20 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] |
| 12184 | Logical necessity overrules all other necessities [McFetridge] |
| 15083 | The fundamental case of logical necessity is the valid conclusion of an inference [McFetridge, by Hale] |
| 15084 | In the McFetridge view, logical necessity means a consequent must be true if the antecedent is [McFetridge, by Hale] |
| 12180 | Logical necessity requires that a valid argument be necessary [McFetridge] |
| 12181 | Traditionally, logical necessity is the strongest, and entails any other necessities [McFetridge] |
| 12183 | It is only logical necessity if there is absolutely no sense in which it could be false [McFetridge] |
| 12192 | The mark of logical necessity is deduction from any suppositions whatever [McFetridge] |
| 12182 | We assert epistemic possibility without commitment to logical possibility [McFetridge] |
| 12187 | Objectual modal realists believe in possible worlds; non-objectual ones rest it on the actual world [McFetridge] |
| 12186 | Modal realists hold that necessities and possibilities are part of the totality of facts [McFetridge] |
| 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] |