![Sample our Humanities journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5939/TOC-Subject-Sample-2021-Humanities.jpg"})
ABSTRACT
I present a new objection to Bundle Theory. The objection rests on the repeatability of universals, and targets every version of Bundle Theory that assumes that concrete particulars constituted by the same universals are numerically identical. The only way that bundle theorists can elude this objection is to admit the possibility of distinct bundles constituted by the same universals. If even this view is untenable, then Bundle Theory as such is hopeless. Finally, I show how the present inquiry reshapes the dialectical relationship between Bundle Theory and the principle of Identity of Indiscernibles.
Notes
1 In this article, I will not be concerned with so-called trope bundle theory—namely, the view that concrete particulars are bundles of tropes [Williams Citation1953; Campbell Citation1990].
2 One might contrast the concept of density with the stronger concept of saturation: a set of universals A is saturated iff (i) A is dense, and (ii) it is not possible that there is a concrete particular that instantiates all of the members of A and also instantiates universals that do not belong to A. According to this definition, every saturated set of universals is ipso facto dense. If one accepted that every dense set is also saturated, that would be sufficient to warrant that (5) follows from (4). However, I do not see any argument in favour of the necessary equivalence of density and saturation, so it is worth showing that (5) can be defended by other considerations, too.
3 There are weaker versions stating that, necessarily, two particulars are identical if they have exactly the same properties, including even relational properties. The version with which I am concerned here is stronger and much more controversial, since it states that sharing the same qualitative properties is sufficient for identity.
4 In contemporary literature, the locus classicus of this debate is Black's [Citation1952] discussion of the possibility of a world hosting only two indiscernible spheres, located at a certain distance from each other. A discussion of the possible defences of the Strong Identity of Indiscernibles from such alleged counter-examples is offered by Hawley [Citation2009].
5 O'Leary-Hawthorne [1995] argues that, since immanent universals can be multiply located, a whole bundle can be multiply located, too: a world like the one considered by Black [Citation1952] is a world where there is only one concrete particular that is multiply located, and thus it is located at a certain distance from itself. This strategy is also discussed by Hawley [Citation2009].
6 In a footnote, Rodriguez-Pereyra says that this theoretical possibility has been pointed out to him by Nick Jones [2017: 609].
7 A view along these lines has been defended by Losonsky [Citation1987], who explicitly rejects the project of analysing concrete particulars in terms of properties.
8 My worry with calling certain parts ‘logical’ is that it seems to suggest that they have some relevant relationship with logic conceived as theory of valid inference, which is not the case. Likewise, to call certain parts ‘spatial’, as contrasted with logical, suggests that the latter are not located in space, whereas at least according to the immanent view of universals the latter do have a spatial location. With this mind, my preference for Koslicki's terminology is motivated by its being less misleading than Paul's.
9 Williams [1953] famously conferred this title on tropes instead of on universals.
10 Arguably there are some objections that target every version of Bundle Theory, but in what follows I will be concerned only with those objections that specifically target Non-Extensional Bundle Theory.
11 The Extensionality Principle can be proved in every system of mereology that includes the principles of reflexivity, antisymmetry, and transitivity of parthood, together with the so-called Strong Supplementation Principle [Varzi Citation2016].
12 Schaffer talks about grounding instead of ontological dependence, but his terminology is misleading, since usually grounding is categorially restricted to facts.
13 To be more precise, this implication follows from the assumption that a bundle depends on all and only the universals by which it is constituted, which is logically stronger than the Principle of (Formal) Reduction. However, from a bundle-theoretic standpoint, that assumption seems innocuous.
14 Of course, Simons's view does not entail that tropes are ̒nothing over and above̓ the concrete particulars to which they belong, because, even if they depend on those concrete particulars, they are not mere sums of them. For analogous reasons, Schaffer's priority monism does not entail that each subcosmic object is nothing over and above the whole cosmos. With this in mind, here I am not concerned with Simons or Schaffer being committed to any reductionist view, but only with them maintaining that distinct entities can depend on the same entity or entities.
15 Rodriguez-Pereyra [2004] presents this theory as an alternative version of Bundle Theory. As I have observed in section 2, according to my semi-stipulative terminology this view does not qualify as a version of Bundle Theory at all, since it rejects what I take to be the defining assumption of Bundle Theory—namely, the claim that concrete particulars are bundles of universals. Needless to say, Rodriguez-Pereyra's theory is not committed to the Principle of Identity, so it is not targeted by the Repeatability Argument.
16 I thank David Oderberg, James Stazicker, Euan Metz, Jonathan Shaheen, audiences in Reading, Stockholm, and Edinburgh, and two anonymous AJP referees for their helpful comments.