73 ideas
| 7846 | Nietzsche thinks philosophy makes us more profound, but not better [Nietzsche, by Ansell Pearson] |
| 20107 | How many mediocre thinkers are occupied with influential problems! [Nietzsche] |
| 20352 | Nietzsche has a metaphysics, as well as perspectives - the ontology is the perspectives [Nietzsche, by Richardson] |
| 20379 | Reason is just another organic drive, developing late, and fighting for equality [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] |
| 10865 | The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg] |
| 10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter] |
| 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] |
| 17889 | CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner] |
| 8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
| 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] |
| 15893 | Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine] |
| 18174 | Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy] |
| 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] |
| 20123 | First see nature as non-human, then fit ourselves into this view of nature [Nietzsche] |
| 20105 | Storms are wonderful expressions of free powers! [Nietzsche] |
| 20376 | We begin with concepts of kinds, from individuals; but that is not the essence of individuals [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] |
| 22501 | Nietzsche classified actions by the nature of the agent, not the nature of the act [Nietzsche, by Foot] |
| 22500 | Nietzsche failed to see that moral actions can be voluntary without free will [Foot on Nietzsche] |
| 9261 | The 'Ethics' is disappointing, because it fails to try to justify our duties [Prichard] |
| 20128 | Each person has a fixed constitution, which makes them a particular type of person [Nietzsche, by Leiter] |
| 22503 | Nietzsche could only revalue human values for a different species [Nietzsche, by Foot] |
| 8041 | The superman is a monstrous oddity, not a serious idea [MacIntyre on Nietzsche] |
| 20135 | Nietzsche's higher type of man is much more important than the idealised 'superman' [Nietzsche, by Leiter] |
| 20353 | The 'will to power' is basically applied to drives and forces, not to people [Nietzsche, by Richardson] |
| 20113 | Friendly chats undermine my philosophy; wanting to be right at the expense of love is folly [Nietzsche] |
| 22475 | Moral generalisation is wrong, because we should evaluate individual acts [Nietzsche, by Foot] |
| 9262 | The mistake is to think we can prove what can only be seen directly in moral thinking [Prichard] |
| 22476 | Nietzsche thought our psychology means there can't be universal human virtues [Nietzsche, by Foot] |
| 9260 | Virtues won't generate an obligation, so it isn't a basis for morality [Prichard] |
| 9259 | We feel obligations to overcome our own failings, and these are not relations to other people [Prichard] |
| 9258 | If pain were instrinsically wrong, it would be immoral to inflict it on ourselves [Prichard] |
| 20104 | Nietzsche tried to lead a thought-provoking life [Safranski on Nietzsche] |
| 7847 | Initially nihilism was cosmic, but later Nietzsche saw it as a cultural matter [Nietzsche, by Ansell Pearson] |
| 9782 | Nietzsche urges that nihilism be active, and will nothing itself [Nietzsche, by Zizek] |
| 20102 | Flight from boredom leads to art [Nietzsche] |
| 20106 | Nietzsche was fascinated by a will that can turn against itself [Nietzsche, by Safranski] |
| 20124 | Reliving life countless times - this gives the value back to life which religion took away [Nietzsche] |
| 20367 | Individual development is more important than the state, but a community is necessary [Nietzsche] |
| 20371 | Nietzsche thinks we should join a society, in order to criticise, heal and renew it [Nietzsche, by Richardson] |
| 20108 | Every culture loses its identity and power if it lacks a major myth [Nietzsche] |
| 10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
| 13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |