Defending the Junk Argument* . Introduction Unrestricted composition is one of the most controversial doctrines of classical mereology. An objection has been put forward to the view that mereological composition is necessarily unre- stricted by appealing to the possibility of so-called ‘junky’ worlds. A world is junky if everything in that world is a proper part of something (i.e. 8x9y(x < y) is true).¹ e junk argument, due to Bohn [, , ], proceeds as follows: (i) If a world is junky, then the unrestricted fusion axiom for mereology is false at that world. (ii) Junky worlds are metaphysically possible. (iii) erefore, the unrestricted fusion axiom for mereology is either metaphysically contingent or necessarily false. Much attention has been devoted to the defence of premise (ii). I do not wish to challenge the case for (ii).² However, more recently premise (i) has come under fire. For example, Contessa [] and Spencer [] have each provided independent reasons that ‘universalists’ should dispatch the argument by rejecting premise (i). In this paper, I undertake a defence of premise (i) against a variety of objections. In §, I put forward a new objection to premise (i): Bohn’s defence of it presupposes far too much. In particular, I show that Bohn’s suppositions entail mereological extensionalism; that is, these assumptions rule out the view that objects with the same proper parts may be distinct. Two of the most prominent non-extensional mereologies are introduced: the unsupplemented view, and the mutual parts view. A non-extensionalist, then, might have strong reasons for accepting universalism but rejecting the argument. *is paper is a . Please do not cite without permission. Comments are welcome. ¹is is the converse of the notion of a gunky world in which everything in that world has something as a proper part. ²But see Watson [] for discussion. Bohn’s main defence involves three criteria for metaphysical possibility: con- ceivability, advocacy, and consistency. But if we can conceive of junky worlds, and several prominent philosophers have taken the idea seriously, and there are no logical contradictions lurking, then we are hard pressed to deny the mere possibility of the world being junky. ([], ) For the record, I do not think these three criteria are sufficient for metaphysical possibility, but the matter is too complicated for discussion here. | . In §§–, I show that one can defend premise (i) from a much weaker set of assumptions. Hence variants of the junk argument can be shown to apply to non-extensional mereological systems as well. I address unsupplemented mereologies in § which explicitly reject one of Bohn’s assumptions. In order to avoid begging the question against such views, I show that a variant of the junk argument survives even without appeal to any kind of supplementation. § argues that the mutual parts theorist who accepts unrestricted composition can avoid Bohn’s argument. However, the kind of junk compatible the the mutual parts view is only counterfeit — it satisfies the definition in letter, but not in spirit. A revision in the definition of junk yields the desired result. § takes on Contessa’s objection to premise (i). Contessa contends that those who accept unrestricted composition should only accept the existence of binary sums rather than infinitary fusions. I argue this conception of unrestricted composition is problematic: it is in conflict with the existence of gunk satisfying an intuitive remainder principle. Ithenconsiderapossibleresponse based on the mereology of Bostock [], and suggest that it’s not really a version of unrestricted fusion and so changes the terms of the debate. It may well be the most plausible version of a junky mereology, but it hardly constitutes a counterinstance to premise (i). In§, Iconsiderarecentresponsetopremise(i)bySpencer[]. Spencer’s view is that there is no absolutely unrestricted universal quantifier. So, any statement of the unrestricted fusion axiom will simply not rule out the existence of junky worlds. I argue that in order for this response to provide a counterexample to premise (i), we need some further argument. First, since junky worlds are defined using the universal quantifier, what Spencer’s argument allows appears to be worlds that are inexpressibly junky. But the metaphysical possibility of inexpressibly junky worlds needs an independent defence, and is not given (even implicitly) by the acceptance of premise (ii). Second, we may be simply unable to quantify over all the parts of something, or unable to quantify over all the simples. But neither of these options will yield junky worlds. ird, even if we have a principled reason to think that our quantifier is indefinitely extensible upwards along parthood chains, it’s not clear that the resulting expression of the unrestricted fusion axiom is genuinely unrestricted in the required sense. ese defences of premise (i) show that it is particularly resilient and can be based on extremely minimal assumptions. e upshot, then, is that anyone who wants to reject the junk argument must do so by rejecting premise (ii) instead. | . Analyticity & Extensionalism In his argument for premise (i), Bohn relies on the following assumptions, where < is proper parthood, ≤ improper parthood, and ◦ mereological overlap: Transitivity (x < y ^ y < z) ! x < z Weak Supplementation x < y ! 9z(z ≤ y ^ :z ◦ x)) Weak Supplementation says that if something has a proper part, it must have another part disjoint from the first. In combination with transitivity, this entails the asymmetry and irreflexivity of <. Irreflexivity x 6< x Asymmetry x < y ! y 6< x Bohn’s argument for premise (i) is as follows: [A]ssume universalism is true in all possible worlds and that some possible world w is junky. en universalism is true in w. Consider the plurality of everything there is in w, call it aa. By universal instantiation, 9y(aa compose y); by existential instantiation, aa compose U. Bydefinition[ofjunk],itistruein w that 8x9y(x < y). By universal instantiation, 9y(U < y). But U is composed of everything in w, and hence, by definition, everything in w is a part of it, including itself. But then nothing can have U as a proper part because if so, by [weak] supplementation, there would be something that shares no part with U,andhenceisnotapartof U, which contradicts that everything is a part of U. So, if some possible world is junky, then universalism is not necessarily true. Q.E.D. ([, p. , fn ]) Now, the principles use in the argument are admittedly fairly plausible; however, they are far from uncontroversial.³ In fact, as we will see below, there is a growing number of mereologists who accept unrestricted composition but reject at least one. If that weren’t reason enough to generalise the junk argument, it turns out that these ‘minimal’ principles are enough, when combined with unrestricted composition, to yield full classical extensional mereology. is includes perhaps the ³Indeed, Bohn regards these principles as analytic of parthood. I assume at least some mereological principles without existential import are analytically true, and in virtue of that are necessarily true too. […] Minimal Extensional Mereology is a minimum of mereological necessary truths. is system includes (among other things) the asymmetry and transitivity of proper parthood, as well as a weak supplementation principle. ([], ) I do not think weak supplementation is analytic, but I appreciate more needs to be said. See [XXXXX]. | . most controversial principle of all — extensionality which says that composite objects with the same proper parts are identical.⁴ e argument for this claim is due to Varzi []. Informally, imagine you had a counterexam- ple to extensionality; a statue s and its clay c, suppose, are distinct objects with the same proper parts. By asymmetry, s 6< c, and c 6< s.⁵ By unrestricted fusion, there must be a sum s + c (which is distinct from either s or c, since neither is part of the other). Now, s < s + c; however, there is no part of s + c that is disjoint from s,asanypartof c is also part of s by supposition. is violates weak supplementation. Hence, there can be no such counterexample to extensionality. ere are two ways to avoid Varzi’s argument; as a result, there are two main approaches to mereology without extensionality: the unsupplemented view, and the mutual parts view. Both of these approaches are compatible with unrestricted composition; indeed, many proponents of these views themselves accept it. Since each explicitly rejects one of Bohn’s assumptions, the junk argument begs the question against them. But it does so needlessly, or so I shall argue. Weak Supplementation & Junk e first main non-extensionalist option is the unsupplemented approach which drops the weak supplementation axiom above. e unsupplemented approach has access to a well-developed mereology that includes unrestricted fusion. Here is a candidate list of axioms, where ≤, ◦, and F are defined as above. Asymmetry x < y ! y 6< x Transitivity (x < y ^ y < z) ! x < z Unrestricted Composition 8xx9y F(y, xx). Fusions appearing in the unrestricted composition axiom are defined as follows.⁶ Fusion F(t, xx) iff xx ≤ t ^ 8y(xx ≤ y ! t ≤ y) Here, xx ≤ t means that each x that is among xx is part of t. On this view, proper parthood is still a strict partial order. e major change here is that weak supplementation is explicitly rejected. Some unsupplemented mereologists simply drop the ⁴See Varzi [] to get a flavour of the debate. ⁵For, suppose c < s. Asymmetry implies s 6< c. Hence, s and c are not a counterexample to extensionality. Mutatis mutandis for the supposition that s < c. ⁶is definition of fusion is weaker than the one used in Varzi’s argument. For current purposes, it seems prudent to use the weakest plausible form of the fusion axiom. | . axiom and leave it at that.⁷ Others (primarily Gilmore []) have suggested a replacement axiom to capture the intuition behind weak supplementation without risk of extensionality.⁸ But Bohn’s defence of premise (i) explicitly appeals to weak supplementation.