95 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] |
8721 | An 'impredicative' definition seems circular, because it uses the term being defined [Friend] |
8680 | Classical definitions attempt to refer, but intuitionist/constructivist definitions actually create objects [Friend] |
3678 | Reductio ad absurdum proves an idea by showing that its denial produces contradiction [Friend] |
8705 | Anti-realists see truth as our servant, and epistemically contrained [Friend] |
8713 | In classical/realist logic the connectives are defined by truth-tables [Friend] |
8708 | Double negation elimination is not valid in intuitionist logic [Friend] |
8694 | Free logic was developed for fictional or non-existent objects [Friend] |
8665 | A 'proper subset' of A contains only members of A, but not all of them [Friend] |
8672 | A 'powerset' is all the subsets of a set [Friend] |
8677 | Set theory makes a minimum ontological claim, that the empty set exists [Friend] |
8666 | Infinite sets correspond one-to-one with a subset [Friend] |
8682 | Major set theories differ in their axioms, and also over the additional axioms of choice and infinity [Friend] |
8709 | The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false [Friend] |
8711 | Intuitionists read the universal quantifier as "we have a procedure for checking every..." [Friend] |
8675 | Paradoxes can be solved by talking more loosely of 'classes' instead of 'sets' [Friend] |
8674 | The Burali-Forti paradox asks whether the set of all ordinals is itself an ordinal [Friend] |
8667 | The 'integers' are the positive and negative natural numbers, plus zero [Friend] |
8668 | The 'rational' numbers are those representable as fractions [Friend] |
8670 | A number is 'irrational' if it cannot be represented as a fraction [Friend] |
8661 | The natural numbers are primitive, and the ordinals are up one level of abstraction [Friend] |
8664 | Cardinal numbers answer 'how many?', with the order being irrelevant [Friend] |
8671 | The 'real' numbers (rationals and irrationals combined) is the Continuum, which has no gaps [Friend] |
8663 | Raising omega to successive powers of omega reveal an infinity of infinities [Friend] |
8662 | The first limit ordinal is omega (greater, but without predecessor), and the second is twice-omega [Friend] |
8669 | Between any two rational numbers there is an infinite number of rational numbers [Friend] |
8676 | Is mathematics based on sets, types, categories, models or topology? [Friend] |
8678 | Most mathematical theories can be translated into the language of set theory [Friend] |
8701 | The number 8 in isolation from the other numbers is of no interest [Friend] |
8702 | In structuralism the number 8 is not quite the same in different structures, only equivalent [Friend] |
8699 | Are structures 'ante rem' (before reality), or are they 'in re' (grounded in physics)? [Friend] |
8696 | Structuralist says maths concerns concepts about base objects, not base objects themselves [Friend] |
8695 | Structuralism focuses on relations, predicates and functions, with objects being inessential [Friend] |
8700 | 'In re' structuralism says that the process of abstraction is pattern-spotting [Friend] |
8681 | The big problem for platonists is epistemic: how do we perceive, intuit, know or detect mathematical facts? [Friend] |
8712 | Mathematics should be treated as true whenever it is indispensable to our best physical theory [Friend] |
8716 | Formalism is unconstrained, so cannot indicate importance, or directions for research [Friend] |
8706 | Constructivism rejects too much mathematics [Friend] |
8707 | Intuitionists typically retain bivalence but reject the law of excluded middle [Friend] |
22772 | Personality overcomes subjective limitations and posits Dasein as its own [Hegel] |
8704 | Structuralists call a mathematical 'object' simply a 'place in a structure' [Friend] |
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] |
8685 | Studying biology presumes the laws of chemistry, and it could never contradict them [Friend] |
8688 | Concepts can be presented extensionally (as objects) or intensionally (as a characterization) [Friend] |
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] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
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] |