16 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] |
16078 | Clay is intrinsically and atomically the same as statue (and that lacks 'modal properties') [Rudder Baker] |
16077 | The clay is not a statue - it borrows that property from the statue it constitutes [Rudder Baker] |
16080 | Is it possible for two things that are identical to become two separate things? [Rudder Baker] |
16076 | Constitution is not identity, as consideration of essential predicates shows [Rudder Baker] |
16081 | The constitution view gives a unified account of the relation of persons/bodies, statues/bronze etc [Rudder Baker] |
16082 | Statues essentially have relational properties lacked by lumps [Rudder Baker] |
20759 | Feelings are prior to intelligence; we should be content to live with our simplest feelings [Rousseau] |
19854 | We all owe labour in return for our keep, and every idle citizen is a thief [Rousseau] |