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NON-WELLFOUNDED MEREOLOGY

  • AARON J. COTNOIR (a1) and ANDREW BACON (a2)
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.

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*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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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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