19 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] |
8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
10718 | A natural number is a property of sets [Maddy, by Oliver] |
8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
6479 | Noninterference requires justification as much as interference does [Nagel] |
6450 | Morality must be motivating, and not because of pre-moral motives [Nagel] |
6447 | Game theory misses out the motivation arising from the impersonal standpoint [Nagel] |
6446 | In ethics we abstract from our identity, but not from our humanity [Nagel] |
6477 | I can only universalise a maxim if everyone else could also universalise it [Nagel] |
6448 | A legitimate system is one accepted as both impartial and reasonably partial [Nagel] |
6478 | Democracy is opposed to equality, if the poor are not a majority [Nagel] |