50 ideas
| 6211 | Laughter is a sudden glory in realising the infirmity of others, or our own formerly [Hobbes] |
| 21474 | Metaphysics studies the inexplicable ends of explanation [Schopenhauer] |
| 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] |
| 21470 | For me the objective thing-in-itself is the will [Schopenhauer] |
| 21479 | Knowledge is not power! Ignorant people possess supreme authority [Schopenhauer] |
| 21476 | A priori propositions are those we could never be seriously motivated to challenge [Schopenhauer] |
| 21473 | All knowledge and explanation rests on the inexplicable [Schopenhauer] |
| 21478 | Half our thinking is unconscious, and we reach conclusions while unaware of premises [Schopenhauer] |
| 6213 | A man cannot will to will, or will to will to will, so the idea of a voluntary will is absurd [Hobbes] |
| 21477 | We don't control our own thinking [Schopenhauer] |
| 6208 | Conceptions and apparitions are just motion in some internal substance of the head [Hobbes] |
| 21475 | All of our concepts are borrowed from perceptual knowledge [Schopenhauer] |
| 21372 | Aesthetics concerns how we can take pleasure in an object, with no reference to the will [Schopenhauer] |
| 21488 | The beautiful is a perception of Plato's Forms, which eliminates the will [Schopenhauer] |
| 21483 | Man is essentially a dreadful wild animal [Schopenhauer] |
| 6209 | There is no absolute good, for even the goodness of God is goodness to us [Hobbes] |
| 6210 | Life has no end (not even happiness), because we have desires, which presuppose a further end [Hobbes] |
| 21466 | Pleasure is weaker, and pain stronger, than we expect [Schopenhauer] |
| 21484 | A man's character can be learned from a single characteristic action [Schopenhauer] |
| 21482 | The five Chinese virtues: pity, justice, politeness, wisdom, honesty [Schopenhauer] |
| 21481 | Buddhists wisely start with the cardinal vices [Schopenhauer] |
| 21480 | Boredom is only felt by those clever enough to need activity [Schopenhauer] |
| 21469 | Human life is a mistake, shown by boredom, which is direct awareness of the fact [Schopenhauer] |
| 21485 | The state only exists to defend citizens, from exterior threats, and from one another [Schopenhauer] |
| 21486 | Poverty and slavery are virtually two words for the same thing [Schopenhauer] |
| 21487 | The freedom of the press to sell poison outweighs its usefulness [Schopenhauer] |
| 21471 | If suicide was quick and easy, most people would have done it by now [Schopenhauer] |
| 6212 | Lust involves pleasure, and also the sense of power in pleasing others [Hobbes] |
| 21467 | Would humanity still exist if sex wasn't both desired and pleasurable? [Schopenhauer] |
| 21472 | Only religion introduces serious issues to uneducated people [Schopenhauer] |
| 21468 | The Creator created the possibilities for worlds, so should have made a better one than this possible [Schopenhauer] |