Abstract
Is part of a perfectly natural, or fundamental, relation? Philosophers have been hesitant to take a stand on this issue. One reason for this hesitancy is the worry that, if parthood is perfectly natural, then the perfectly natural properties and relations are not suitably “independent” of one another. (Roughly, the perfectly natural properties are not suitably independent if there are necessary connections among them.) In this paper, I argue that parthood is a perfectly natural relation. In so doing, I argue that this “independence” worry is unfounded. I conclude by noting some consequences of the naturalness of parthood.
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15 June 2017
An erratum to this article has been published.
Notes
Lewis (1983).
Parthood plays a key role within Lewis’s metaphysical framework. As Bennett (2015) notes, mereology “is central to [Lewis’s] thought, appearing in his discussions of set theory, modality, vagueness, structural universals, and elsewhere.” Note that Lewis takes the part of relation to be “perfectly understood” and not in need of any further analysis (1991, p. 75). Given that the properties that are not perfectly natural “are connected to the most elite [the perfectly natural properties] by chains of definability” ([1984] 1999, p. 66), this suggests that Lewis would take part of to be perfectly natural.
“It seems a little strange to discuss naturalness of relations in a general way when we have only one really clear example: the spatiotemporal relations.” (Lewis 1986a, p. 67).
“Whether [parthood and identity] should count as perfectly natural is a vexed issue: they don’t fit so well with Independence, but do fit quite well with many of the other roles.” (Dorr and Hawthorne 2013, p. 19).
Another reason sometimes noted is that the perfectly natural properties and relations should be the ones mentioned by an ideal physics, and part of does not seem to be the sort of relation that would figure in such a theory. (Thanks to Dan Greco and Ted Sider for pushing this line of thought). While this paper is not primarily concerned with this line of argument against the naturalness of parthood, it is worth addressing briefly. First, even if the our actual physics included no mention of the parthood relation, the set of perfectly natural properties is not determined solely by the ones instantiated at the actual world—if part of plays a role in the physics of some world, and so is perfectly natural at some world, then it is perfectly natural at all worlds at which it is instantiated. Second, I think it is plausible that parthood does figure importantly in our physical theories. Consider, for example, the additivity of mass; given Newtonian physics, an object with two proper parts, one with 2 g mass and one with 3 g mass, has a mass of 5 g. But in relativistic physics, (rest) mass isn’t additive in this way (Okun 1989, 2009). (For example, consider a particle composed of two smaller particles, orbiting each other. The rest mass of this particle is greater than the sum of the rest masses of the smaller particles, because of the additional contributions of their kinetic and potential energy.) So the way in which the mass of the parts of an object relate to the mass of the whole is not a straightforward matter, and there are worlds (like the actual world) where the mass of an object is not the sum of the masses of the object’s parts. And so it seems plausible that parthood is, in fact, a relation that may be crucially invoked in an ideal physical theory. Another example comes from Hartry Field’s (1980) project of nominalizing physics. In reformulating physical theories to avoid quantification over abstract entities like numbers, Field crucially invokes the logic of mereology. So if Field’s approach is on the right track, then the parthood relation plays a key role in physics.
In this paper I focus on the relation part of, though one may substitute one’s preferred mereological primitive instead (e.g., proper part of, overlap, etc.). The main thrust is that some mereological relation must be perfectly natural. See also Parsons (2014).
Suppose one wants to make a distinction between the ideology of a theory and the ontological commitments of that theory, such that the “parthood” predicate appears in the ideology of the theory but does not appear in its ontology (i.e., it does not appear in the scope of the theory’s unrestricted quantifier). In that case, does it even make sense to ask whether parthood is perfectly natural? Yes. First, we are assuming that properties are abundant. Take the set of ordered n-tuples that corresponds to the parthood predicate; given abundance, there is some relation corresponding to that set. So we can certainly ask whether this abundant relation is perfectly natural. Second, even if one is a nominalist about properties, one can still ask whether predicates are perfectly natural. (Perhaps the predicate “is massive” is perfectly natural, while the predicate “is happy” is not.) So for any property or predicate, one can coherently ask whether it is perfectly natural.
See Lewis (1983).
See Bennett and McLaughlin (2011).
Though one of the ways that Dorr and Hawthorne suggest we understand this requirement seems to assume that the qualitative need only intermediately globally supervene on the perfectly natural. See Dorr and Hawthorne (2013, p. 11).
One could reject this assumption without affecting my arguments (see also footnote 21). Here I am following Varzi (2014) in taking these three features as our starting point.
Ned Markosian formulates Brute (or “Brutal”) Composition as the thesis that “there is no true, non-trivial, and finitely long answer to the Special Composition Question.” (Markosian 1998, p. 214).
