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The ontological parsimony of mereology

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Abstract

Lewis (Parts of classes, Wiley-Blackwell, Oxford, 1991, 84) famously argued that mereology is ontologically innocent. Many who have considered this claim believe he was mistaken. Mereology is not innocent, because its acceptance entails the acceptance of sums, new objects that were not previously part of one’s ontology. This argument, the argument from ontological parsimony, has two versions: a qualitative and a quantitative one. I argue that the defender of mereology can neutralize both arguments by holding that, given mereology, a commitment to the parts of an object is not an extra ontological commitment, made in addition to the commitment to the object; and that if the parts of an object are ‘ontologically innocent’, then sums cannot fail to be innocent either.

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Notes

  1. For various axiomatizations of classical mereology, see (Hovda 2009). For a general overview of various mereological systems and their philosophical implications, see (Varzi 2015).

  2. I will use the terms ‘sum’, ‘fusion’, and ‘composite object’ interchangeably.

  3. As Cotnoir (2014, 9) points out, the Composition as Identity thesis comes in at least three versions: Strong Composition as Identity (SCI) holds that the parts taken collectively are numerically identical to the whole; Moderate Composition as Identity (MCI) states that the parts taken collectively are non-numerically identical to the whole; Weak Composition as Identity (WCI) is the thesis that the parts taken collectively stand in a relation to the whole that is analogous to identity. SCI is defended in (Bohn 2014a, b; Wallace 2011a, b, 2014); MCI in (Baxter 1988a, b); WCI in (Lewis 1991; Varzi 2000, 2014). Armstrong (1997, 17–18) defends either MCI or WCI.

  4. Tom and Jerry made their first appearance in the Composition as Identity debate in (Yi 1999).

  5. I use the acronym ‘ANE’ for the Argument from quaNtitative Extravagence and ‘ALE’ (below) for the Argument from quaLitative Extravagance.

  6. Forget for a moment that cats and mice both belong to the kingdom Animalia. For the argument we need two objects of two different kinds; we could take whatever objects of whatever ontological kind or category are deemed appropriate, as long as the two are different in kind.

  7. Two other notions of simplicity (which will be ignored here for the sake of simplicity) are syntactical simplicity and ideological parsimony.

  8. Various extensionality principles, such as Unique Composition, Extensionality of Composition, and Extensionality of Parthood, are valid in mereology. For discussion, see (Varzi 2008).

  9. Of course, if Argle’s claim that Tom exists is false, whereas Bargle’s claim that Tom* exists is true, we should take sides with Bargle. However, principles of theory-choice are only relevant if there is no way of telling which of the theories on offer is true (or correct): they all explain the phenomena, and therefore we should look at theoretical virtues like simplicity in order to choose. Hence, I will suppose that we do not know (and cannot know) whether mereology is correct. I am only interested in the question whether we should eschew mereology on the basis of a principle of ontological parsimony.

  10. I say ‘rather similar’, since Varzi seems to hold that counting objects is the same as counting ontological commitments: “[I]f (…) commitment to the fusion is just the same as commitment to each of those things [i.e. its parts], then on the weak reading of Composition as Identity L3 [i.e. mereology is ontologically innocent] would sin against Quine.”(Varzi 2014, 63) Instead, Varzi suggests that truths about fusions make the same commitments as truths about their parts (Ibid.).

  11. EP is crucial here, as it is in Varzi’s M, since without it one cannot hold that the object one is committed to could not exist were it not for the parts it has; and without this latter claim ontological commitment to some composite object O does not entail ontological commitment to its parts.

  12. Actually, given UMC, Bargle has seven objects to which he is ontologically committed: next to the four I mention there is also the sum of x and y, the sum of y and z, and the sum of x and z. This does not matter for my argument.

  13. Cf. footnote 9 above.

  14. Existential Monism should be distinguished from Priority Monism as defended in (Schaffer 2010) which is the view according to which the universe is ontologically prior to its parts.

  15. It may be a problem for such a procedure that the singleton has to be something different from the object that is its single member. Claiming that the singleton should not be counted next to its sole member makes set theory impossible (likewise for the singleton of a given singleton). You have to take the singleton as something else and count it next to its member; but no such demand is made by mereology. In mereology you need not (and cannot) get something new out of only one thing (the sum of Lewis is just Lewis, not singleton-Lewis). You do get something ‘new’ out of the many in mereology, namely the sum of the many. But, as I have said, this should not be counted as a new ontological commitment. Moreover, in set theory the set of two objects is different from the ordered set of those same two objects. Thus, set theory is not as hyper-extensional as mereology—which might make it less obvious that something like ‘Innocence of Membership’ (as analogous to ‘Innocence of Parthood’) can be defended and that such a principle would be sufficient to defend ‘Innocence of Set-Formation’ (as analogous to ‘Innocence of Composition’). (Defending the latter principle might be further hindered by the fact that there cannot be, on pain of paradox, a set of everything in set theory, whereas there is a sum of everything in mereology, viz. the universe).

  16. Thanks to an anonymous reviewer for pressing me on this point.

  17. All this does not mean that we cannot compare the ontological commitments of theories. It does mean that it is possible that for some theory T1 the commitment to x is an additional commitment within T1 whereas in another theory T2, commitment to that same x is not an additional commitment within T2. To compare theories, the distinguishable constraints that a theory puts on the world are what matters. The difficulty with comparison, however, lies in the fact that ‘distinguishable’ here means ‘distinguishable within the own theory’.

  18. Since one can define identity in terms of parthood, the suggestion here is that we should take identity as a (quasi-) mereological relation. This means mereology is seen as a theory of partial-identity, very much in line with (Armstrong 1997, 17–18).

  19. For a defense of the importance of existence questions (contra the neo-Aristotelian account of ontological commitment), see (Daly and Liggins 2014).

  20. Arguments for coincident non-identical objects that stand in a relation of constitution (i.e. ‘The Standard View’) can be found in Baker (1997); Fine (2003); Johnston (1992); Koslicki (2004); Lowe (1995); Simons (1987, 210–252); and Thomson (1998).

  21. For a defense of restricted composition under which there are few weird objects, see (Markosian 1998, 2008).

  22. For example, Simons (2003).

  23. Most explicitly, Rescher (1955). (Cf. Johansson (2004), who objects to the idea that all parthood predicates pick out transitive parthood relations, insisting that some might pick out three-place parthood relations that fail to be transitive).

  24. This expression comes from Armstrong (1997, 12), but note that for Armstrong the ticket to the free-lunch is supervenience: what supervenes is—usually—ontologically innocent. For mereology, no such thing is needed: IP and IC are silent about supervenience.

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Acknowledgments

Thanks to the participants of the Higher Seminar in Philosophy at Lund University (Autumn 2014) where I presented some of this material. Many thanks also to Erik J. Olsson, Tobias Hansson Wahlberg and an anonymous referee of Philosophical Studies for helpful comments on earlier drafts.

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    Jeroen Smid

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Smid, J. The ontological parsimony of mereology. Philos Stud 172, 3253–3271 (2015). https://doi.org/10.1007/s11098-015-0468-3

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