63 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] |
| 8166 | Truth is part of semantics, since valid inference preserves truth [Dummett] |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 8173 | Language can violate bivalence because of non-referring terms or ill-defined predicates [Dummett] |
| 8179 | The law of excluded middle is the logical reflection of the principle of bivalence [Dummett] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| 8184 | Philosophers should not presume reality, but only invoke it when language requires it [Dummett] |
| 8185 | We can't make sense of a world not apprehended by a mind [Dummett] |
| 8163 | Since 'no bird here' and 'no squirrel here' seem the same, we must talk of 'atomic' facts [Dummett] |
| 8161 | We know we can state facts, with true statements [Dummett] |
| 8180 | 'That is red or orange' might be considered true, even though 'that is red' and 'that is orange' were not [Dummett] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 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] |
| 8178 | Empirical and a priori knowledge are not distinct, but are extremes of a sliding scale [Dummett] |
| 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] |
| 8175 | A theory of thought will include propositional attitudes as well as propositions [Dummett] |
| 8174 | The theories of meaning and understanding are the only routes to an account of thought [Dummett] |
| 8165 | To 'abstract from' is a logical process, as opposed to the old mental view [Dummett] |
| 8168 | To know the truth-conditions of a sentence, you must already know the meaning [Dummett] |
| 8181 | A justificationist theory of meaning leads to the rejection of classical logic [Dummett] |
| 8182 | Verificationism could be realist, if we imagined the verification by a superhuman power [Dummett] |
| 8183 | If truths about the past depend on memories and current evidence, the past will change [Dummett] |
| 8176 | We could only guess the meanings of 'true' and 'false' when sentences were used [Dummett] |
| 8170 | Sentences are the primary semantic units, because they can say something [Dummett] |
| 8169 | We can't distinguish a proposition from its content [Dummett] |
| 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] |
| 8186 | Time is the measure of change, so we can't speak of time before all change [Dummett] |
| 8167 | If Presentism is correct, we cannot even say that the present changes [Dummett] |