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Full Idea
The null set serves two useful purposes. It is a denotation of last resort for class abstracts that denote no nonempty class. And it is an individual of last resort: we can count on its existence, and fearlessly build the hierarchy of sets from it.
Gist of Idea
The null set plays the role of last resort, for class abstracts and for existence
Source
David Lewis (Mathematics is Megethology [1993], p.09)
Book Ref
-: 'Philosophia Mathematica' [-], p.9
A Reaction
This passage assuages my major reservation about the existence of the null set, but at the expense of confirming that it must be taken as an entirely fictional entity.
| 10807 | Mathematics reduces to set theory, which reduces, with some mereology, to the singleton function [Lewis] |
| 10806 | Megethology is the result of adding plural quantification to mereology [Lewis] |
| 10808 | Mathematics is generalisations about singleton functions [Lewis] |
| 10809 | We can accept the null set, but not a null class, a class lacking members [Lewis] |
| 10810 | I say that absolutely any things can have a mereological fusion [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] |
| 10813 | What on earth is the relationship between a singleton and an element? [Lewis] |
| 10814 | Are all singletons exact intrinsic duplicates? [Lewis] |
| 10815 | We don't need 'abstract structures' to have structural truths about successor functions [Lewis] |
| 10816 | We can use mereology to simulate quantification over relations [Lewis] |