78 ideas
| 14888 | Wisdom prevents us from being ruled by the moment [Nietzsche] |
| 14863 | Unlike science, true wisdom involves good taste [Nietzsche] |
| 14890 | Suffering is the meaning of existence [Nietzsche] |
| 14861 | Philosophy ennobles the world, by producing an artistic conception of our knowledge [Nietzsche] |
| 14885 | The first aim of a philosopher is a life, not some works [Nietzsche] |
| 14887 | You should only develop a philosophy if you are willing to live by it [Nietzsche] |
| 14889 | Philosophy is pointless if it does not advocate, and live, a new way of life [Nietzsche] |
| 14862 | Philosophy is more valuable than much of science, because of its beauty [Nietzsche] |
| 14878 | It would better if there was no thought [Nietzsche] |
| 14881 | Why do people want philosophers? [Nietzsche] |
| 14876 | Philosophy is always secondary, because it cannot support a popular culture [Nietzsche] |
| 14860 | Kant has undermined our belief in metaphysics [Nietzsche] |
| 14859 | If philosophy controls science, then it has to determine its scope, and its value [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] |
| 14880 | Logic is just slavery to language [Nietzsche] |
| 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] |
| 14869 | If some sort of experience is at the root of matter, then human knowledge is close to its essence [Nietzsche] |
| 14875 | Belief matters more than knowledge, and only begins when knowledge ceases [Nietzsche] |
| 14866 | It always remains possible that the world just is the way it appears [Nietzsche] |
| 14872 | Our knowledge is illogical, because it rests on false identities between things [Nietzsche] |
| 14879 | The most extreme scepticism is when you even give up logic [Nietzsche] |
| 14873 | If we find a hypothesis that explains many things, we conclude that it explains everything [Nietzsche] |
| 14868 | Our primary faculty is perception of structure, as when looking in a mirror [Nietzsche] |
| 14870 | We experience causation between willing and acting, and thereby explain conjunctions of changes [Nietzsche] |
| 3444 | If actions are not caused by other events, and are not causeless, they must be caused by the person [Chisholm] |
| 3446 | For Hobbes (but not for Kant) a person's actions can be deduced from their desires and beliefs [Chisholm] |
| 9268 | If free will miraculously interrupts causation, animals might do that; why would we want to do it? [Frankfurt on Chisholm] |
| 14867 | It is just madness to think that the mind is supernatural (or even divine!) [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] |
| 3442 | Responsibility seems to conflict with events being either caused or not caused [Chisholm] |
| 3443 | Desires may rule us, but are we responsible for our desires? [Chisholm] |
| 14884 | The shortest path to happiness is forgetfulness, the path of animals (but of little value) [Nietzsche] |
| 14886 | Education is contrary to human nature [Nietzsche] |
| 14883 | We should evaluate the past morally [Nietzsche] |
| 14882 | Protest against vivisection - living things should not become objects of scientific investigation [Nietzsche] |
| 14865 | We do not know the nature of one single causality [Nietzsche] |
| 3445 | Causation among objects relates either events or states [Chisholm] |
| 14871 | Laws of nature are merely complex networks of relations [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] |
| 14864 | The Greeks lack a normative theology: each person has their own poetic view of things [Nietzsche] |