19 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] |
| 9175 | We may fix the reference of 'Cicero' by a description, but thereafter the name is rigid [Kripke] |
| 9171 | The function of names is simply to refer [Kripke] |
| 9174 | It is necessary that this table is not made of ice, but we don't know it a priori [Kripke] |
| 9172 | A 'rigid designator' designates the same object in all possible worlds [Kripke] |
| 9173 | We cannot say that Nixon might have been a different man from the one he actually was [Kripke] |
| 9176 | Modal statements about this table never refer to counterparts; that confuses epistemology and metaphysics [Kripke] |
| 14802 | Physical and psychical laws of mind are either independent, or derived in one or other direction [Peirce] |
| 9177 | Identity theorists must deny that pains can be imagined without brain states [Kripke] |
| 9178 | Pain, unlike heat, is picked out by an essential property [Kripke] |
| 14800 | The world is full of variety, but laws seem to produce uniformity [Peirce] |
| 14801 | Darwinian evolution is chance, with the destruction of bad results [Peirce] |