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Full Idea
We can take the theory of singleton functions, and hence set theory, and hence mathematics, to consist of generalisations about all singleton functions.
Gist of Idea
Mathematics is generalisations about singleton functions
Source
David Lewis (Mathematics is Megethology [1993], p.03)
Book Ref
-: 'Philosophia Mathematica' [-], p.3
A Reaction
At first glance this sounds like a fancy version of the somewhat discredited Greek idea that mathematics is built on the concept of a 'unit'.
| 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] |