100 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] |
9738 | Each line of a truth table is a model [Fitting/Mendelsohn] |
9727 | Modal logic adds □ (necessarily) and ◊ (possibly) to classical logic [Fitting/Mendelsohn] |
9726 | We let 'R' be the accessibility relation: xRy is read 'y is accessible from x' [Fitting/Mendelsohn] |
9737 | The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ [Fitting/Mendelsohn] |
13136 | The prefix σ names a possible world, and σ.n names a world accessible from that one [Fitting/Mendelsohn] |
13727 | A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [Fitting/Mendelsohn] |
9734 | Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x' [Fitting/Mendelsohn] |
9736 | A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn] |
9735 | A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn] |
9741 | Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn] |
13149 | S5: a) if n ◊X then kX b) if n ¬□X then k ¬X c) if n □X then k X d) if n ¬◊X then k ¬X [Fitting/Mendelsohn] |
13141 | Negation: if σ ¬¬X then σ X [Fitting/Mendelsohn] |
13138 | Disj: a) if σ ¬(X∨Y) then σ ¬X and σ ¬Y b) if σ X∨Y then σ X or σ Y [Fitting/Mendelsohn] |
13142 | Existential: a) if σ ◊X then σ.n X b) if σ ¬□X then σ.n ¬X [n is new] [Fitting/Mendelsohn] |
13144 | T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [Fitting/Mendelsohn] |
13145 | D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [Fitting/Mendelsohn] |
13146 | B symmetric: a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [n occurs] [Fitting/Mendelsohn] |
13147 | 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [Fitting/Mendelsohn] |
13148 | 4r rev-trans: a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [n occurs] [Fitting/Mendelsohn] |
9740 | If a proposition is possibly true in a world, it is true in some world accessible from that world [Fitting/Mendelsohn] |
9739 | If a proposition is necessarily true in a world, it is true in all worlds accessible from that world [Fitting/Mendelsohn] |
13137 | Conj: a) if σ X∧Y then σ X and σ Y b) if σ ¬(X∧Y) then σ ¬X or σ ¬Y [Fitting/Mendelsohn] |
13140 | Bicon: a)if σ(X↔Y) then σ(X→Y) and σ(Y→X) b) [not biconditional, one or other fails] [Fitting/Mendelsohn] |
13139 | Implic: a) if σ ¬(X→Y) then σ X and σ ¬Y b) if σ X→Y then σ ¬X or σ Y [Fitting/Mendelsohn] |
13143 | Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [Fitting/Mendelsohn] |
9742 | The system K has no accessibility conditions [Fitting/Mendelsohn] |
13114 | □P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed [Fitting/Mendelsohn] |
9743 | The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
9744 | The system T has the 'reflexive' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
9746 | The system K4 has the 'transitive' condition on its accessibility relation [Fitting/Mendelsohn] |
9745 | The system B has the 'reflexive' and 'symmetric' conditions on its accessibility relation [Fitting/Mendelsohn] |
9747 | The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
9748 | System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
9404 | Modality affects content, because P→◊P is valid, but ◊P→P isn't [Fitting/Mendelsohn] |
13112 | In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn] |
13111 | Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn] |
13113 | F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn] |
13728 | The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn] |
13729 | The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn] |
9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
22772 | Personality overcomes subjective limitations and posits Dasein as its own [Hegel] |
13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
13725 | □ must be sensitive as to whether it picks out an object by essential or by contingent properties [Fitting/Mendelsohn] |
13731 | Objects retain their possible properties across worlds, so a bundle theory of them seems best [Fitting/Mendelsohn] |
13726 | Counterpart relations are neither symmetric nor transitive, so there is no logic of equality for them [Fitting/Mendelsohn] |
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] |
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] |
5049 | Intelligent pleasure is the perception of beauty, order and perfection [Leibniz] |
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] |
5048 | Perfection is simply quantity of reality [Leibniz] |
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] |
5050 | Evil serves a greater good, and pain is necessary for higher pleasure [Leibniz] |