No universalism without gunk? Composition as identity and the universality of identity


Philosophers disagree whether composition as identity entails mereological universalism. Bricker (Inquiry 59(3):264–294, 2016) has recently considered an argument which concludes that composition as identity supports universalism. The key step in this argument is the thesis that any objects are identical to some object, which Bricker justifies with the principle of the universality of identity. I will spell out this principle in more detail and argue that it has an unexpected consequence. If the universality of identity holds, then composition as identity not only leads us to universalism, but also leads to the view that there are no mereological atoms.

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  1. 1.

    A mereological atom is an object with no proper part (Casati and Varzi 1999, p. 39). A gunky object is an object whose parts all have at least one proper part (Lewis 1991, p. 20).

  2. 2.

    Universalism is endorsed, for instance, by Bricker (2016, pp. 264–265), Lewis (1991, pp. 75–87), and Varzi (2014, p. 48). Cameron (2010), Rosen and Dorr (2002), and Sider (2013) are among the supporters of nihilism. Restricted views of composition are defended by Korman (2015), Merricks (2001), and van Inwagen (1990).

  3. 3.

    Bricker (2016), Lewis (1991, \(\S \)3), and Varzi (2014) embrace both views. Koslicki (2008, \(\S \)2–3), Simons (2006; 2016, p. 60), and van Inwagen (1990, 1994) criticise both theories. Lando stands out as a universalist who explicitly rejects Composition as Identity, see \(\S \)10–14 and the appendix in Lando (2017).

  4. 4.

    Bohn (2014), Merricks (2005, pp. 629–631), and Sider (2007, pp. 59–62) argue that there is such a connection, while Cameron (2012) and McDaniel (2010) deny that Composition as Identity entails universalism.

  5. 5.

    See Baxter (1988a, b, 2014), Bricker (2016, p. 266), Cotnoir (2013), and Cotnoir (2014, pp. 9–11).

  6. 6.

    Given the concept of many-one identity, it is a natural question to ask whether that relation can also hold between one object and many, or whether there is a fourth kind of identity, “one-many identity”. Bricker explicitly allows for many-one identity to hold between one object and many objects (Bricker 2016, pp. 268–269). In contrast, Cotnoir distinguishes between many-one and one–many identity (Cotnoir 2013, p. 303). For our concerns here, there is no need to answer this question, though we will come back to it in the next section.

  7. 7.

    I will use here, and in the following, plural variables, xx, yy, zz. Plural variables can take on singular values, such as Anne, or John F. Kennedy, as well as plural values, such as Anne and Bob, or the Kennedys. See also, Ben-Yami (2004), Linnebo (2017), McKay (2006), Oliver and Smiley (2013).

  8. 8.

    I am grateful to an anonymous reviewer for highlighting the above suspicion.

  9. 9.

    See fn.6 and section 3.2.

  10. 10.

    Some might object that my view of composition as an irreflexive relation is a non-standard position and differs from Bricker’s understanding of composition. Yet, let me briefly give some reasons why one might think that composition is an irreflexive relation. One of the central claims of Composition as Identity is that there is no additional ontological commitment to an object, given the commitment to the parts which compose it (Bricker 2016, pp. 266–267), (Cotnoir 2014, p. 7), (Lewis 1991, pp. 81–82), (Varzi 2014, p. 47). Taking this claim to involve a reflexive composition relation (or improper parthood) means, in my view, interpreting Composition as Identity as a trivially true and quite uninteresting position: If the objects yy which compose an object x include that x itself, then there cannot be any additional commitment to x, given the commitment to the yy, since x is one of the yy. At first sight, this worry might seem ungrounded since we have some yy, which don’t include their composite object, for instance a stick and a brush that compose a broom. However, it strikes me as odd that, given a reflexive composition relation, the claim that a commitment to a composite object x is nothing over and above a commitment to its parts yy is trivial in some cases, if x is the only object among the yy, while it is not trivial in other cases, if x is not among the yy.

  11. 11.

    Given the suggestion that composition is an irreflexive relation, and the fact that plural variables can be assigned singular values, we have to slightly adjust our formulation of mereological universalism, which differs from Bricker’s (2016, p. 268). We have to add the condition that the composing objects xx have to be many objects in order to compose some object y. This is necessary because the possibility that there is only one object among the xx, in which case it will not compose anything, cannot be excluded. Moreover, by adding this condition to our principle, we can hold on to it without getting into conflict with plural terms that fail to refer, such as “Sherlock Holmes and Dr Watson” or “the twelve Olympians”, see Oliver and Smiley (2013, \(\S \)5.3).

  12. 12.

    Cotnoir (2013) calls this relation general identity.

  13. 13.

    It should be noted that Bricker uses schematic letters for variables when giving his account. To avoid possible confusion, I should point out that this disagrees with my suggested usage here when a neutral variable connects with an existential quantifier: when \(\alpha \) is a schematic letter, \(\exists \alpha F \alpha \) represents the claim that there are some objects xx that are F and that there is some object x that is F.

  14. 14.

    With first-order logic, I mean the system developed by Frege (1879), and presented, for instance, in Priest (2008, \(\S \)12) and Sider (2010, \(\S \)4–5.3).

  15. 15.

    However, if we take EPU to contain schematic letters instead of neutral variables, it would be legitimate to claim that UI, or the version of UI that is formulated with schematic letters, entails EPU.

  16. 16.

    Bricker can apparently avoid this worry. He does not introduce a symbol in his language for many-one identity, but uses the symbol for his generalized identity relation which can take either plural or singular arguments in either place.

  17. 17.

    Another alternative formalisation, using the predicate being among (\(\prec \)) commonly used in plural logic, is the following: \(\forall x \exists yy ( x \simeq yy \wedge \exists z_{1} \exists z_{2} (z_{1} \prec yy \wedge z_{2} \prec yy \wedge z_{1} \ne z_{2}))\).

  18. 18.

    A further complication comes into play if we consider questions about modality. If we take the universality of identity to be a necessary truth, it would seem natural to take Ex Uno Plura, and therefore the claim that any object is gunky, to be a necessary truth. This might be a worrisome result since even if one thinks that there are no atoms in the actual world, one might not want to exclude the possibility that there are atoms. Thanks to an anonymous reviewer for mentioning this worry.

  19. 19.

    Thanks to A. J. Cotnoir, Louis deRosset, Mark Moyer, Zach Weber and Justin Zylstra, as well as the participants of the Arché Metaphysics Seminar at the University of St Andrews for discussion and comments on earlier versions of this paper. I would also like to thank two anonymous reviewers for helpful suggestions and feedback on earlier drafts.


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Lechthaler, M. No universalism without gunk? Composition as identity and the universality of identity. Synthese (2019).

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  • Composition as identity
  • Universalism
  • Gunk
  • Universality of identity
  • Mereology