95 ideas
| 18330 | Judging by the positive forces, the Renaissance was the last great age [Nietzsche] |
| 2900 | I revere Heraclitus [Nietzsche] |
| 2913 | Thucydides was the perfect anti-platonist sophist [Nietzsche] |
| 2909 | Thinking has to be learned in the way dancing has to be learned [Nietzsche] |
| 2892 | Wanting a system in philosophy is a lack of integrity [Nietzsche] |
| 2896 | I want to understand the Socratic idea that 'reason equals virtue equals happiness' [Nietzsche] |
| 2897 | With dialectics the rabble gets on top [Nietzsche] |
| 2898 | Anything which must first be proved is of little value [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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 18317 | The 'real being' of things is a nothingness constructed from contradictions in the actual world [Nietzsche] |
| 18315 | We get the concept of 'being' from the concept of the 'ego' [Nietzsche] |
| 18316 | The grounds for an assertion that the world is only apparent actually establish its reality [Nietzsche] |
| 18314 | In language we treat 'ego' as a substance, and it is thus that we create the concept 'thing' [Nietzsche] |
| 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] |
| 18309 | The evidence of the senses is falsified by reason [Nietzsche] |
| 18323 | Any explanation will be accepted as true if it gives pleasure and a feeling of power [Nietzsche] |
| 18310 | The 'highest' concepts are the most general and empty concepts [Nietzsche] |
| 20368 | There are no 'individual' persons; we are each the sum of humanity up to this moment [Nietzsche] |
| 2899 | The fanatical rationality of Greek philosophy shows that they were in a state of emergency [Nietzsche] |
| 18313 | The big error is to think the will is a faculty producing effects; in fact, it is just a word [Nietzsche] |
| 20133 | The 'motive' is superficial, and may even hide the antecedents of a deed [Nietzsche] |
| 18326 | The beautiful never stands alone; it derives from man's pleasure in man [Nietzsche] |
| 20101 | Without music life would be a mistake [Nietzsche] |
| 2902 | Healthy morality is dominated by an instinct for life [Nietzsche] |
| 18311 | Philosophers hate values having an origin, and want values to be self-sufficient [Nietzsche] |
| 18324 | There are no moral facts, and moralists believe in realities which do not exist [Nietzsche] |
| 2904 | The doctrine of free will has been invented essentially in order to blame and punish people [Nietzsche] |
| 2895 | The value of life cannot be estimated [Nietzsche] |
| 18322 | When we establish values, that is life itself establishing them, through us [Nietzsche] |
| 2893 | In every age the wisest people have judged life to be worthless [Nietzsche] |
| 18308 | A philosopher fails in wisdom if he thinks the value of life is a problem [Nietzsche] |
| 2894 | Value judgements about life can never be true [Nietzsche] |
| 18321 | To evaluate life one must know it, but also be situated outside of it [Nietzsche] |
| 18319 | Love is the spiritualisation of sensuality [Nietzsche] |
| 2903 | A good human will be virtuous because they are happy [Nietzsche] |
| 2891 | Only the English actually strive after happiness [Nietzsche] |
| 18327 | A wholly altruistic morality, with no egoism, is a thoroughly bad thing [Nietzsche] |
| 15606 | Military idea: what does not kill me makes me stronger [Nietzsche] |
| 18328 | Invalids are parasites [Nietzsche] |
| 18331 | Democracy is organisational power in decline [Nietzsche] |
| 18332 | The creation of institutions needs a determination which is necessarily anti-liberal [Nietzsche] |
| 2911 | True justice is equality for equals and inequality for unequals [Nietzsche] |
| 18320 | To renounce war is to renounce the grand life [Nietzsche] |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| 2908 | There is a need for educators who are themselves educated [Nietzsche] |
| 18329 | Sometimes it is an error to have been born - but we can rectify it [Nietzsche] |
| 2905 | 'Purpose' is just a human fiction [Nietzsche] |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| 18312 | The supreme general but empty concepts must be compatible, and hence we get 'God' [Nietzsche] |
| 2906 | By denying God we deny human accountability, and thus we redeem the world [Nietzsche] |
| 2901 | How could the Church intelligently fight against passion if it preferred poorness of spirit to intelligence? [Nietzsche] |
| 18325 | Christians believe that only God can know what is good for man [Nietzsche] |
| 18318 | People who disparage actual life avenge themselves by imagining a better one [Nietzsche] |