Abstract
In a series of publications, L. A. Paul has defended a version of the bundle theory according to which material objects are nothing but mereological sums of ‘their’ properties. This ‘mereological’ bundle theory improves in important ways on earlier bundle theories, but here I present a new argument against it. The argument is roughly this: (1) Material objects occupy space; (2) even if properties have spatial characteristics, they do not quite occupy space; (3) on no plausible construal of mereological composition does a mereological sum of non-space-occupying entities occupy space; therefore, (4) material objects are not mereological sums of properties.
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Notes
I use the term ‘entity’ not for concrete particulars but in the most generic way possible, to stand for the ontological summum genus.
There is another strand in trope theory that construes abstractness as a certain type of incompleteness—tropes are abstract because they are only fragments of being. However, as Donald Williams himself noted, strictly speaking this leads to the conclusion that ‘everything but the World All is abstract in this broad sense’ (1953, p. 14).
Typically, generics are produced with so-called bare plurals, as in ‘Dogs have four legs.’ The fact that some dogs are three-legged makes the universally quantified claim ‘All dogs are four-legged’ false, but depending on how many and which dogs are three-legged, the fact that some dogs are three-legged is consistent with the truth of the generic ‘Dogs are four-legged.’ What the correct semantics for generics is a lively area of debate in both linguistics and philosophy (see Leslie and Lerner 2016); we need not take a stand on it here.
Some attempts to address the insubstantiality worry may manage to address other aspects of what we expect substances to be like, but fail to recover this aspect of concreteness. Simons (1994), for instance, attempts to recover existential independence of substances within a trope-bundle framework. Even if Simons succeeded, however, this would not yet capture the aspect of space-occupation.
Consider for example the option of interpreting bundle theory as holding that objects turn out to be really just complex properties. (This is an odd way to interpret bundle theory, since there is no role for bundling in it at all, but let us bracket that issue.) If the thought is that reflection on the very notion of a material object instructs us that there is no object-property dichotomy because the notion of an object is really just the notion of a complex property, this is certainly false. The very subject-predicate structure of our language and thought indicate clearly a presumption of dichotomy. If the thought is instead that ontological investigation instructs us that the ultimate nature of objects is just the nature of complex properties, this would be more plausible but would run straight into the problem raised by the space-occupation argument: if a material object occupies space, whereas a complex property does not, it is unclear how they could share a nature.
More recently, Giberman (2014) has proposed an account of tropes that casts them as space-occupying entities. However, Giberman’s idea of a trope is highly heterodox, insofar as he understands tropes to be not abstract particulars but concrete particulars (2014, p. 455). This construal suggests that the kind of entity he has in mind is very different from the kind of entity most trope theorists have had in mind. I will return to the possibility of construing tropes as concrete particulars at the end of my discussion of Campbell.
Campbell himself does not seem to take a stand on this. Giberman (2014) appears to construe tropes along the (b) option.
This would make them concrete universals, as opposed to the abstract universals they are typically taken to be. Trope theorists also allowed for entities they called concrete universals, but they had in mind something quite different, properties such as being Socrates and being Quine.
In a different but somewhat related context, Cody Gilmore (2003) has proposed that apparent two-place spatial relations, such as ‘x is a mile from y,’ are in reality four-place relations, in this case ‘x in location Lx is a mile from y in location Ly.’ It is not clear how to apply this to ‘x is a mile from x’ (where this does not mean ‘a part of x is a mile from another part of x’). But even if we knew how to apply it, a bundle theorist could not make use of it unless, as noted in §1, she could identify locations independently of objects—which she may not wish to do.
This phenomenon sometimes inspires the kind of ‘ontic structural realism’ according to which the only entities that are real at the fundamental physical level are the relations between particles, such as the distance between the particle here and the particle there (Ladyman and Ross 2007). Sometimes the view goes as far as to deny that there are really particles which serve as relata, sometimes it states (more modestly) that the particles exist but only as junctures in a web of relations, hence as derivative rather than fundamental entities.
The attraction of superstring theory, it is worth noting, is mostly armchair-ish. The motivation for it has to do with a certain disunity in our fundamental understanding of the universe, namely, the fact that of four fundamental forces current physics posits, three are accounted for beautifully by quantum mechanics but the fourth (gravity) eludes quantum–mechanical explanation. Superstring theory offers an elegantly unified treatment of all four forces, but as noted it suffers from complete absence of empirical evidence.
Typically, the relevant notion of grounding is construed as primitive and unanalyzable, picking out a sui generis asymmetric non-causal determination relation between facts, in which the fundament is ontologically prior to the terminus (Fine 2001).
There are many debates about the nature of the relevant kind of explanation, as well as on its precise relationship to grounding. I bracket these debates here, hoping the point I want to make is neutral on them.
Alternatively, the very existence of material objects could be denied. This would of course be a much more radical view (though certainly one defended by some metaphysicians, e.g. Ladyman and Ross 2007), and not one in which sums of properties are used to account for material objects. This view is not subject to the space-occupation argument, since as noted my target is only views on which material objects can be assayed in terms of bundles of properties, not views on which there are no material objects.
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Acknowledgements
This work was supported by the French National Research Agency’s Grant ANR-17-EURE-0017, as well as by Grant 675415 of the European Union’s Horizon 2020 Research and Innovation program. For comments on an earlier draft, I am indebted to Jonathan Schaffer and three anonymous referees for Synthese. I have also benefited from presenting the paper at a June 2017 conference on composition at Collège de France; I am grateful to the audience there, in particular Alexandre Guay, Ghislain Guigon, Olivier Massin, and Achille Varzi. Finally, I benefited also from discussing some of the central ideas in my Spring 2017 ENS seminar on the metaphysics of properties; I am grateful to my students there, in particular Sophia Arbeiter, Nicolas Chargelegue, Géraldine Carranante, Lylian Paquet, Victor Tamburini, Samuel Zamour, and especially Michele Impagnatiello.
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Kriegel, U. The concreteness of objects: an argument against mereological bundle theory. Synthese 199, 5107–5124 (2021). https://doi.org/10.1007/s11229-020-03017-z
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DOI: https://doi.org/10.1007/s11229-020-03017-z