39 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] |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
12735 | Everything has a fixed power, as required by God, and by the possibility of reasoning [Leibniz] |
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] |