The Review of Symbolic Logic

Research Article

NON-WELLFOUNDED MEREOLOGY

AARON J. COTNOIRa1 c1 and ANDREW BACONa2 c2

a1 Northern Institute of Philosophy, University of Aberdeen

a2 Oxford University, Magdalen College

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.

(Received April 29 2011)

Correspondence:

c1 NORTHERN INSTITUTE OF PHILOSOPHY, UNIVERSITY OF ABERDEEN, OLD BREWERY, ABERDEEN, AB24 3UB, UNITED KINGDOM E-mail: a.cotnoir@abdn.ac.uk

c2 MAGDALEN COLLEGE, OXFORD, OX1 4AU, UNITED KINGDOM