22 ideas
21544 | It seems that when a proposition is false, something must fail to subsist [Russell] |
13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
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] |
14238 | A class is an aggregate of objects; if you destroy them, you destroy the class; there is no empty class [Frege] |
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] |
21539 | Excluded middle can be stated psychologically, as denial of p implies assertion of not-p [Russell] |
21538 | If two people perceive the same object, the object of perception can't be in the mind [Russell] |
21534 | The only thing we can say about relations is that they relate [Russell] |
21540 | Relational propositions seem to be 'about' their terms, rather than about the relation [Russell] |
21536 | When I perceive a melody, I do not perceive the notes as existing [Russell] |
21535 | Objects only exist if they 'occupy' space and time [Russell] |
21533 | Contingency arises from tensed verbs changing the propositions to which they refer [Russell] |
21537 | I assume we perceive the actual objects, and not their 'presentations' [Russell] |
21532 | Full empiricism is not tenable, but empirical investigation is always essential [Russell] |
21542 | Do incorrect judgements have non-existent, or mental, or external objects? [Russell] |
21541 | The complexity of the content correlates with the complexity of the object [Russell] |
21543 | If p is false, then believing not-p is knowing a truth, so negative propositions must exist [Russell] |