81 ideas
| 7834 | Great philosophies are confessions by the author, growing out of moral intentions [Nietzsche] |
| 7080 | Metaphysics divided the old unified Greek world into two [Nietzsche, by Critchley] |
| 11090 | Why do we want truth, rather than falsehood or ignorance? The value of truth is a problem [Nietzsche] |
| 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] |
| 9735 | A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn] |
| 9736 | A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn] |
| 9741 | Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [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] |
| 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] |
| 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] |
| 13141 | Negation: if σ ¬¬X then σ X [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] |
| 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] |
| 13144 | T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [Fitting/Mendelsohn] |
| 13143 | Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [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] |
| 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] |
| 9739 | If a proposition is necessarily true in a world, it is true in all worlds accessible from that world [Fitting/Mendelsohn] |
| 9740 | If a proposition is possibly true in a world, it is true in some world accessible from that world [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] |
| 13111 | Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn] |
| 13112 | In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn] |
| 13113 | F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn] |
| 13729 | The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn] |
| 13728 | The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn] |
| 9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
| 7079 | Nietzsche resists nihilism through new values, for a world of becoming, without worship [Nietzsche, by Critchley] |
| 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] |
| 2878 | We see an approximation of a tree, not the full detail [Nietzsche] |
| 20140 | We shouldn't object to a false judgement, if it enhances and preserves life [Nietzsche] |
| 9382 | Subjects may be unaware of their epistemic 'entitlements', unlike their 'justifications' [Burge] |
| 2877 | Morality becomes a problem when we compare many moralities [Nietzsche] |
| 20355 | The ranking of a person's innermost drives reveals their true nature [Nietzsche] |
| 2871 | Wanting 'freedom of will' is wanting to pull oneself into existence out of the swamp of nothingness by one's own hair [Nietzsche] |
| 2291 | A thought comes when 'it' wants, not when 'I' want [Nietzsche] |
| 20381 | It is psychology which reveals the basic problems [Nietzsche] |
| 2860 | The most boring and dangerous of all errors is Plato's invention of pure spirit and goodness [Nietzsche] |
| 1568 | Nietzsche felt that Plato's views downgraded the human body and its brevity of life [Nietzsche, by Roochnik] |
| 2883 | Noble people see themselves as the determiners of values [Nietzsche] |
| 23440 | Nietzsche's judgement of actions by psychology instead of outcome was poisonous [Foot on Nietzsche] |
| 2875 | That which is done out of love always takes place beyond good and evil [Nietzsche] |
| 2868 | Nature is totally indifferent, so you should try to be different from it, not live by it [Nietzsche] |
| 2882 | Morality originally judged people, and actions only later on [Nietzsche] |
| 2872 | In the earliest phase of human history only consequences mattered [Nietzsche] |
| 2885 | The noble soul has reverence for itself [Nietzsche] |
| 20134 | Moralities extravagantly address themselves to 'all', by falsely generalising [Nietzsche] |
| 2881 | Virtue has been greatly harmed by the boringness of its advocates [Nietzsche] |
| 20382 | The four virtues are courage, insight, sympathy, solitude [Nietzsche] |
| 2879 | In ancient Rome pity was considered neither good nor bad [Nietzsche] |
| 2859 | The idea of the categorical imperative is just that we should all be very obedient [Nietzsche] |
| 2884 | The morality of slaves is the morality of utility [Nietzsche] |
| 2880 | The greatest possibilities in man are still unexhausted [Nietzsche] |
| 7078 | The freedom of the subject means the collapse of moral certainty [Nietzsche, by Critchley] |
| 2876 | The thought of suicide is a great reassurance on bad nights [Nietzsche] |
| 2874 | Man is the animal whose nature has not yet been fixed [Nietzsche] |
| 6869 | Nietzsche thinks the human condition is to overcome and remake itself [Nietzsche, by Ansell Pearson] |
| 20137 | The great person engages wholly with life, and is happy to endlessly relive the life they created [Nietzsche] |
| 20139 | Only aristocratic societies can elevate the human species [Nietzsche] |
| 20373 | A healthy aristocracy has no qualms about using multitudes of men as instruments [Nietzsche] |
| 22394 | Democracy diminishes mankind, making them mediocre and lowering their value [Nietzsche] |
| 2867 | Christianity is Platonism for the people [Nietzsche] |