75 ideas
| 2930 | The main aim of philosophy must be to determine the order of rank among values [Nietzsche] |
| 20143 | Scientific knowledge is nothing without a prior philosophical 'faith' [Nietzsche] |
| 23722 | Objectivity is not disinterestedness (impossible), but the ability to switch perspectives [Nietzsche] |
| 4417 | Only that which has no history is definable [Nietzsche] |
| 23715 | Psychologists should be brave and proud, and prefer truth to desires, even when it is ugly [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] |
| 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] |
| 8447 | In 'Etna is higher than Vesuvius' the whole of Etna, including all the lava, can't be the reference [Frege] |
| 8448 | Any object can have many different names, each with a distinct sense [Frege] |
| 9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
| 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] |
| 4421 | Philosophers have never asked why there is a will to truth in the first place [Nietzsche] |
| 23719 | Forgetfulness is a strong positive ability, not mental laziness [Nietzsche] |
| 4420 | There is only 'perspective' seeing and knowing, and so the best objectivity is multiple points of view [Nietzsche] |
| 4414 | Philosophers invented "free will" so that our virtues would be permanently interesting to the gods [Nietzsche] |
| 4419 | People who think in words are orators rather than thinkers, and think about facts instead of thinking facts [Nietzsche] |
| 8446 | We understand new propositions by constructing their sense from the words [Frege] |
| 8449 | Senses can't be subjective, because propositions would be private, and disagreement impossible [Frege] |
| 4411 | It is a delusion to separate the man from the deed, like the flash from the lightning [Nietzsche] |
| 3793 | We must question the very value of moral values [Nietzsche] |
| 4408 | The concept of 'good' was created by aristocrats to describe their own actions [Nietzsche] |
| 23716 | A strong rounded person soon forgets enemies, misfortunes, and even misdeeds [Nietzsche] |
| 20129 | All animals strive for the ideal conditions to express their power, and hate any hindrances [Nietzsche] |
| 4409 | Only the decline of aristocratic morality led to concerns about "egoism" [Nietzsche] |
| 3259 | Nietzsche rejects impersonal morality, and asserts the idea of living well [Nietzsche, by Nagel] |
| 4416 | Basic justice is the negotiation of agreement among equals, and the imposition of agreement [Nietzsche] |
| 4418 | A masterful and violent person need have nothing to do with contracts [Nietzsche] |
| 4407 | Plato, Spinoza and Kant are very different, but united in their low estimation of pity [Nietzsche] |
| 4415 | Guilt and obligation originated in the relationship of buying and selling, credit and debt [Nietzsche] |
| 23718 | If we say birds of prey could become lambs, that makes them responsible for being birds of prey [Nietzsche] |
| 23717 | Modern nihilism is now feeling tired of mankind [Nietzsche] |
| 23721 | Old tribes always felt an obligation to the earlier generations, and the founders [Nietzsche] |
| 20142 | The state begins with brutal conquest of a disorganised people, not with a 'contract' [Nietzsche] |
| 23720 | Punishment makes people harder, more alienated, and hostile [Nietzsche] |
| 4410 | The truly great haters in world history have always been priests [Nietzsche] |