14 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] |
| 13168 | My formal unifying atoms are substantial forms, which are forces like appetites [Leibniz] |
| 13169 | I call Aristotle's entelechies 'primitive forces', which originate activity [Leibniz] |
| 13170 | The analysis of things leads to atoms of substance, which found both composition and action [Leibniz] |
| 13171 | Substance must necessarily involve progress and change [Leibniz] |
| 18284 | Particulars can be verified or falsified, but general statements can only be falsified (conclusively) [Popper] |
| 13167 | We need the metaphysical notion of force to explain mechanics, and not just extended mass [Leibniz] |