99 ideas
| 21979 | Wisdom emerges at the end of a process [Hegel] |
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| 22766 | Philosophy is exploration of the rational [Hegel] |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| 22768 | Subjective and objective are not firmly opposed, but merge into one another [Hegel] |
| 13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
| 13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
| 13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
| 13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
| 13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
| 13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
| 13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
| 13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
| 13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
| 13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
| 13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| 13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
| 13441 | Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
| 13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| 13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
| 13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
| 13505 | Model theory studies how set theory can model sets of sentences [Hart,WD] |
| 13511 | Model theory is mostly confined to first-order theories [Hart,WD] |
| 13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
| 13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
| 13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
| 13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
| 13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
| 13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD] |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| 13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
| 13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
| 13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
| 13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
| 13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
| 22772 | Personality overcomes subjective limitations and posits Dasein as its own [Hegel] |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| 13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
| 13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
| 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] |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| 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] |
| 18678 | Maybe final value rests on the extrinsic property of being valued by a rational agent [Korsgaard, by Orsi] |
| 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] |
| 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] |
| 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] |