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The aim of philosophy, abstractly formulated, is to understand how things in the broadest possible sense of the term hang together in the broadest possible sense of the term.

Wilfrid Sellars (1962).


A variety of relations widely invoked by philosophers—composition, constitution, realization, micro-basing, emergence, and many others—are species of what I call ‘building relations’. I argue that they are conceptually intertwined, articulate what it takes for a relation to count as a building relation, and argue that—contra appearances—it is an open possibility that these relations are all determinates of a common determinable, or even that there is really only one building relation.

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  1. Note the scare quotes. This is only a metaphor; the issue does not literally have anything to do with size!

  2. Though see Baxter (1988a, b), van Inwagen (1994), and Sider (2007) for exploration of the rather radical claim that composition is actually identity.

  3. This explains the dispute between Gillett (2002, 2003) on the one hand, and Polger (2007) and Polger and Shapiro (2008) on the other hand. I think Polger and Shapiro are wrong to be so dismissive of the idea that Gillett is simply talking about something else, but probably right to think that the notion that is one–one and ‘flat’ is the notion tightly linked to functionalism, and worthy of the label ‘realization’.

  4. Polger and Shapiro (2008) have recently taken Gillett (2003, 2004) to task for claiming that property instances, rather than properties themselves, are the relata of the realization relation. (It is worth noting that Melnyk (2003, 2006) also takes property instances to be the relata of the realization relation.) Polger and Shapiro’s argument is not convincing. They claim, as a reductio, that taking property instances to be the relata renders multiple realization impossible. However, their argument rests upon the premise that realization and multiple realization involve the same entities—that the multiply realized entity must itself be realized. I take this assumption to be much less obvious than Polger and Shapiro do. I see nothing wrong defining multiple realization as follows (assuming we have an antecedent definition of realization in hand): property P is multiply realized by properties Q, R, and S just in case some of P’s instances are realized by instances of Q, some by instances of R, and some by instances of S. (For Gillett’s own response, see forthcoming).

  5. I suppose it might matter for other purposes; Polger (2007) and Polger and Shapiro (2008) think it does.

  6. Kim calls the resulting properties “micro-based” or “microstructural” properties.

  7. Both Kim (1997, p. 291) and O’Connor and Wong (2005, p. 663) explicitly take their notions to derive from the one Armstrong uses to construct structural universals (1978, pp. 69–71; also 1986). However, Kim and O’Connor and Wong clearly take composition to be involved, and Armstrong does not: he thinks that he needs a notion of “nonmereological composition”. If so, the relation Armstrong himself appeals to would appear elsewhere, on the list of further candidate building relations I offer in a few pages.

  8. Kim is quite right to point out a difference between “levels” and “orders”, and to distinguish the way a first-order property realizes a second-order (functional) one from microbased realization (1997, 1998). However, he is probably wrong on two counts, though neither of them matter much for the purposes at hand. First, he is definitely wrong—even by his own lights (1988)—to say that the concept of supervenience requires that the supervenient properties must be instantiated by the same entity as the subvening ones, and thus entails that the microbased properties of an entity do not supervene on the properties of its parts (1997, pp. 290–291; 1998, pp. 85–86; 2005, p. 57). (See Bontly (2002) for more detailed discussion.) Second, I suspect (though am not sure) that he is wrong to think that the distinction prevents the exclusion problem from generalizing (1997, 1998, 2005).

  9. Van Gulick calls it “radical kind emergence” (2001, p. 17).

  10. Why is grounding a mere entry on the list, rather than the overarching relation under discussion in this paper? Well, the first point to note is that the term ‘grounding’ is occasionally used in a quite generic sense, and on that use it is perhaps synonymous with my term ‘building’. But the second point to note is that when the label is introduced in a more specific way, it is too specific to be what I have in mind by ‘building’. Grounding is widely taken to be hyperintensional—it can hold asymmetrically between relata both of which necessitate each other. Not all building relations need be like that. It is also often (not always) taken to hold only between propositions or states of affairs. Again, not all building relations are like that.

  11. In characterizing Armstrong’s idea, McDaniel (2009b) even uses the same ‘building’ metaphor that I do: “structure-making is allegedly a kind of composition relation that ‘builds’ states of affairs out of particulars and universals and structural universals out of simpler universals” (p. 251).

  12. The problem is that supervenience—in, I believe, all of its extant forms—is reflexive and can hold symmetrically. Building relations must be irreflexive and asymmetric; see Sect. 6, especially note 24. Still, though, perhaps we can say that supervenience can hold in a building way—that instances of the supervenience relation that hold asymmetrically between distinct relata do qualify as instances of building. See also Kit Fine’s discussion of generative operations versus generative applications of operations (unpublished).

