17 ideas
13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [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] |
8439 | Maybe each event has only one possible causal history [Bennett] |
8440 | Maybe an event's time of occurrence is essential to it [Bennett] |
12251 | Substantial forms are not understood, and explain nothing [Descartes] |
8441 | Delaying a fire doesn't cause it, but hastening it might [Bennett] |
8436 | Either cause and effect are subsumed under a conditional because of properties, or it is counterfactual [Bennett] |
8435 | Causes are between events ('the explosion') or between facts/states of affairs ('a bomb dropped') [Bennett] |
8437 | The full counterfactual story asserts a series of events, because counterfactuals are not transitive [Bennett] |
8438 | A counterfactual about an event implies something about the event's essence [Bennett] |
16772 | An angelic mind would not experience pain, even when connected to a human body [Descartes, by Pasnau] |