23 ideas
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] |
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] |
8525 | Relations need terms, so they must be second-order entities based on first-order tropes [Campbell,K] |
8518 | Events are trope-sequences, in which tropes replace one another [Campbell,K] |
8513 | Two red cloths are separate instances of redness, because you can dye one of them blue [Campbell,K] |
8514 | Red could only recur in a variety of objects if it was many, which makes them particulars [Campbell,K] |
8522 | Tropes solve the Companionship Difficulty, since the resemblance is only between abstract particulars [Campbell,K] |
8523 | Tropes solve the Imperfect Community problem, as they can only resemble in one respect [Campbell,K] |
8524 | Trope theory makes space central to reality, as tropes must have a shape and size [Campbell,K] |
8521 | Nominalism has the problem that without humans nothing would resemble anything else [Campbell,K] |
8515 | Tropes are basic particulars, so concrete particulars are collections of co-located tropes [Campbell,K] |
8519 | Bundles must be unique, so the Identity of Indiscernibles is a necessity - which it isn't! [Campbell,K] |
4033 | Two pure spheres in non-absolute space are identical but indiscernible [Campbell,K] |
3102 | Why don't we experience or remember going to sleep at night? [Magee] |
8512 | Abstractions come before the mind by concentrating on a part of what is presented [Campbell,K] |
8517 | Causal conditions are particular abstract instances of properties, which makes them tropes [Campbell,K] |
8516 | Davidson can't explain causation entirely by events, because conditions are also involved [Campbell,K] |