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