35 ideas
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] |
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] |
5311 | If observation goes up a level, we expect the laws of the lower level to remain in force [Wilson,EO] |
5312 | A child first sees objects as distinct, and later as members of groups [Wilson,EO] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
12432 | Explanation of necessity must rest on something necessary or something contingent [Hale] |
12434 | Why is this necessary, and what is necessity in general; why is this necessary truth true, and why necessary? [Hale] |
12435 | The explanation of a necessity can be by a truth (which may only happen to be a necessary truth) [Hale] |
12433 | If necessity rests on linguistic conventions, those are contingent, so there is no necessity [Hale] |
12436 | Concept-identities explain how we know necessities, not why they are necessary [Hale] |
5309 | Beliefs are really enabling mechanisms for survival [Wilson,EO] |
5310 | Philosophers study the consequences of ethics instead of its origins [Wilson,EO] |
5313 | The rules of human decision-making converge and overlap in a 'human nature' [Wilson,EO] |
5316 | We undermine altruism by rewarding it, but we reward it to encourage it [Wilson,EO] |
5318 | Pure hard-core altruism based on kin selection is the enemy of civilisation [Wilson,EO] |
5317 | The actor is most convincing who believes that his performance is real [Wilson,EO] |
5308 | The only human purpose is that created by our genetic history [Wilson,EO] |
5314 | Cultural evolution is Lamarckian and fast, biological evolution is Darwinian and slow [Wilson,EO] |
5315 | Over 99 percent of human evolution has been in the hunter-gatherer phase [Wilson,EO] |
5320 | It is estimated that mankind has produced 100,000 religions [Wilson,EO] |