45 ideas
| 3240 | There is more insight in fundamental perplexity about problems than in their supposed solutions [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] |
| 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] |
| 10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| 10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
| 10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| 10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
| 10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
| 10871 | Axiom of Existence: there exists at least one set [Clegg] |
| 10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| 10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
| 10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
| 10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
| 10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
| 10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
| 21982 | I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L] |
| 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] |
| 3247 | Epistemology is centrally about what we should believe, not the definition of knowledge [Nagel] |
| 3252 | Scepticism is based on ideas which scepticism makes impossible [Nagel] |
| 3251 | Observed regularities are only predictable if we assume hidden necessity [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] |
| 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] |
| 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] |
| 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] |
| 3255 | We find new motives by discovering reasons for action different from our preexisting motives [Nagel] |
| 3262 | Utilitarianism is too demanding [Nagel] |