70 ideas
| 18290 | But what is the reasoning of the body, that it requires the wisdom you seek? [Nietzsche] |
| 18303 | Reject wisdom that lacks laughter [Nietzsche] |
| 21901 | 'Difference' refers to that which eludes capture [Deleuze, by May] |
| 18305 | To love truth, you must know how to lie [Nietzsche] |
| 15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine] |
| 13444 | Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD] |
| 18098 | Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock] |
| 15505 | If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis] |
| 10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter] |
| 10865 | The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg] |
| 13016 | The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy] |
| 14199 | Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley] |
| 10082 | There are infinite sets that are not enumerable [Cantor, by Smith,P] |
| 13483 | Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it [Cantor, by Hart,WD] |
| 8710 | The powerset of all the cardinal numbers is required to be greater than itself [Cantor, by Friend] |
| 15910 | Cantor named the third realm between the finite and the Absolute the 'transfinite' [Cantor, by Lavine] |
| 15905 | Cantor proved the points on a plane are in one-to-one correspondence to the points on a line [Cantor, by Lavine] |
| 9983 | Cantor took the ordinal numbers to be primary [Cantor, by Tait] |
| 17798 | Cantor presented the totality of natural numbers as finite, not infinite [Cantor, by Mayberry] |
| 9971 | Cantor introduced the distinction between cardinals and ordinals [Cantor, by Tait] |
| 9892 | Cantor showed that ordinals are more basic than cardinals [Cantor, by Dummett] |
| 14136 | A cardinal is an abstraction, from the nature of a set's elements, and from their order [Cantor] |
| 15906 | Cantor tried to prove points on a line matched naturals or reals - but nothing in between [Cantor, by Lavine] |
| 11015 | Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 [Cantor, by Read] |
| 15903 | A real is associated with an infinite set of infinite Cauchy sequences of rationals [Cantor, by Lavine] |
| 18251 | Irrational numbers are the limits of Cauchy sequences of rational numbers [Cantor, by Lavine] |
| 15902 | Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties [Cantor, by Lavine] |
| 15908 | It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers [Cantor, by Lavine] |
| 13464 | Cantor proposes that there won't be a potential infinity if there is no actual infinity [Cantor, by Hart,WD] |
| 10112 | The naturals won't map onto the reals, so there are different sizes of infinity [Cantor, by George/Velleman] |
| 8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
| 17889 | CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner] |
| 13447 | Cantor: there is no size between naturals and reals, or between a set and its power set [Cantor, by Hart,WD] |
| 10883 | Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers [Cantor, by Horsten] |
| 13528 | Continuum Hypothesis: there are no sets between N and P(N) [Cantor, by Wolf,RS] |
| 9555 | Continuum Hypothesis: no cardinal greater than aleph-null but less than cardinality of the continuum [Cantor, by Chihara] |
| 18174 | Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy] |
| 15893 | Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine] |
| 18173 | Cardinality strictly concerns one-one correspondence, to test infinite sameness of size [Cantor, by Maddy] |
| 10232 | Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro] |
| 18176 | Pure mathematics is pure set theory [Cantor] |
| 8631 | Cantor says that maths originates only by abstraction from objects [Cantor, by Frege] |
| 21902 | 'Being' is univocal, but its subject matter is actually 'difference' [Deleuze] |
| 21908 | Ontology can be continual creation, not to know being, but to probe the unknowable [Deleuze] |
| 21903 | Ontology does not tell what there is; it is just a strange adventure [Deleuze, by May] |
| 21904 | Being is a problem to be engaged, not solved, and needs a new mode of thinking [Deleuze, by May] |
| 20757 | The powerful self behind your thoughts and feelings is your body [Nietzsche] |
| 18289 | Forget the word 'I'; 'I' is performed by the intelligence of your body [Nietzsche] |
| 8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
| 13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
| 18299 | The will is constantly frustrated by the past [Nietzsche] |
| 18297 | We created meanings, to maintain ourselves [Nietzsche] |
| 18293 | The noble man wants new virtues; the good man preserves what is old [Nietzsche] |
| 18301 | We only really love children and work [Nietzsche] |
| 18307 | I want my work, not happiness! [Nietzsche] |
| 18291 | Virtues can destroy one another, through jealousy [Nietzsche] |
| 18287 | People now find both wealth and poverty too much of a burden [Nietzsche] |
| 18295 | If you want friends, you must be a fighter [Nietzsche] |
| 18286 | The greatest experience possible is contempt for your own happiness, reason and virtue [Nietzsche] |
| 18296 | An enduring people needs its own individual values [Nietzsche] |
| 18294 | The state coldly claims that it is the people, but that is a lie [Nietzsche] |
| 18304 | Saints want to live as they desire, or not to live at all [Nietzsche] |
| 18300 | Whenever we have seen suffering, we have wanted the revenge of punishment [Nietzsche] |
| 18302 | Man and woman are deeply strange to one another! [Nietzsche] |
| 10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
| 18292 | I can only believe in a God who can dance [Nietzsche] |
| 13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |
| 18298 | Not being a god is insupportable, so there are no gods! [Nietzsche] |
| 18288 | Heaven was invented by the sick and the dying [Nietzsche] |
| 18306 | We don't want heaven; now that we are men, we want the kingdom of earth [Nietzsche] |