McDaniel (2006) argues that gunky objects may occupy non-gunky regions.
Dorr and Hawthorne call this “Non-Supervenience” (2013, p. 13).
Another understanding of independence that Dorr and Hawthorne consider is what they call “Combinatorialism,” taken from Lewis (2009), where he writes: “we can take apart the distinct elements of possibility and rearrange them… Here let us take them [the distinct elements] to include not only spatiotemporal parts, but also abstract parts—specifically, the fundamental properties” (2009, pp. 208–209). Dorr and Hawthorne take this to mean that “no perfectly natural property is entailed by any other.” (2013, p. 14)
The general idea is this: for any perfectly natural n-adic relation R, the instantiation of R by some objects does not place any constraints on what other perfectly natural relations those objects or any others may instantiate. And more generally, for any perfectly natural n-adic relations R 1, …, R n, whether R 1(x 1, …, x n), …, R n(y 1, …, y n) obtains does not place any constraints on what other perfectly natural relations anything may instantiate.
Combinatorialism is violated if part of is perfectly natural. This is because parthood is transitive: if a is a part of b and b is a part of c, then a is a part of c. And any necessarily transitive relation will conflict with Combinatorialism. Similarly any necessarily asymmetric relation will conflict with Combinatorialism—for if some relation R is asymmetric, then a bearing R to b means that b cannot also bear R to a. If the perfectly natural properties and relations satisfy Combinatorialism, then there are no perfectly natural relations that are either asymmetric or transitive.
I am not here arguing that Combinatorialism is thereby untenable. But it is worth pointing out that Combinatorialism is a very strong principle, and is inconsistent with many tacit assumptions regarding the perfectly natural. For consider the spatial distance relations—a paradigm case of perfectly natural relations. If some object a is three feet from b and b is three feet from c, then it is not possible for a to be just any distance from c, for the distances between them must satisfy the triangle inequality.
Moreover, all quantitative properties and relations are in tension with Combinatorialism. For if a is three feet from b, then a cannot be four feet from b. If c has three grams mass, then c cannot also have four grams mass. And so on. If Combinatorialism is true, then no quantitative properties and relations are perfectly natural. But quantitative properties and relations are often considered paradigmatic examples of the perfectly natural, for they are the sorts of properties and relations posited by our best fundamental physics. (And replacing monadic quantitative properties with relations like betweenness and congruence will not help, since these relations violate Combinatorialism as well.) So, even apart from the question of whether parthood is perfectly natural, it is not clear how to square Combinatorialism with the claim that the perfectly natural properties and relations comprise a (weak global) supervenience base for the qualitative. So I will set aside this understanding of independence.
Thanks to Cian Dorr for pointing out this particularly simple example.
This assumes, of course, that one grants that the Devils example is possible. But one might maintain that this example is not possible. For instance, one might say that any objects that instantiate parthood relations must also instantiate spatiotemporal relations (and, presumably, that the parthood relations supervene on the spatiotemporal relations). If so, then because the Devils do not instantiate any spatiotemporal relations, and this example is impossible. I pursue this line of thought in Sect. 7.
One response to this line of argument is to claim that mereological properties and relations, including properties like having a proper part instantiating cursedness, are not qualitative. If they are not qualitative, then they need not supervene on the perfectly natural, and Devil 1 and Devil 2 do not constitute a counterexample to the argument in Sect. 4.
The term “qualitative” is ambiguous, and there are a few different distinctions it might be used to name. Clearly there is some sense of qualitative where it is used to refer to “Humean” or “descriptive” properties like color and shape, and to exclude so-called “logical” or “structural” properties. And there is another sense of qualitative where it is used to mean something like “non-haecceitistic.”
Luckily, I do not need to take a definitive stance on which set of properties “qualitative” refers to. All I need is for the qualitative properties to be those that play (closely enough) the roles we need them to play. So, for instance, two things are duplicates when they’re alike with respect to their perfectly natural properties. Take Devil 1 and Devil 2—if parthood isn’t qualitative, then they’re duplicates. But clearly they’re not duplicates; they differ in an important way.
Here’s another case. The laws of nature are deterministic iff any worlds alike with respect to their laws and their histories up to a time t are alike after t as well (see Lewis 1983). So take two worlds, w 1 and w 2, with the same laws L and the same histories H up to t. At t, Devil 1 appears at w 1, and Devil 2 appears at w 2. Clearly these worlds diverge, as they differ after t. And since they diverge, it follows that the laws L are not deterministic. Or that’s what should follow. If parthood isn’t qualitative, then these worlds are exactly alike before and after t. And so the apparent divergence of w 1 and w 2 does not in fact show that the laws L are indeterministic, which is the wrong result.
