20 ideas
| 10807 | Mathematics reduces to set theory, which reduces, with some mereology, to the singleton function [Lewis] |
| 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] |
| 10809 | We can accept the null set, but not a null class, a class lacking members [Lewis] |
| 10811 | The null set plays the role of last resort, for class abstracts and for existence [Lewis] |
| 10812 | The null set is not a little speck of sheer nothingness, a black hole in Reality [Lewis] |
| 13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
| 10813 | What on earth is the relationship between a singleton and an element? [Lewis] |
| 10814 | Are all singletons exact intrinsic duplicates? [Lewis] |
| 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] |
| 10806 | Megethology is the result of adding plural quantification to mereology [Lewis] |
| 10816 | We can use mereology to simulate quantification over relations [Lewis] |
| 10808 | Mathematics is generalisations about singleton functions [Lewis] |
| 10815 | We don't need 'abstract structures' to have structural truths about successor functions [Lewis] |
| 10810 | I say that absolutely any things can have a mereological fusion [Lewis] |
| 22489 | 'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot] |