16 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] |
| 14221 | Serious essentialism says everything has essences, they're not things, and they ground necessities [Shalkowski] |
| 14222 | Essences are what it is to be that (kind of) thing - in fact, they are the thing's identity [Shalkowski] |
| 14226 | We distinguish objects by their attributes, not by their essences [Shalkowski] |
| 14225 | Critics say that essences are too mysterious to be known [Shalkowski] |
| 14223 | De dicto necessity has linguistic entities as their source, so it is a type of de re necessity [Shalkowski] |
| 14224 | Equilateral and equiangular aren't the same, as we have to prove their connection [Shalkowski] |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |