Abstract
The statue and the lump of clay that constitutes it fail to share all of their kind and modal properties. Therefore, by Leibniz’s Law, the statue is not the lump. Question: What grounds the kind and modal differences between the statue and the lump? In virtue of what is it that the lump of clay, but not the statue, can survive being smashed? This is the grounding problem. Now a number of solutions to the grounding problem require that we substantially revise our view of reality. In this paper, I provide a solution to this problem that does not require such a revision. I then show how my solution to the grounding problem can solve a related problem and answer a related question. The upshot is that the solution I offer is not only non-revisionary, but also fruitful.
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Notes
Fine (2003) has developed a number of new Leibniz's Law arguments in favor of thinking that the statue is not the lump that do not rely on the traditional kind and modal differences. Call the kind of differences Fine relies on 'Finean-differences'. In Sect. 2.5, I show why my solution to the traditional differences between the statue and the lump is also a solution to these Finean-differences.
Some no-thingers are van Inwagen (1990), Merricks (2001), and Rosen and Dorr (2002). Some one-thingers are Lewis (1986), Burke (1994), Gallois (1998), Rea (2000), Sider (2001), and Wasserman (2002). (Wasserman's case is unique in that he claims that the statue and the lump are identical if they temporally coincide, and not identical if they don't. Wasserman is what Fine (2003) calls a moderate monist.)
Bennett tries to show why it is not so bizarre by appealing to a principle of plenitude: for any region of space that is occupied by an object, there is an object for each possible combination of modal properties. And, or so the thought goes, “because each region is full in this way, there is nothing in virtue of which any particular object has the modal properties it does” (2004, p. 355). So, according to Bennett, the apparent bizarreness is just that, apparent. Here is a worry. That modal properties are not brute is perfectly compatible with Bennett's principle of plenitude. For suppose that her principle is true, that a and b are coincident, that a has modal profile M1 and b modal profile M2, and that M1 and M2 exhaust the possible combinations of modal properties in the region of space that a and b occupy. All this is consistent with a having M1 in virtue of N1 (where N1 is a non-modal profile of a), and b having M2 in virtue of N2 (where N2 is a non-modal profile of b). So that modal properties are not brute is perfectly compatible with Bennett's principle of plenitude. But then in what way does this principle make the bruteness of modal properties palatable? Given that Bennett's principle is consistent with non-brute modal properties, whether or not a modal property is had brutely does not depend on the number of instantiated combinations of modal properties. But then why should Bennett's principle make the brute-modal-property pill easier to swallow?.
This claim is surely plausible if we restrict it to kind properties. After all, I belong to the kind Human in virtue of my parts being arranged such that DNA materials, a heart, lungs, a nervous system, etc. are all parts of me. Therefore, the fact that I am human is not a brute fact about me.
There are solutions that, though I find them implausible, are not revisionary. For example, deRosset (2011) appeals to the identity of the statue and the lump in order to ground their different kind and modal properties, and such an appeal is not revisionary. However, I cannot accept it. For even if the identity of the statue does ground its kind and modal properties, it would seem that something grounds its identity. For the identities of dependent objects (which statues and lumps are) depend on the identities of what they depend on. But now we have a grounding problem concerning the difference in identities between the statue and the lump.
Baker (1995, 1997) has also provided a multi-thinger solution to the grounding problem by appealing to the surroundings of the statue and the lump. I do not think that this solution is revisionary. I do, however, find it unsatisfactory. For my reasons why, see Olson (2001, pp. 346–348).
Here then is the procedure you should employ when you want to translate predicate talk, where at least one of the names that flank the predicate refers to an individual, to operator talk. First translate such predicate talk to factualist talk, where the names flanking the predicate refer to facts. Then translate factualist talk to operator talk.
Given the popularity of factualism, it is worth stating these principles in factualist friendly language:
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Necessitation fact . If the facts Γ ground the fact that p, then necessarily, if all the facts in Γ exist (or obtain), then the fact that p exists (or obtains).
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Link fact . If the facts Γ ground the fact that y exists, then facts about the facts in Γ ground facts about y.
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Skiles's (forthcoming) interesting paper bears directly on this paper. For Skiles uses, as one of his examples where Necessitation fails, cases involving parts and wholes. One of those cases (though not the case Skiles standardly uses, which involves a Theseus-style scenario) involves a recycling scenario (McKay 1986). Skiles says
Suppose that in an earlier epoch the existence of o [a sandwich] is grounded in Γ. Afterward, o rots and as a result permanently ceases to exist as the as [the parts of o] scatter throughout the environment. But millennia afterward in a later epoch, the as come back into the arrangement they were once in during the earlier epoch, composing a new sandwich distinct from the original. Here again, it seems plausible to say that even though all the facts in Γ obtain during this later epoch, [o exists] does not.
Consider though my moving across town in my car. And suppose that, in order to properly fit everything in my car, I have to disassemble my bike. So my bike ceases to exist during the move, its parts not arranged in the right manner to compose it. After my drive across town, I put the parts of the past bike together again exactly as they were before. Do I now have a brand new bike? It would seem not. The bike I now have before me is the very bike I had prior to the disassembly. Or at least, this is quite reasonable. But then why should we think that even though all the facts in Γ obtain during this later epoch, [o exists] does not? The cases are exactly analogous, minus one case taking place over years and the other over, at most, hours. But why is this at all relevant?
This is, of course, to simplify matters a bit. For notice that what A, B, and C are is important. Suppose that A, B, and C are each dry bits of dirt. Then their being in contact with one another would not seem to ground their composing a lump. This is not so if A, B, and C are bits of clay.
I say ‘roughly' since Pyra could survive A (B) moving slightly to the side in such a way that A's (B's) wider base is no longer in full contact with B's (C's) narrow base.
For someone who thinks that, ultimately speaking, wholes do not exist in virtue of how their parts are arranged, see Schaffer (2010).
I am using ‘[p]' to stand for ‘the fact that p'.
Some may be inclined to think that statues are essentially artifacts, and so we should include among the grounds of Pyra being-made-by-such-and-such. But I argue in Sect. 4.2 that artifacts are not essentially artifacts, and so statues are not essentially artifacts.
Though my project is not to show how these different grounds explain the kind and modal properties of the objects they ground, it would be nice if I could. Here then is a try: Focusing on their modal properties, Lumpy can survive Pyra being smashed because were Pyra smashed, Lumpy's grounds, [A is in contact with B], [B is in contact with C], would still exist. But then, given Necessitation, Lumpy would still exist. And Pyra cannot survive being smashed because were Pyra smashed, then nothing resembling what Pyra's grounds are—[A is in kontact with B] and [B is in kontact with C]—would exist. At best we would be left with a partial, and not a full, ground of Pyra. And if Pyra is not fully grounded, then Pyra does not exist.
In addition to [A is in contact with B] and [B is in contact with C], we need the differentia in order to fully ground [A is in kontact with B] and [B is in kontact with C].
Very similar reasoning shows why it is not mysterious that Pyra and Sumy have different kind and modal properties.
I would like to thank both Kathrin Koslicki and Alexander Skiles for raising this objection.
Of course, in referring to their grounds I used the word 'grounds'. But this no more commits me to referring to G-Properties than referring to someone by means of the phrase 'the wife of' commits me to referring to W-Properties, where something is a W-Property just in case it is the property being-the-wife-of-so-and-so. In both of these cases, I am using a property, not mentioning it.
Thanks to an anonymous referee for raising this worry.
I would like to thank an anonymous referee for suggesting that I appeal to a sparse theory of relations here.
An anonymous referee voiced the following worry. If Brutalism is true, and so if there is nothing in virtue of which the xs compose something, then how is it that how the xs are arranged ground the whole they do? As the referee made clear, what we have here are two questions. They are
In virtue of what is it the case that the xs compose something?
In virtue of what is it the case that some composite object (a pyramid) exists?
