Set-Theoretic Mereology

Authors

Joel David Hamkins, CUNY Graduate CenterFollow
Makoto Kikuchi, Tokyo Institute of Technology

Document Type

Article

Publication Date

5-16-2016

Abstract

We consider a set-theoretic version of mereology based on the inclusion relation ⊆ and analyze how well it might serve as a foundation of mathematics. After establishing the non-definability of ∈ from ⊆, we identify the natural axioms for ⊆-based mereology, which constitute a finitely axiomatizable, complete, decidable theory. Ultimately, for these reasons, we conclude that this form of set-theoretic mereology cannot by itself serve as a foundation of mathematics. Meanwhile, augmented forms of set-theoretic mereology, such as that obtained by adding the singleton operator, are foundationally robust.

Comments

This article was originally published in Logic and Logical Philosophy, available at DOI: 10.12775/LLP.2016.007.

This work was distributed under the terms of the Creative Commons Attribution Non-Commercial license (CC BY NC).