15 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] |
21515 | Incoherence may be more important for enquiry than coherence [Olsson] |
21514 | Coherence is the capacity to answer objections [Olsson] |
21496 | Mere agreement of testimonies is not enough to make truth very likely [Olsson] |
21499 | Coherence is only needed if the information sources are not fully reliable [Olsson] |
21502 | A purely coherent theory cannot be true of the world without some contact with the world [Olsson] |
21512 | Extending a system makes it less probable, so extending coherence can't make it more probable [Olsson] |
4422 | The end need not be the goal, as in the playing of a melody (and yet it must be completed) [Nietzsche] |