Ideas from 'Mathematics is Megethology' by David Lewis [1993], by Theme Structure

[found in 'Philosophia Mathematica' (ed/tr -) [- ,]].

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4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematics reduces to set theory, which reduces, with some mereology, to the singleton function
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
The null set is not a little speck of sheer nothingness, a black hole in Reality
We can accept the null set, but not a null class, a class lacking members
The null set plays the role of last resort, for class abstracts and for existence
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Set
What on earth is the relationship between a singleton and an element?
Are all singletons exact intrinsic duplicates?
4. Formal Logic / G. Formal Mereology / 1. Mereology
Megethology is the result of adding plural quantification to mereology
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
We can use mereology to simulate quantification over relations
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Number / a. Axioms for numbers
Mathematics is generalisations about singleton functions
6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / e. Structuralism critique
We don't need 'abstract structures' to have structural truths about successor functions
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
I say that absolutely any things can have a mereological fusion