Set-theoretic mereology

Author: 

HAMKINS, J

Publication Date: 

1 September 2016

Journal: 

Logic and Logical Philosophy

Last Updated: 

2019-07-01T07:17:29.48+01:00

Issue: 

3

Volume: 

25

DOI: 

10.12775/LLP.2016.007

page: 

285-308

abstract: 

© 2016 by Nicolaus Copernicus University. 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.

Symplectic id: 

916842

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article