13 ideas
13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [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] |
16383 | Puzzled Pierre has two mental files about the same object [Recanati on Kripke] |
22375 | Moral judgements need more than the relevant facts, if the same facts lead to 'x is good' and 'x is bad' [Foot] |
22377 | Whether someone is rude is judged by agreed criteria, so the facts dictate the value [Foot] |
22378 | We can't affirm a duty without saying why it matters if it is not performed [Foot] |
22376 | Facts and values are connected if we cannot choose what counts as evidence of rightness [Foot] |