In sum, the properties that supervene on the perfectly natural need to play, more or less, the roles expected of them. Given this, it seems that parthood is qualitative in the sense required. (Thanks to Sam Cowling and Phil Bricker for discussion).
There are a few reasons to be unhappy with Location. One obvious reason is that it rules out objects located outside of spacetime. As a result, it is incompatible with views according to which some objects are contingently nonconcrete or non-spatiotemporal (see Linsky and Zalta (1996) and Williamson (1998)). Second, it rules out the possibility of a point-sized object inhabiting a gunky spacetime. For a gunky spacetime does not have any point-sized regions—so it does not have any region that a point-sized object can exactly “fit into.” See Gilmore (2006, p. 203). (See also McDaniel (2006) for arguments that pointy objects may inhabit gunky regions).
There are a few reasons to be unhappy with Identity. One sort of view ruled out by Identity is a theory of immanent universals, according to which universals are located wherever they are instantiated. On such a view, multiple things (an object and a universal) are exactly located at the same region, which would conflict with Identity. Similarly, one might adopt a view according to which sets are located where their members are—for instance, my singleton set is exactly located at the region at which I am exactly located. On this view, again, multiple things are exactly located at the same region, which conflicts with Identity.
Conflict with Identity may also come from paradoxes of material constitution. Consider a statue made up of a lump of clay. The lump can survive squashing, the statue cannot; and so it seems the statue is not identical to the lump. Wiggins (1968) and Thomson (1998) propose views according to which the statue and the lump are not identical. Wiggins holds that the statue and the lump share all their parts; this requires rejecting Uniqueness of Composition, according to which objects with the same parts are identical. Thomson (1998) argues that the statue and the lump are parts of one another (Cotnoir (2010) and (2014) defends the “mutual parts” view and argues that it requires replacing the assumption that parthood is anti-symmetric with the assumption that it is asymmetric). But this entails that two objects are exactly located at the same spatiotemporal region—which is ruled out by Identity.
Another source of conflict comes from physics. For instance: consider two point-sized particles travelling towards each another. What will happen when these particles meet? On some views, it is nomologically possible for them to pass through one another. But then there would be a time at which they are exactly located at the same region, which is ruled out by Identity. Another instance: some have argued that, on some interpretations of quantum mechanics, qualitatively indiscernible particles like bosons can be co-located. This, too, conflicts with Identity. In general, one might be wary of metaphysical principles that rule out apparent nomological possibilities. (For discussion of all of these, see Gilmore 2013).
See Sider (2011, pp. 217–220).
Fine (2012, p. 60) suggests that existence cannot be reduced to identity or other related notions.
See Sider (2011, p. 216).
One position impacted by Minimality is the view that there are multiple fundamental mereological relations (see McDaniel (2004) and (2009)). If any of these mereological relations supervene on any others, then Minimality precludes such a view. But if we abandon Minimality, then the door is open to adopting this sort of parthood pluralism.
“I have conceded that Humean supervenience is a contingent, therefore an empirical, issue… [W]hat I uphold is not so much the truth of Humean supervenience as the tenability of it. If physics itself were to teach me that it is false, I wouldn’t grieve.” (Lewis 1986b, p. xi).
See, for example, Bricker (2016).
There are other reasons to be unhappy with the claim that the referent of “part of” is fixed by the mereological axioms (including possibly contentious ones like Unrestricted Composition). First, one might think it is implausible that this is the only kind of constraint on the meaning of “part of.” Second, when applied more widely claims of this sort may lead to the widespread semantic indeterminacy of Putnam’s Paradox (thanks here to an anonymous referee).
References
Bennett, K. (2015). Perfectly understood, unproblematic, and certain: Lewis on mereology. In B. Loewer & J. Schaffer (Eds.), A companion to David Lewis (pp. 250–261). Oxford: Blackwell.
Bennett, K., & McLaughlin, B. (2011). Supervenience. Stanford: Stanford Encyclopedia of Philosophy.
Bricker, P. (2016). Composition as a kind of identity. Inquiry, 59, 264–294.
Cotnoir, A. (2010). Anti-symmetry and non-extensional mereology. Philosophical Quarterly, 60, 396–405.
Dorr, C., & Hawthorne, J. (2013). Naturalness. In K. Bennett & D. Zimmerman (Eds.), Oxford studies in metaphysics (8th ed., pp. 3–77). Oxford: Oxford University Press.
Eddon, M. (2013). Fundamental properties of fundamental properties. In K. Bennett & D. Zimmerman (Eds.), Oxford studies in metaphysics (pp. 78–104). Oxford: Oxford University Press.
