80 ideas
| 20121 | Grammar only reveals popular metaphysics [Nietzsche] |
| 24082 | Is the will to truth the desire to avoid deception? [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] |
| 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] |
| 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] |
| 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] |
| 13143 | Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [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] |
| 13148 | 4r rev-trans: a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [n occurs] [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] |
| 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] |
| 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] |
| 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] |
| 20360 | We Germans value becoming and development more highly than mere being of what 'is' [Nietzsche] |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| 24077 | Necessity is thought to require an event, but is only an after-effect of the event [Nietzsche] |
| 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] |
| 20126 | The strength of knowledge is not its truth, but its entrenchment in our culture [Nietzsche] |
| 20119 | We became increasingly conscious of our sense impressions in order to communicate them [Nietzsche] |
| 20122 | We have no organ for knowledge or truth; we only 'know' what is useful to the human herd [Nietzsche] |
| 4423 | We assume causes, geometry, motion, bodies etc to live, but they haven't been proved [Nietzsche] |
| 6579 | Nietzsche's perspectivism says our worldview depends on our personality [Nietzsche, by Fogelin] |
| 24083 | It would be absurd to say we are only permitted our own single perspective [Nietzsche] |
| 20115 | All of our normal mental life could be conducted without consciousness [Nietzsche] |
| 20117 | Only the need for communication has led to consciousness developing [Nietzsche] |
| 20118 | Only our conscious thought is verbal, and this shows the origin of consciousness [Nietzsche] |
| 20116 | Most of our lives, even the important parts, take place outside of consciousness [Nietzsche] |
| 20120 | Whatever moves into consciousness becomes thereby much more superficial [Nietzsche] |
| 2932 | 'Know thyself' is impossible and ridiculous [Nietzsche] |
| 24078 | Thoughts cannot be fully reproduced in words [Nietzsche] |
| 24081 | Most of our intellectual activity is unconscious [Nietzsche] |
| 2933 | Why do you listen to the voice of your conscience? [Nietzsche] |
| 20141 | Higher human beings see and hear far more than others, and do it more thoughtfully [Nietzsche] |
| 24076 | A morality ranks human drives and actions, for the sake of the herd, and subordinating individuals [Nietzsche] |
| 22471 | Nietzsche thought it 'childish' to say morality isn't binding because it varies between cultures [Nietzsche, by Foot] |
| 5049 | Intelligent pleasure is the perception of beauty, order and perfection [Leibniz] |
| 2935 | No two actions are the same [Nietzsche] |
| 20198 | Many virtues are harmful traps, but that is why other people praise them [Nietzsche] |
| 4275 | You cannot advocate joyful wisdom while rejecting pity, because the two are complementary [Scruton on Nietzsche] |
| 2934 | To see one's own judgement as a universal law is selfish [Nietzsche] |
| 24080 | We should give style to our character - by applying an artistic plan to its strengths and weaknesses [Nietzsche] |
| 20125 | The ethical teacher exists to give purpose to what happens necessarily and without purpose [Nietzsche] |
| 9306 | To ward off boredom at any cost is vulgar [Nietzsche] |
| 24079 | The best life is the dangerous life [Nietzsche] |
| 2936 | Imagine if before each of your actions you had to accept repeating the action over and over again [Nietzsche] |
| 6842 | Nietzsche says facing up to the eternal return of meaninglessness is the response to nihilism [Nietzsche, by Critchley] |
| 5048 | Perfection is simply quantity of reality [Leibniz] |
| 2931 | God is dead, and we have killed him [Nietzsche] |
| 5050 | Evil serves a greater good, and pain is necessary for higher pleasure [Leibniz] |