Abstract
It is customary practice to define ‘x is composed of the ys’ as ‘x is a sum of the ys and the ys are pairwise disjoint (i.e., no two of them have any parts in common)’. This predicate has played a central role in the debate on the special composition question and on related metaphysical issues concerning the mereological structure of objects. In this note we show that the customary characterization is nonetheless inadequate. We do so by constructing a mereological model where everything qualifies as composed of atoms even though some elements in the domain are gunky, i.e., can be divided indefinitely into smaller and smaller proper parts.
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Notes
Or, if one wishes to avoid plural quantification and stick to a standard first-order syntax, the analogous but weaker predicate ‘x is composed of the φs’, where ‘φ’ is an open formula.
This is because any element in D M of the form I ∪ P is such that the position of I in the binary tree rooted at G is exactly the same as the position of P in the binary tree rooted at A. For, suppose x ∩ G ⊆ y. Then x ∩ G must be in the sub-tree rooted at y ∩ G. But then x ∩ A will be in the sub-tree rooted at y ∩ A. Hence x ∩ A ⊆ y ∩ A ⊆ y. Similarly, if x ∩ A ⊆ y, we must have x ∩ G ⊆ y ∩ G ⊆ y.
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Acknowledgments
Many thanks to two anonymous referees for very helpful comments on an earlier draft of this paper, which led to substantive revisions. Part of this work was carried out within research project NSC 101-2410-H-194-033-MY3, kindly funded by the Ministry of Science and Technology of Taiwan.
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Tsai, Hc., Varzi, A.C. Atoms, Gunk, and the Limits of ‘Composition’. Erkenn 81, 231–235 (2016). https://doi.org/10.1007/s10670-015-9736-z
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DOI: https://doi.org/10.1007/s10670-015-9736-z