96 ideas
| 21979 | Wisdom emerges at the end of a process [Hegel] |
| 22766 | Philosophy is exploration of the rational [Hegel] |
| 22768 | Subjective and objective are not firmly opposed, but merge into one another [Hegel] |
| 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] |
| 22772 | Personality overcomes subjective limitations and posits Dasein as its own [Hegel] |
| 22780 | It is a rejection of intellectual dignity to say that we cannot know the truth [Hegel] |
| 22770 | A person is a being which is aware of its own self-directed and free subjectivity [Hegel] |
| 22788 | A human only become a somebody as a member of a social estate [Hegel] |
| 22792 | Individuals attain their right by discovering their self-consciousness in institutions [Hegel] |
| 21780 | A free will primarily wills its own freedoom [Hegel, by Houlgate] |
| 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] |
| 22769 | The concept of the will is the free will which wills its freedom [Hegel] |
| 21787 | Evil enters a good will when we believe we are doing right, but allow no criticism of our choice [Hegel, by Houlgate] |
| 21786 | Conscience is the right of the self to know what is right and obligatory, and thus make them true [Hegel] |
| 22784 | Love is ethical life in its natural form [Hegel] |
| 21836 | Philosophers after Aristotle endorsed the medical analogy for eudaimonia [Nussbaum, by Flanagan] |
| 8029 | You can't have a morality which is supplied by the individual, but is also genuinely universal [Hegel, by MacIntyre] |
| 22771 | Be a person, and respect other persons [Hegel] |
| 22051 | The categorical imperative lacks roots in a historical culture [Hegel, by Bowie] |
| 22781 | The categorical imperative is fine if you already have a set of moral principles [Hegel] |
| 22779 | The good is realised freedom [Hegel] |
| 22787 | The family is the first basis of the state, but estates are a necessary second [Hegel] |
| 22790 | We cannot assert rights which are unnatural [Hegel] |
| 22767 | I aim to portray the state as a rational entity [Hegel] |
| 22789 | Society draws people, and requires their work, making them wholly dependent on it [Hegel] |
| 22791 | The state is the march of God in the world [Hegel] |
| 22778 | Individuals can't leave the state, because they are natural citizens, and humans require a state [Hegel] |
| 22794 | A fully developed state is conscious and knows what it wills [Hegel] |
| 22799 | The people do not have the ability to know the general will [Hegel] |
| 22801 | The great man of the ages is the one who reveals and accomplishes the will of his time [Hegel] |
| 22796 | A constitution embodies a nation's rights and condition [Hegel] |
| 22777 | Individuals must dedicate themselves to the ethical whole, and give their lives when asked [Hegel] |
| 21791 | Social groups must focus on the state, which must in turn respect their inclusion and their will [Hegel] |
| 22795 | People can achieve respect for their state by insight into its essence [Hegel] |
| 21988 | In the 1840s Hegel seemed to defend society being right as it is, as a manifestation of Mind [Hegel, by Singer] |
| 22800 | Majority rule means obligations can be imposed on me [Hegel] |
| 21792 | The state should reflect all interests, and not just popular will, or a popular party [Hegel, by Houlgate] |
| 22797 | In modern states an individual's actions should be their choice [Hegel] |
| 21790 | Moral individuals become ethical when they see the social aspect of a matter [Hegel, by Houlgate] |
| 8030 | For Hegel, the moral life can only be led within a certain type of community [Hegel, by MacIntyre] |
| 22785 | Even educated women are unsuited to science, philosophy, art and government [Hegel] |
| 21789 | Slaves have no duties because they have no rights [Hegel] |
| 22776 | Slaves are partly responsible for their own condition [Hegel] |
| 21778 | True liberal freedom is to pursue something, while being free to cease the pursuit [Hegel, by Houlgate] |
| 21779 | People assume they are free, but the options available are not under their control [Hegel] |
| 22085 | Freedom requires us to submit to a family, or a corporation, or a state [Hegel, by Houlgate] |
| 22798 | Money is the best way to achieve just equality [Hegel] |
| 22783 | Rights imply duties, and duties imply rights [Hegel] |
| 21782 | Man has an absolute right to appropriate things [Hegel] |
| 22773 | Because only human beings can own property, everything else can become our property [Hegel] |
| 22774 | A community does not have the property-owning rights that a person has [Hegel] |
| 22775 | The owner of a thing is obviously the first person to freely take possession of it [Hegel] |
| 22802 | Wars add strength to a nation, and cure internal dissension [Hegel] |
| 22786 | Children need discipline, to break their self-will and eradicate sensuousness [Hegel] |
| 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] |
| 22782 | To have pagan beliefs and be a pagan are quite different [Hegel] |
| 22793 | Some religions lead to harsh servitude and the debasement of human beings [Hegel] |