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Set-theoretic mereology

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Hamkins J. D., Kikuchi M.

Logic and Logical Philosophy

2016

vol. 25

issue 3 Mereology and Beyond (II)

285-308

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.

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1 Logic and Logical Philosophy

1 2016

1 Hamkins J. D.

1 Kikuchi M.

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Set-theoretic mereology