  13. For the idea that composition never occurs—or at least occurs more rarely than one might have thought—see Van Inwagen (1990), Merricks (2001), Rosen and Dorr (2002).

  14. Compare Goldman (1970) on the level-generation of actions, though he tends to use a ‘by’ locution—I ask to be called on by raising my hand—rather than the language of constitution.

  15. Metaphysicians disagree about whether that is the same notion of ‘part’, and about whether there is only one composition relation. See, for example, van Inwagen (1990, p. 19) and Varzi (2006). See also Winston et al. (1987).

  16. On my usage, a relation is many-one just in case it is a two-place relation that takes a plural argument in the first argument place and a singular argument in the second argument place. (Or, I suppose, it could be a multigrade relation with at least three argument places, the last of which is somehow privileged.) There is another use of the term ‘many-one’ (and mutatis mutandis for ‘one–one’, ‘one–many’, and ‘many–many’). On this alternate use, a two-place relation R is many-one just in case for all a and b such that aRb, things other than a bear R to b, but a bears R to nothing but b.

    • ∀x∀y {[xRy → [(∃z1z1Ry& z1 ≠ x) & (∀z2 z2Ry x = z2)]}

    van Inwagen (1994, 207n2) complains about Lewis’ usage in Parts of Classes (1991), which suggests that Lewis may have been one of the first to use the term in the way I have in mind.

  17. It might be claimed that another important difference is that some of the relations can be captured by means of ‘makes it the case’ locutions, and others cannot. For example, such locutions sound much better in cases of microbased determination than cases of composition; ‘a’s being F and b’s being G make it the case that c is H’ is fine, while ‘a and b make it the case that c’ is not even grammatical. But this is just a shadow cast by the difference in relata. Only propositions or states of affairs can be “made the case.”

  18. A live question here is whether any building relations are absolutely fundamental, in the sense that they are not themselves in any way built. (That is one notion of absolute fundamentality that is live in the literature; another is perfect naturalness. See my MS b.) I am currently inclined to think that the answer is ‘no’. For one reason, see Schaffer’s recombinability argument (forthcoming). For another reason, see Sider’s appeal to a principle he calls Purity (MS). For yet another reason, note that nominalists do not think that any relations or properties are truly fundamental. Now, it’s clear that if I claim that all building relations are in some way built, I owe a response to the Bradley-style regress that appears to ensue. I will not do so here. I have brought the issue up for one and only one reason: it affects the definitions of building relation monism and pluralism. In the main text, I have characterized them in terms of relative fundamentality only, so that the question remains live even if no building relations are absolutely fundamental.

  19. This is clear in the definitions and citations I provided in Sect. 2 above. It is also worth mentioning that part of the reason that Polger (2007) and Polger and Shapiro (2008) do not want to take Gillett’s notion of ‘dimensioned realization’—basically what I call microbased determination—to be an account of realization is simply that “the dimensioned view draws realization too near to material composition…. Gillett’s view is that when the carbon atoms compose the diamond, the properties of the carbon atoms realize the properties of the diamond. For Gillett, realization and composition go hand in hand” (Polger 2007, p. 248).

  20. It is tempting to suggest that building relation nihilism entails that everything is fundamental—that there are no derivative entities—but that is not quite right. It will emerge later that although all building relations are relations of relative fundamentality, not all relations of relative fundamentality are building relations. So in principle there could be relations of relative fundamentality even in a world in which nothing is ‘built’. Nonetheless, this point is small, and one is not led too far astray by thinking of the building relation nihilist as claiming that the world is flat: no entities are more fundamental than any others.

  21. L. A. Paul sometimes seems inclined to say this, but she assures me that it is not overzealous, merely zealous to exactly the right degree.

  22. I intend to be fairly neutral here, largely because I do not think we yet have an adequate grasp what might be called “version of” relations. There seem to be plenty of cases where x is in some sense a kind of or version of y, but is neither a determinate of y nor a species of y in the traditional senses (see Sanford (2006) and Funkhouser (2006) for overviews). So it is not clear that the determinate-determinable relation and the traditional species-genus relation are the only options here. Of the two, however, the determinate-determinable relation is a prima facie better candidate than the species-genus relation for characterizing building relation monism. There is no differentia that can be added to the generic R to yield familiar building relations like composition or grounding.

