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Single Idea 10809

[filed under theme 4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set ]

Full Idea

In my usage of 'class', there is no such things as the null class. I don't mind calling some memberless thing - some individual - the null set. But that doesn't make it a memberless class. Rather, that makes it a 'set' that is not a class.

Gist of Idea

We can accept the null set, but not a null class, a class lacking members

Source

David Lewis (Mathematics is Megethology [1993], p.05)

Book Ref

-: 'Philosophia Mathematica' [-], p.5


A Reaction

Lewis calls this usage 'idiosyncratic', but it strikes me as excellent. Set theorists can have their vital null class, and sensible people can be left to say, with Lewis, that classes of things must have members.


The 11 ideas from 'Mathematics is Megethology'

Mathematics reduces to set theory, which reduces, with some mereology, to the singleton function [Lewis]
Megethology is the result of adding plural quantification to mereology [Lewis]
Mathematics is generalisations about singleton functions [Lewis]
We can accept the null set, but not a null class, a class lacking members [Lewis]
I say that absolutely any things can have a mereological fusion [Lewis]
The null set plays the role of last resort, for class abstracts and for existence [Lewis]
The null set is not a little speck of sheer nothingness, a black hole in Reality [Lewis]
What on earth is the relationship between a singleton and an element? [Lewis]
Are all singletons exact intrinsic duplicates? [Lewis]
We don't need 'abstract structures' to have structural truths about successor functions [Lewis]
We can use mereology to simulate quantification over relations [Lewis]