102 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] |
| 9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
| 9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
| 9705 | 'fld R' indicates the 'field' of all objects in the relation [Enderton] |
| 9704 | 'ran R' indicates the 'range' of objects being related to [Enderton] |
| 9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
| 9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
| 13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
| 9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton] |
| 9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
| 13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
| 13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
| 9699 | The 'powerset' of a set is all the subsets of a given set [Enderton] |
| 9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
| 9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
| 9701 | A 'relation' is a set of ordered pairs [Enderton] |
| 9706 | A 'function' is a relation in which each object is related to just one other object [Enderton] |
| 9708 | A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton] |
| 9709 | A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton] |
| 9711 | A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton] |
| 9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton] |
| 9717 | A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton] |
| 13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
| 13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
| 13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
| 9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
| 9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
| 13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
| 13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
| 9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
| 9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
| 9721 | A logical truth or tautology is a logical consequence of the empty set [Enderton] |
| 9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
| 9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
| 9720 | A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton] |
| 9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
| 9996 | Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton] |
| 9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
| 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] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 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] |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| 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] |
| 3251 | Observed regularities are only predictable if we assume hidden necessity [Nagel] |
| 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] |
| 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] |
| 3277 | In judging disputes, should we use one standard, or those of each individual? [Nagel] |
| 3274 | Equality can either be defended as good for society, or as good for individual rights [Nagel] |
| 3273 | Equality nowadays is seen as political, social, legal and economic [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] |
| 3290 | Given the nature of heat and of water, it is literally impossible for water not to boil at the right heat [Nagel] |