    Yet note that if building relation monism is characterized in terms of the determinate-determinable relation—i.e. if the more specific building relations are taken to be determinates in the traditional sense of the one most fundamental building relation—then it must also be claimed that determinates are not always more fundamental than the determinables under which they fall. This strikes me as correct, even though the opposite is frequently assumed to be the case. Having mass, for example, is presumably a more fundamental property than having mass 2.187 grams. See Wilson MS for more discussion, and thanks to both Erica Shumener and Jeff Engelhardt for pointing this out to me.

  23. Compare the fact that those who want to say that there is more than one fundamental composition relation need to shoulder the burden of saying why they all count as forms of composition (see McDaniel 2004, 2009; Hawley 2006).

  24. To say that building relations permit ‘in virtue of’ locutions is not to make the too-simple claim that a bears some building relation R to b just in case b in virtue of a. That depends upon the particular building relation, and thus also on the nature of a and b. If the relata are facts, then aRb might well yield the truth of ‘b in virtue of a’. But in other cases, the correct ‘in virtue of’ sentence will vary: ‘b exists in virtue of a’ or ‘the fact that b holds in virtue of the fact that a’, and so forth. See also note 17.

  25. There is a real question, I think, about how best to treat relations that can hold either symmetrically or asymmetrically, as well as relations that are reflexive, but can also hold between distinct relata (i.e., any reflexive relation other than identity). Consider two salient examples: supervenience in all its guises (see McLaughlin and Bennett 2005, especially §3.2 and 3.5), and Sydney Shoemaker’s definition of property realization. A simple version of that definition states that property Q realizes property P just in case P’s forward-looking causal powers are a subset of Q’s, and Q’s backward-looking causal powers are a subset of P’s (2007, p. 12; subsequent refinements of the definition do not affect the claim at hand). Because this is in terms of subsets, not proper subsets, each property realizes itself.

    Both supervenience and Shoemaker-realization, then, are reflexive non-identity relations that can hold either symmetrically or non-symmetrically. Shall we therefore say that neither is a building relation at all? Or shall we say that some of their instances—the ones that hold asymmetrically, between distinct relata—are instances of building, and some are not? I am inclined towards the latter, but I will often talk the former way for simplicity.

  26. Although building relations have inverses that are also directed—decomposition, for example—in such cases it is the output side that is more fundamental.

  27. Note that the claim of relative fundamentality is singular, not general. Suppose object c of kind K3 is composed of a and b, of kinds K1 and K2 respectively. Then c is less fundamental than a and b. But it needn’t follow that K3s are less fundamental than K1s or K2s.

  28. Thanks to David Braun and Earl Conee for pressing this objection.

  29. This is certainly a—if not the—central notion of fundamentality in the literature. (For one example, note how Schaffer defines fundamentality as ungroundedness in 2009, §3.1.) However, there are other notions run together with this in the literature, notably naturalness. See my MS b for more discussion.

  30. I do not mean to assume that causes always precede their effects—perhaps backwards causation is possible in cases of time travel (Lewis 1973, p. 566). But certainly, typical instances of the causal relation hold between earlier and later events. (The remarks in this note also apply to the suggestion in the main text that causation is irreflexive and asymmetric.)

  31. Thanks to Penelope Mackie for pressing this objection.

  32. Four-dimensionalists who believe that persisting objects are mereological sums—or built in some other, non-mereological way—of temporal parts need to believe in an atemporal building relation. That tempestuous teenager timeslice is part of me simpliciter, not at a particular time (see Sider 2001, pp. 55–60).

  33. See also Bedau’s sketch of why emergence is a “perennial philosophical puzzle” (1997, p. 375).

  34. ‘Chimera’ in its lesser-used sense; see OED entry 2 and 3c.

  35. It is actually left open that all of the different relational predicates refer to the single fundamental determinable relation that I explore in the following paragraphs.

  36. A more careful version of this argument would instead begin with the claim that there are lots of relational predicates that certainly appear to be able to take as arguments terms referring to a variety of sorts of things. The ‘is two feet from’ predicate can take as arguments terms referring to objects, events, and various other (spatially located) ontological categories. The following sentences are equally well-formed, at least ignoring the fact that we often don’t have tidy nouns for events:

    1. (1)

      the cat is two feet from the squirrel.

    2. (2)

      the boiling of the kettle is two feet from the whirring of the blender.

    This more careful version continues by explicitly moving from talk of the predicates to talk of the relations to which the predicates refer. There is absolutely no pressure to think that those two sentences invoke different relations. If they did, it would have to either be the case that English contains two distinct but homonymous ‘is two feet from’ predicates, or else that the single predicate ‘is two feet from’ surreptitiously picks out different relations on different occasions of use. But there is no reason to believe either claim. Indeed, there is reason to believe that the predicates pick out the same relation in those two sentences—namely, that (1) and (2) entail

    1. (3)

      the boiling of the kettle is the same distance from the whirring of the blender as the cat is from the squirrel.

