Abstract
A modus tollens against zero-dimensional material objects is presented from the premises (i) that if there are zero-dimensional material objects then there are bare particulars, and (ii) that there are no bare particulars. The argument for the first premise proceeds by elimination. First, bare particular theory and bundle theory are motivated as the most appealing theories of property exemplification. It is then argued that the bundle theorist’s Ockhamism ought to lead her to reject spatiotemporally located zero-dimensional property instances. Finally, it is argued that since she must accept such instances if she accepts zero-dimensional material object bundles, she ought to avoid the latter. This leaves bare particular theory as the default view of zero-dimensional material objects. The argument for the second premise invokes the thesis that the exemplification of at least one sparse property is a prerequisite for the existence of any particular. It is argued from Humean considerations that bare particulars fail this prerequisite.
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Notes
An object is concrete just in case it bears spatiotemporal relations.
I have in mind the notion of sparseness advanced by Lewis (1983, 1986), according to which a property is sparse if it is needed in order to completely characterize the world without redundancy. Sparse properties “carve at the joints,” ground resemblance, and have a place in the minimal supervenience base.
An object is composed of gunk just in case all its parts have proper parts (Lewis 1991).
There are, of course, other debates in the metaphysics of properties, for example, the dispositional/categorical debate. However, my concern is with debates over what properties in general are, not with debates over sub-species of properties.
Reference to tropes as ‘abstract particulars’ (Campbell 1990) derives from the sense of ‘abstract’ that involves mentally separating one item from another, not the sense that opposes concreteness.
This is not to say that the realist must understand property instances as fundamental.
Some readers will be familiar with a further terminological distinction for bare particulars: the ‘thin’/‘thick’ distinction. I prefer to set this distinction aside because of its vast potential for confusion in the wake of the variety of ways that it has been employed by different theorists. I refer the curious reader to (Armstrong 1989), (Robinson 2009), and (Sider 2006) for a sampling of the variety.
See Rodriguez-Pereyra (2004).
Their proponents do not always make clear whether these theories reject objects full stop or only at the fundamental level. In the latter case, it is not always clear in what ways the theories in question differ from bundle theory. I mention these subtleties only to set them aside.
Among the theories left out are various alternative forms of nominalism. In defense of their omission, I refer the reader to the arguments against them in (Armstrong 1978). Also omitted are neo-Aristotelian views of substance ala Michael Loux (1998). While such views do not fit neatly into either the bundle or bare particular families, their idiosyncrasies do not render them immune to the arguments in this paper. The neo-Aristotelian who favors zero-dimensional material objects must still accept either bare particulars or concrete, zero-dimensional instances of universals.
Moreover, it is unclear to me whether Rodriguez-Pereyra’s resemblance nominalism is committed to bare particulars. The thought here is that, whatever the individuals are like that stand in the relevant primitive resemblance relations, it seems possible that at least one of them might have failed to stand in any non-trivial instance of resemblance. (The trivial instance that I have in mind is reflexive resemblance; but to whatever extent such a relation makes any sense in this case, it would amount to the property of being a bare particular.) But this is just to say that it is possible that one of them lacks any properties whatsoever, save for the trivial properties of being a particular, being an object, being self-identical, etc. If Rodriguez-Pereyra’s view is indeed committed to bare particulars, then it is not in tension with 1.1.
It might be suggested that circumvention of commitment to an implausible version of the principle of the identity of indiscernibles (PII) provides independent motivation for bare particulars. (Thank you to an anonymous referee for making this point.) There is a vast literature on PII and bundle theory that begins with Max Black’s example of indiscernible spheres (1952) and remains active today. Importantly, however, this literature is concerned only with immanent universal bundle theories, for trope bundle theories are not plausibly committed to PII. The circumvention of PII is thus not compelling motivation for bare particulars generally. At most, it motivates bare particulars for those who are committed to immanent universals. Moreover, the aforementioned literature has not produced any decisive arguments to show even that immanent universal bundle theorists are committed to PII, though the issue is of course controversial. What matters for present purposes is that the controversy does not bear on 2.1 or 2.2.
Notice that the requirement that an item be like something does not entail that the item resembles any distinct item. It may be utterly unique and yet still be like something.
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Acknowledgments
I would like to thank audiences at the 2009 Pacific APA meeting and the 2009 UMass Metaphysics Conference for feedback on an earlier version of this paper. My respective commentators at those events, Raul Saucedo and Sam Cowling, were particularly helpful. Many thanks also to Jim Binkoski, Einar Bohn, Mark Crimmins, John Perry, Jonathan Schaffer, Alex Skiles, and an anonymous referee.
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Giberman, D. Against zero-dimensional material objects (and other bare particulars). Philos Stud 160, 305–321 (2012). https://doi.org/10.1007/s11098-011-9720-7
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DOI: https://doi.org/10.1007/s11098-011-9720-7