22 ideas
11223 | Definitions usually have a term, a 'definiendum' containing the term, and a defining 'definiens' [Gupta] |
11215 | Notable definitions have been of piety (Plato), God (Anselm), number (Frege), and truth (Tarski) [Gupta] |
11225 | A definition needs to apply to the same object across possible worlds [Gupta] |
11227 | The 'revision theory' says that definitions are rules for improving output [Gupta] |
11224 | Traditional definitions are general identities, which are sentential and reductive [Gupta] |
11226 | Traditional definitions need: same category, mention of the term, and conservativeness and eliminability [Gupta] |
11221 | A definition can be 'extensionally', 'intensionally' or 'sense' adequate [Gupta] |
11217 | Chemists aim at real definition of things; lexicographers aim at nominal definition of usage [Gupta] |
11216 | If definitions aim at different ideals, then defining essence is not a unitary activity [Gupta] |
11218 | Stipulative definition assigns meaning to a term, ignoring prior meanings [Gupta] |
11220 | Ostensive definitions look simple, but are complex and barely explicable [Gupta] |
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] |
11222 | The ordered pair <x,y> is defined as the set {{x},{x,y}}, capturing function, not meaning [Gupta] |
16713 | Philosophers are the forefathers of heretics [Tertullian] |
6610 | I believe because it is absurd [Tertullian] |