These questions are surely distinct. One is asking for the ground of a relational fact—the fact that the xs compose something. The other the ground of a composite object. And it is coherent to think that an answer to one of these questions will not influence an answer to the second. For example, suppose you think that, in some cases, wholes are prior to their parts and that, in other cases, parts are prior to their wholes. So you must think that neither composition nor decomposition determine the direction of grounding (Schaffer 2009 seems to hold this view). But then your answer to the first question above can come wildly apart from your answer to the second. According to this view, composition and grounding are two very different relations.
Or, to take the other extreme, suppose you think that composition determines the direction of grounding because you think that composition is itself a kind of grounding relation (Wilson and Jessica 2014; Bennett manuscript). Still, it is coherent to think that facts about grounding (and therefore facts about composition if composition is a kind of grounding) are brute even though it trivially follows from all this that composite objects are grounded (since composition is itself a kind of grounding relation). In short, it is coherent to think that answers to the first question above can come apart from answers to the second. But then one can, in principle, accept brutal composition and still think that composite objects are grounded in how their parts are arranged (in fact, this is exactly what Paul (forthcoming) thinks, though for her the parts of such objects are properties).
It is worth noting that someone who accepts a liberal answer to the Special Composition Question will, in all likelihood, have no problems with a revisionary metaphysic since such a position already commits one to metaphysically revisionary claims.
This is no mark against Rea. He was using the tools of the day, supervenience, whereas I am using the tools of today, grounding.
Rea himself told me, in conversation, that when his 1997 solution was discussed with other philosophers at the time, a number expressed, in discussion, skepticism over the claim that there are these humanwise and lumpwise arrangements of microparticles that Socrates and the lump, respectively, supervene on.
Indeed, even though I did not use a human and a lump of tissue in order to illustrate the grounding problem, I have, by going into some detail on what exactly grounds Pyra, Lumpy, and Sumy, shown that there is no in principle problem for cases that involve a human and a lump of tissue coinciding. A solution of the same kind (albeit one that is much more complex) can be given for a human and a lump of tissue that was given for Pyra, Lumpy, and Sumy.
For an overview of problems and questions related to the grounding problem, see Paul (2010).
Unsurprisingly, we also have a straightforward explanation for why Pyra and Lumpy are co-located. For what grounds Pyra and what grounds Lumpy are co-located. And given the following principle,
If material objects x and y are grounded in facts that are co-located, then x and y are co-located,
it follows that Pyra and Lumpy are co-located.
Priority monists (Schaffer 2010) will most likely reject it since they think that everything that is grounded is grounded in the cosmos. But of course, this does not entail that this principle is implausible.
Mereological sums are the only kinds of wholes that Uniqueness is true of (Johnston 2006, pp. 688–689). Why? Because mereological sums are grounded in their parts. And so for any two mereological sums, x and y, if x and y have all the same proper parts, and therefore all the same grounds, then, given G-Uniqueness, x = y.
This answer is similar to an answer Doepke (1996) gives.
Given that, if God exists, then God necessarily exists, it follows that with respect to the actual world, World 3 is impossible. That's fine. When talking about necessary matters, we can, and do, reason about the impossible.
See Rea (1998, pp. 353–354) for a different reason to think that artifacts are not essentially artifacts.
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Acknowledgments
I would like to thank the audience at the 2012 Jentzsch Prize Winner Colloquium in Boulder Colorado, especially Kelly Vincent and Michael Huemer. I would also like to thank the University of Notre Dame's Center for Philosophy of Religion, where I was on fellowship for the 2012/2013 academic year, for providing me with the time and resources to complete this paper. This paper has benefited greatly thanks to comments from, and discussions with, Graeme Forbes, Kathrin Koslicki, Graham Oddie, and Alexander Skiles. Special thanks go to Michael Rea for a very helpful, and encouraging, discussion on his 1997 solution and this paper's solution, and to an anonymous referee for this journal. This referee read my paper carefully, understood it, and provided two sets of detailed comments that greatly improved it. Whoever you are, thank you. Finally, as I forever will, I would like to thank my wife, Amy Greenip, for her always present support and encouragement in my work.
