can only exist in the mind, as memory or anticipation [Augustine, by Bardon] |
| 5980 | How can ten days ahead be a short time, if it doesn't exist? [Augustine] |
| 5979 | If the past is no longer, and the future is not yet, how can they exist? [Augustine] |
| 5981 | The whole of the current year is not present, so how can it exist? [Augustine] |
| 5978 | I know what time is, until someone asks me to explain it [Augustine] |
| 5983 | I disagree with the idea that time is nothing but cosmic movement [Augustine] |
| 5977 | Heaven and earth must be created, because they are subject to change [Augustine] |
| 22887 | If God existed before creation, why would a perfect being desire to change things? [Augustine, by Bardon] |
| 5976 | If God is outside time in eternity, can He hear prayers? [Augustine] |