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Set-theoretic mereology

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 o...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.12775/llp.2016.007

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Institution:
University of Oxford
Division:
Humanities Division
Department:
Philosophy
Oxford college:
University College
Role:
Author
Publisher:
Uniwersytet Mikołaja Kopernika w Toruniu Publisher's website
Journal:
Logic and Logical Philosophy Journal website
Volume:
25
Issue:
3
Publication date:
2016-09-01
Acceptance date:
2016-06-01
DOI:
EISSN:
2300-9802
ISSN:
1425-3305
Source identifiers:
916842
Keywords:
Pubs id:
pubs:916842
UUID:
uuid:3cccc2ed-09da-40d5-acf6-b7e2aa6284f5
Local pid:
pubs:916842
Deposit date:
2019-02-06

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