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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.
Cotnoir , A & Bacon , A 2012 , ' Non-wellfounded mereology ' The Review of Symbolic Logic , vol 5 , no. 2 , pp. 187-204 . DOI: 10.1017/S1755020311000293
The Review of Symbolic Logic
This is an author version of this article. The published version is available at http://journals.cambridge.org (c) Association for Symbolic Logic, 2011
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