116 ideas
| 3240 | There is more insight in fundamental perplexity about problems than in their supposed solutions [Nagel] |
| 3269 | If your life is to be meaningful as part of some large thing, the large thing must be meaningful [Nagel] |
| 3242 | Philosophy is the childhood of the intellect, and a culture can't skip it [Nagel] |
| 3241 | It seems mad, but the aim of philosophy is to climb outside of our own minds [Nagel] |
| 1489 | Modern philosophy tends to be a theory-constructing extension of science, but there is also problem-solving [Nagel] |
| 3248 | Realism invites scepticism because it claims to be objective [Nagel] |
| 20989 | Views are objective if they don't rely on a person's character, social position or species [Nagel] |
| 22354 | Things cause perceptions, properties have other effects, hence we reach a 'view from nowhere' [Nagel, by Reiss/Sprenger] |
| 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] |
| 4242 | Pure supervenience explains nothing, and is a sign of something fundamental we don't know [Nagel] |
| 3291 | Emergent properties appear at high levels of complexity, but aren't explainable by the lower levels [Nagel] |
| 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] |
| 3249 | Modern science depends on the distinction between primary and secondary qualities [Nagel] |
| 22429 | We achieve objectivity by dropping secondary qualities, to focus on structural primary qualities [Nagel] |
| 3296 | Sense-data are a false objectification of what is essentially subjective [Nagel] |
| 3247 | Epistemology is centrally about what we should believe, not the definition of knowledge [Nagel] |
| 3271 | We can't control our own beliefs [Nagel] |
| 3270 | Justifications come to an end when we want them to [Nagel] |
| 3252 | Scepticism is based on ideas which scepticism makes impossible [Nagel] |
| 1490 | You would have to be very morally lazy to ignore criticisms of your own culture [Nagel] |
| 22190 | If a theory is more informative it is less probable [Gorham] |
| 22189 | Why abandon a theory if you don't have a better one? [Gorham] |
| 22192 | Is Newton simpler with universal simultaneity, or Einstein simpler without absolute time? [Gorham] |
| 22194 | Structural Realism says mathematical structures persist after theory rejection [Gorham] |
| 22195 | Structural Realists must show the mathematics is both crucial and separate [Gorham] |
| 22197 | Theories aren't just for organising present experience if they concern the past or future [Gorham] |
| 22196 | For most scientists their concepts are not just useful, but are meant to be true and accurate [Gorham] |
| 3251 | Observed regularities are only predictable if we assume hidden necessity [Nagel] |
| 22193 | Consilience makes the component sciences more likely [Gorham] |
| 3295 | Inner v outer brings astonishment that we are a particular person [Nagel] |
| 2957 | Brain bisection suggests unity of mind isn't all-or-nothing [Nagel, by Lockwood] |
| 3286 | An organism is conscious if and only if there is something it is like to be that organism [Nagel] |
| 3285 | We may be unable to abandon personal identity, even when split-brains have undermined it [Nagel] |
| 3293 | If you assert that we have an ego, you can still ask if that future ego will be me [Nagel] |
| 3244 | Personal identity cannot be fully known a priori [Nagel] |
| 3245 | The question of whether a future experience will be mine presupposes personal identity [Nagel] |
| 3246 | I can't even conceive of my brain being split in two [Nagel] |
| 3292 | The most difficult problem of free will is saying what the problem is [Nagel] |
| 3288 | Can we describe our experiences to zombies? [Nagel] |
| 4883 | Nagel's title creates an impenetrable mystery, by ignoring a bat's ways that may not be "like" anything [Dennett on Nagel] |
| 3287 | We can't be objective about experience [Nagel] |
| 4989 | Physicalism should explain how subjective experience is possible, but not 'what it is like' [Kirk,R on Nagel] |
| 4001 | The meaning of a word contains all its possible uses as well as its actual ones [Nagel] |
| 6479 | Noninterference requires justification as much as interference does [Nagel] |
| 6450 | Morality must be motivating, and not because of pre-moral motives [Nagel] |
| 3284 | There is no one theory of how to act (or what to believe) [Nagel] |
| 3257 | Total objectivity can't see value, but it sees many people with values [Nagel] |
| 3265 | We don't worry about the time before we were born the way we worry about death [Nagel] |
| 3263 | If our own life lacks meaning, devotion to others won't give it meaning [Nagel] |
| 3256 | Pain doesn't have a further property of badness; it gives a reason for its avoidance [Nagel] |
| 3272 | Moral luck can arise in character, preconditions, actual circumstances, and outcome [Nagel] |
| 6447 | Game theory misses out the motivation arising from the impersonal standpoint [Nagel] |
| 3261 | Something may be 'rational' either because it is required or because it is acceptable [Nagel] |
| 3258 | If cockroaches can't think about their actions, they have no duties [Nagel] |
| 6446 | In ethics we abstract from our identity, but not from our humanity [Nagel] |
| 3282 | The general form of moral reasoning is putting yourself in other people's shoes [Nagel] |
| 3294 | As far as possible we should become instruments to realise what is best from an eternal point of view [Nagel] |
| 3254 | If we can decide how to live after stepping outside of ourselves, we have the basis of a moral theory [Nagel] |
| 3264 | We should see others' viewpoints, but not lose touch with our own values [Nagel] |
| 6477 | I can only universalise a maxim if everyone else could also universalise it [Nagel] |
| 3255 | We find new motives by discovering reasons for action different from our preexisting motives [Nagel] |
| 3262 | Utilitarianism is too demanding [Nagel] |
| 3268 | If a small brief life is absurd, then so is a long and large one [Nagel] |
| 3278 | An egalitarian system must give priority to those with the worst prospects in life [Nagel] |
| 6448 | A legitimate system is one accepted as both impartial and reasonably partial [Nagel] |
| 3277 | In judging disputes, should we use one standard, or those of each individual? [Nagel] |
| 3275 | Equality was once opposed to aristocracy, but now it opposes public utility and individual rights [Nagel] |
| 3281 | The ideal of acceptability to each individual underlies the appeal to equality [Nagel] |
| 3273 | Equality nowadays is seen as political, social, legal and economic [Nagel] |
| 3274 | Equality can either be defended as good for society, or as good for individual rights [Nagel] |
| 6478 | Democracy is opposed to equality, if the poor are not a majority [Nagel] |
| 3276 | A morality of rights is very minimal, leaving a lot of human life without restrictions or duties [Nagel] |
| 22198 | Aristotelian physics has circular celestial motion and linear earthly motion [Gorham] |
| 3290 | Given the nature of heat and of water, it is literally impossible for water not to boil at the right heat [Nagel] |