104 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] |
17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
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] |
10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
17751 | Gödel proved the completeness of first order predicate logic in 1930 [Gödel, by Walicki] |
8679 | We perceive the objects of set theory, just as we perceive with our senses [Gödel] |
17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
18062 | Set-theory paradoxes are no worse than sense deception in physics [Gödel] |
10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
10868 | The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg] |
13517 | If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD] |
17885 | Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner] |
10614 | The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel] |
3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
9590 | Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman] |
11069 | Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna] |
10118 | First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman] |
10122 | Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman] |
10611 | There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P] |
10867 | 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg] |
10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
10271 | Basic mathematics is related to abstract elements of our empirical ideas [Gödel] |
10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
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] |
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] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
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] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |