21 ideas
13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
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] |
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] |
5655 | Happiness is not satisfaction of desires, but fulfilment of values [Bradley, by Scruton] |
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] |