Set-theoretic mereology

• Authors: Hamkins Joel David , Kikuchi Makoto
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

mereology; set theory; foundations of mathematics

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2016
• Volume: 25
• Issue: 3 Mereology and Beyond (II)
• Pages: 285-308

Dates

online

2016-05-16

Contributors

author

Hamkins Joel David

• Mathematics, Philosophy, Computer Science, The Graduate Center of The City University of New York, 365 Fifth Avenue, New York, NY 10016 & Mathematics, College of Staten Island of CUNY, Staten Island, NY 10314, http://jdh.hamkins.org

author

Kikuchi Makoto

• Graduate School of System Informatics, Kobe University, Rokkodai, Nada, Kobe 657-8501, Japan, http://www2.kobe-u.ac.jp/~mkikuchi/index-e.html

References

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Identifiers

DOI

10.12775/LLP.2016.007