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NON-WELLFOUNDED MEREOLOGY

Published online by Cambridge University Press:  09 December 2011

AARON J. COTNOIR  and
ANDREW BACON
AARON J. COTNOIR*
Affiliation:
Northern Institute of Philosophy, University of Aberdeen
ANDREW BACON*
Affiliation:
Oxford University, Magdalen College
*
*NORTHERN INSTITUTE OF PHILOSOPHY, UNIVERSITY OF ABERDEEN, OLD BREWERY, ABERDEEN, AB24 3UB, UNITED KINGDOM E-mail:a.cotnoir@abdn.ac.uk
†MAGDALEN COLLEGE, OXFORD, OX1 4AU, UNITED KINGDOM
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Abstract

This paper is a systematic exploration of non-wellfounded mereology. Motivations and applications suggested in the literature are considered. Some are exotic like Borges’ Aleph, and the trinity; other examples are less so, like time traveling bricks, and even Geach’s Tibbles the Cat. The authors point out that the transitivity of non-wellfounded parthood is inconsistent with extensionality. A non-wellfounded mereology is developed with careful consideration paid to rival notions of supplementation and fusion. Two equivalent axiomatizations are given, and are compared to classical mereology. We provide a class of models with respect to which the non-wellfounded mereology is sound and complete.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 5 , Issue 2 , June 2012 , pp. 187 - 204
Copyright
Copyright © Association for Symbolic Logic 2011

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