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Full Idea
We can simulate quantification over relations using megethology. Roughly, a quantifier over relations is a plural quantifier over things that encode ordered pairs by mereological means.
Clarification
For 'megethology' see Idea 10806
Gist of Idea
We can use mereology to simulate quantification over relations
Source
David Lewis (Mathematics is Megethology [1993], p.18)
Book Ref
-: 'Philosophia Mathematica' [-], p.18
A Reaction
[He credits this idea to Burgess and Haven] The point is to avoid second-order logic, which quantifies over relations as ordered n-tuple sets.
| 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] |