18 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] |
9390 | Logic guides thinking, but it isn't a substitute for it [Rumfitt] |
14650 | Maybe proper names involve essentialism [Plantinga] |
14648 | Could I name all of the real numbers in one fell swoop? Call them all 'Charley'? [Plantinga] |
14647 | Surely self-identity is essential to Socrates? [Plantinga] |
9389 | Vague membership of sets is possible if the set is defined by its concept, not its members [Rumfitt] |
14646 | An object has a property essentially if it couldn't conceivably have lacked it [Plantinga] |
14649 | Can we find an appropriate 'de dicto' paraphrase for any 'de re' proposition? [Plantinga] |
14642 | Expressing modality about a statement is 'de dicto'; expressing it of property-possession is 'de re' [Plantinga] |
14643 | 'De dicto' true and 'de re' false is possible, and so is 'de dicto' false and 'de re' true [Plantinga] |
14651 | What Socrates could have been, and could have become, are different? [Plantinga] |