Non-wellfounded Mereology

Review of Symbolic Logic 5 (2):187-204 (2012)
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.
Keywords mereology  wellfounded  extensionality
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DOI 10.1017/S1755020311000293
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A. J. Cotnoir (2013). Beyond Atomism. Thought: A Journal of Philosophy 2 (1):67-72.

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