Does Universalism Entail Extensionalism?

Abstract

Does a commitment to mereological universalism automatically bring along a commitment to the controversial doctrine of mereological extensionalism -the view that objects with the same proper parts are identical? A recent argument suggests the answer is 'yes'. is paper attempts a systematic response to the argument, considering nearly every available line of reply. It argues that only one approach -the mutual parts view -can yield a viable mereology where universalism does not entail extensionalism.

Are The Statue and The Clay Mutual Parts?

“…Whereas, Strong Supplementation* concerns some cooked‐up relation expressed in its antecedent, Weak Supplementation* concerns an interesting notion. Cotnoir (, ) distinguishes between two notions of proper parthood: non‐identical parthood and parthood with remainder, claiming that Weak Supplementation* captures the latter notion.…”

“…Although the intuitive case for Mutual Parthood from Strong Supplementation fails, Cotnoir () argues that Strong Supplementation provides a theoretical reason for Mutual Parthood. In short, he argues that Weak Supplementation is to be rejected, even accepting No Parthood, but that any mereology that rejects both Weak and Strong Supplementation is inadequate.…”

“…Cotnoir (), replying to Varzi, argues that there are problems with any anti‐extensionalist rejection of Strong Supplementation, and so provides a distinct argument for Mutual Parthood from the failure of Extensionality. Varzi () argues that

Universal Fusion: ∀xx ∃y (y is a fusion of xx)

…”

“…We should note that no parthood theorists are now in the same position as constituting parthood theorists in having to deny both Strong and Weak Supplementation, and also both Strong and Weak Inclusion, assuming fusions are located. Furthermore, Cotnoir () argues that we cannot simply deny both Strong and Weak Supplementation, since any such mereology is unacceptable. If he is correct, then Constituting Parthood must be rejected, as must any no parthood view that denies Extensionality and countenances the fusion of distinct coincident objects.…”

“…Assuming that Moderate Pluralism is true, we can ask what relations hold between coincident material objects such as the statue and the clay? Many moderate pluralists claim that the clay constitutes the statue. Some moderate pluralists, notably Cotnoir (, , ; see also Cotnoir and Bacon ), Hawthorne (), Hovda (), and Thomson (, 1988), have argued that the statue and the clay are mutual parts, endorsing

Mutual Parthood: If x and y are distinct coincident objects, then x is a part of y and y is a part of x.

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