Abstract
I propose a new theory of mereology based on a mereological reflection principle. Reflective mereology has natural fusion principles but also refutes certain principles of classical mereology such as Universal Fusion and Fusion Uniqueness. Moreover, reflective mereology avoids Uzquiano’s cardinality problem–the problem that classical mereology tends to clash with set theory when they both quantify over everything. In particular, assuming large cardinals, I construct a model of reflective mereology and second-order ZFCU with Limitation of Size. In the model, classical mereology holds when the quantifiers are restricted to the urelements.
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Acknowledgments
The author would like to thank Patricia Blanchette, Joel David Hamkins, Daniel Nolan, Agustín Rayo, and an anonymous referee for their helpful comments on earlier drafts of this paper.
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Yao, B. Reflective Mereology. J Philos Logic 52, 1171–1196 (2023). https://doi.org/10.1007/s10992-023-09702-x
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DOI: https://doi.org/10.1007/s10992-023-09702-x