Abstract
The bundle theory is a theory about the internal constitution of individuals. It asserts that individuals are entirely composed of universals. Typically, bundle theorists augment their theory with a constitutional approach to individuation entailing the thesis ‘identity of constituents is a sufficient ground for numerical identity’ (CIT). But then the bundle theory runs afoul of Black’s duplication case—a world containing two indiscernible spheres. Here I propose and defend a new version of the bundle theory that denies ‘CIT’, and which instead conjoins it with a structural diversity thesis, according to which being separated by distance is a sufficient ground for numerical diversity. This version accommodates Black’s world as well as the three-spheres world—a world containing three indiscernible spheres, arranged as the vertices of an equilateral triangle. In this paper, I also criticize Rodriguez-Pereyra’s alternative attempt to defend the bundle theory against Black’s case and the case of the three-spheres world.
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Notes
Hector-Neri Castaneda makes a similar distinction (1975, pp. 131–133). He distinguishes what he calls the “ontological issue” about the internal constitution of an individual substance from what he calls the “epistemological issue” about how individuals are individuated. In Castaneda’s view, the individuation problem is clearly epistemological in character and is not discussed at length in that work. In this paper, I take both of these issues to be ontological in character.
As it stands, the sufficiency thesis for numerical identity, viz., that if x and y are at no distance from one another then they are numerically identical, is open to some criticisms. One criticism is that the possibility of coinciding objects must be rule out. Following Locke, a metaphysician may wish to allow the diversity of a piece of bronze and the statue made out of it. But the bundle theory coupled with this sufficiency thesis for numerical identity cannot allow this possibility. Of course, this Lockean metaphysics may well be false; therefore there cannot be coinciding objects. But this should be decided independently of whether one subscribes to the bundle theory or not. An anonymous referee of this journal suggests a more significant criticism. In Special Theory of Relativity, the notion of our usual spatial distance is replaced by the notion of a relativistic spatio-temporal ‘interval’. Now the spatio-temporal interval of any two ‘bundles’ lying on a given light ray is zero. But then the bundle theory coupled with the sufficiency thesis for numerical identity cannot diversify between these two.
I am indebted to an anonymous referee of this journal for this point.
I am grateful to an anonymous referee of this journal for helping me see that the bundle theory’s irreducibly polyadic distance relations must be of finite adicity. Consider again the notion of a relativistic spatio-temporal interval. On the path of a given light ray there are infinitely many ‘bundles’, for any pair of which spatio-temporal interval is zero. This will force us to postulate infinitary distance relations and to understand them as primitives. Not only that but even relations as such cannot distinguish two possible cases: (i) a case where, relative to some choice of coordinates, on a given light ray with the t coordinate, there are integers-many ‘bundles’; and (ii) a case where, relative to the same choice of coordinates, on the same light ray with the t coordinate, there are even-integers-many ‘bundles’.
See also Russell (1911).
Following Hawthorne and Sider (2002) I construe the multigrade compresence as a relation of finite adicity. This seems to be a safe bet as long as the number of natural properties (corresponding to universals) is limited in number.
I am especially grateful here to an anonymous referee of this journal for helping me to clarify this point. As he notes, construing the bundle theorists’ compresence relation in a way that is similar to thisnesses certainly goes against the spirit of the bundle theory.
It may be helpful to note that the two roles attributed to thisnesses are foreshadowed by a distinction, drawn earlier in this paper, between two questions concerning the nature of individual substances: (i) the question concerning internal structure of substances and (ii) the question concerning their numerical diversity.
Vallicella (2000) produces a similar response to the Bradleyan regress. Rather than saying that ‘instantiation’ relation is part of the ideology of the substance-attribute theory, he says that ‘instantiation’, tying a particular with its properties, is an operation that the mind imposes on the world.
I am indebted to Douglas Ehring for this point.
See footnote 11.
In his “Do Relations Individuate?”, Meiland (1966, pp. 65–66) makes a similar point.
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Acknowledgments
I am grateful to Stephen Voss, Barry Stocker, Fiona Tomkinson, Lucas Thorpe, Tonguc Rador, an anonymous reviewer of this journal, and especially John Heil and Berna Kilinc for helpful comments and suggestions on earlier drafts of this paper.
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Demirli, S. Indiscernibility and bundles in a structure. Philos Stud 151, 1–18 (2010). https://doi.org/10.1007/s11098-009-9420-8
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DOI: https://doi.org/10.1007/s11098-009-9420-8