    Thus to deny that a single relation can take a variety of kinds of relata requires thinking not only that we are drowning in relations, but also that our predicates are semantically pretty tricky.

  37. Here too, a more careful version of the argument would instead begin with the claim that there are lots of relational predicates that appear to be able to take either singular or plural arguments into one or all of their argument places. See note 36, though in this case I will leave the details to the reader.

  38. Yi’s claim is actually about predicates, not relations. In his terminology, ‘carries’ and ‘is equinumerous with’ are neutral predicates (2005, pp. 480–481, including n66). He says that a neutral argument place is one that can take either a singular or plural argument, and that a neutral predicate is one that has at least one neutral argument place. Yi then suggests that “most, if not all, of the predicates of, e.g., English are neutral predicates” (p. 481).

  39. Another example is a controversy about existence. Many people, myself included, think that there is only one fundamental form of existence (see Sider forthcoming for further explanation and defense). Others think that there is more than one—that there are many “ways of being” (see McDaniel (2009a, b) and Turner MS for further explanation and defense; both also document the historical primacy of the view). One way to think about the dispute is this: the former sort of people think that although we can of course restrict our quantifiers to a particular ontological category, there is only one fundamental quantifier. The latter sort of people think that the various ‘smaller’ quantifiers—over material objects, over properties, etc.—are not mere restrictions on the basic quantifier, but are in fact more fundamental. On this view, the generic “there is” is in fact gerrymandered. (See Turner MS §2 for further discussion of this characterization of the dispute.)

    It is interestingly hard to see how to adjudicate this dispute in particular, or disputes of this form in general. Note that in the main text I do not exactly argue that there is only a single fundamental identity relation. I merely point out that that certainly appears to be the received view.

  40. The alternative is either to take singular identity as fundamental, and define plural identity in terms of it, or to take plural identity as fundamental and define singular identity in terms of it (see McKay 2006, pp. 128–129).

    Note that the single number-neutral identity relation would be different from the single fundamental building relation R whose existence we are considering, in that the identity relation never holds many-one. (Or does it? See Baxter 1988a, b.) But that is a fact about the nature of identity in particular, not about the nature of relations in general.

  41. Mark Heller suggested the gist of this to me.

  42. Or things(es?) xx and yy, or xx and y, etc. I only frame the argument in terms of singular variables for simplicity.

  43. Or interval t1−n. Recall that I did not require that building relations be synchronic. The case simply requires that x’s bearing R 1 to y be simultaneous with y’s bearing R 2 to x.

  44. To see this, consider the following case, which has the same structure. I bear the is a sister of relation to Steve, and Steve bears the is a brother of relation to me. Those relations are both species of the more general is a sibling of relation, which we each also bear to each other. This is all consistent with the assumption that the latter is more fundamental than the two former relations.

  45. Schaffer is actually neutral about how the One grounds everything, i.e. about the priority structure of the world other than the claim that the One is the only ungrounded entity (2010a, p. 44).

  46. Most of Kim’s more well-known discussions of “downward causation” are discussions of the diachronic case, in which W’s having M at t causes P to be instantiated at a later time. For example, this is where the exclusion problem and worries about the violation of the causal completeness of physics arise. Kim distinguishes the cases in his 1999, and discusses the diachronic case in detail in many places, e.g. Kim (1993, 1999, 2006).

  47. Or there are some xxs and some yys; again, the singular variables are for simplicity only.


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Correspondence to Karen Bennett.

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This paper was originally drafted for a symposium on ontological emergence at the 2009 Central APA. Thanks to Timothy O’Connor for organizing it, and to Jordi Cat and Carl Gillett for discussion and comments. I also presented versions of the paper at the Upstate New York Metaphysics Workshop in May 2009 (sponsored by the Mellon Foundation), and the Bellingham Summer Philosophy Conference in August 2010. Thanks to Sara Bernstein and Erica Shumener for the trenchant comments they gave at Bellingham, and to both audiences for much helpful discussion. I’m particularly grateful to Zach Abrams, Mark Barber, David Braun, Earl Conee, Bob van Gulick, Mark Heller, Kris McDaniel, Alyssa Ney, Ted Sider, and Jonathan Schaffer.

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Bennett, K. Construction area (no hard hat required). Philos Stud 154, 79–104 (2011).

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