92 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] |
22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind] |
9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
18087 | If x changes by less and less, it must approach a limit [Dedekind] |
13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
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] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
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] |
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] |
9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
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] |
3029 | Stilpo said if Athena is a daughter of Zeus, then a statue is only the child of a sculptor, and so is not a god [Stilpo, by Diog. Laertius] |