Field, H. (1980). Science without numbers. Princeton: Princeton University Press.
Fine, K. (2012). Guide to ground. In F. Correia & B. Schneider (Eds.), Metaphysical grounding (pp. 37–80). Cambridge: Cambridge University Press.
Gilmore, C. (2006). Where in the relativistic world are we? Philosophical Perspectives, 20, 199–236.
Gilmore, C. (2013). Mereology and location. Stanford: Stanford Encyclopedia of Philosophy.
Lewis, D. (1983). New work for a theory of universals. Australasian Journal of Philosophy 61, 343–377, (Reprinted in Lewis 1999: 8–55).
Lewis, D. (1984). Putnam’s paradox. Australasian Journal of Philosophy 62, 221–236, (Reprinted in Lewis 1999: 56–77).
Lewis, D. (1986a). On the plurality of worlds. Oxford: Blackwell.
Lewis, D. (1986b). Philosophical papers (Vol. 2). Oxford: Oxford University Press.
Lewis, D. (1999). Papers in metaphysics and epistemology. Cambridge: Cambridge University Press.
Lewis, D. (2009). Ramseyan humility. In D. Braddon-Mitchell & R. Nola (Eds.), Conceptual analysis and philosophical naturalism (pp. 203–222). Cambridge: MIT Press.
Linsky, B., & Zalta, E. (1996). In defense of the contingently nonconcrete. Philosophical Studies, 84, 283–294.
Markosian, N. (1998). Brutal composition. Philosophical Studies, 92, 211–249.
Markosian, N. (2014). A spatial approach to mereology. In S. Kleinschmidt (Ed.), Mereology and location (pp. 69–90). Oxford: Oxford University Press.
McDaniel, K. (2004). Modal realism with overlap. Australasian Journal of Philosophy, 82, 137–152.
McDaniel, K. (2006). Gunky objects in a simple world. Philo, 9, 39–46.
McDaniel, K. (2009). Structure-making. Australasian Journal of Philosophy, 87, 251–274.
Nolan, D. (2014). Balls and all. In S. Kleinschmidt (Ed.), Mereology and location (pp. 91–116). Oxford: Oxford University Press.
Okun, L. B. (1989). The concept of mass (mass, energy, relativity). Soviet Physics Uspekhi, 32, 629–638.
Okun, L. B. (2009). Mass versus relativistic and rest masses. American Journal of Physics, 77, 430–431.
Parsons, J. (2014). The many primitives of mereology. In S. Kleinschmidt (Ed.), Mereology and location (pp. 3–12). Oxford: Oxford University Press.
Saucedo, R. (2011). Parthood and location. In K. Bennett & D. Zimmerman (Eds.), Oxford studies in metaphysics (6th ed., pp. 225–286). Oxford: Oxford University Press.
Sider, T. (2011). Writing the book of the world. Oxford: Oxford University Press.
Thomson, J. J. (1998). The statue and the clay. Nous, 32, 149–174.
Uzquiano, G. (2011). Mereological harmony. In K. Bennett & D. Zimmerman (Eds.), Oxford studies in metaphysics (6th ed., pp. 199–224). Oxford: Oxford University Press.
Varzi, A. C. (2014). Appendix: Formal theories of parthood. In C. Calosi & P. Graziani (Eds.), Mereology and the sciences (pp. 359–370). Berlin: Springer.
Wiggins, D. (1968). On being in the same place at the same time. Philosophical Review, 77, 90–95.
Williamson, T. (1998). Bare possibilia. Erkenntnis, 48, 257–273.
Acknowledgements
Many thanks to Andrew Cortens, Sam Cowling, Louis DeRosset, Cian Dorr, Kit Fine, Elizabeth Harman, Paul Hovda, Kris McDaniel, Erica Shumener, Ted Sider, Brad Skow, Meghan Sullivan, Richard Woodward, and especially Chris Meacham for helpful comments and discussion. Thanks also to an anonymous referee for extremely generous and constructive comments.
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The original version of this article was revised: Under the section, “Perfect naturalness and supervenience,” in the third paragraph a typo was included along with Phi (
) and under the section “Background” in the last paragraph the R prime (R′) was erroneously published as R acute (Ŕ).
The reference, “Thomson, J. J…” was missed out. The correct symbols and reference are updated in the article.
An erratum to this article is available at https://doi.org/10.1007/s11098-017-0942-1.
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Eddon, M. Parthood and naturalness. Philos Stud 174, 3163–3180 (2017). https://doi.org/10.1007/s11098-016-0852-7
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DOI: https://doi.org/10.1007/s11098-016-0852-7