Ideas from 'Mathematics is Megethology' by David Lewis [1993], by Theme Structure
[found in 'Philosophia Mathematica' (ed/tr -) [- ,]].
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expand these ideas
4. Formal Logic / F. Set Theory ST / 1. Set Theory
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10807
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Mathematics reduces to set theory, which reduces, with some mereology, to the singleton function
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
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10809
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We can accept the null set, but not a null class, a class lacking members
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10812
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The null set is not a little speck of sheer nothingness, a black hole in Reality
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10811
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The null set plays the role of last resort, for class abstracts and for existence
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
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10813
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What on earth is the relationship between a singleton and an element?
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10814
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Are all singletons exact intrinsic duplicates?
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4. Formal Logic / G. Formal Mereology / 1. Mereology
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10806
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Megethology is the result of adding plural quantification to mereology
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5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
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10816
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We can use mereology to simulate quantification over relations
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
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10808
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Mathematics is generalisations about singleton functions
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
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10815
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We don't need 'abstract structures' to have structural truths about successor functions
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9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
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10810
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I say that absolutely any things can have a mereological fusion
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