Abstract
Structuralism and quidditism are competing views of the metaphysics of property individuation: structuralists claim that properties are individuated by their nomological roles; quidditists claim that they are individuated by something else. This paper (1) refutes what many see as the best reason to accept structuralism over quidditism and (2) offers a methodological argument in favor of a quidditism. The standard charge against quidditism is that it commits us to something ontologically otiose: intrinsic aspects of properties, so-called ‘quiddities’. Here I grant that quiddities are ontologically otiose, but deny that quidditism requires them. According to a view I call ‘austere quidditism’, properties are individuated by bare numerical identity. I argue that, as far as ontological parsimony is concerned, austere quidditism and structuralism are on a par. But is austere quidditism a coherent alternative to structuralism? To see that it is, we must get clear on what exactly we mean by ‘property individuation’. What we discover is that structuralism is a counterpart theory for properties, and that austere quidditism is simply the rejection of counterpart theory. I conclude with a methodological argument to the effect that counterpart theory for properties ought to be rejected. This paper begins by situating the debate between structuralists and quidditists within the context of a debate over the epistemic limits of fundamental science. At the center of this debate is David Lewis’s posthumously published ‘Ramseyan Humility’ (2008). In the appendix I explain the precise role of austere quidditism in Lewis’s argument.
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Notes
In preparing this paper, I received an incredible amount of help from my friends and colleagues. In particular, I would like to thank Yuval Avnur, Greg Keenan, Ivan Mayerhofer, David Braddon-Mitchell, Shamik Dasgupta, Kenny Easwaran, Andy Egan, Jim Joyce, Amy Kind, Jim Kreines, Heather Lowe, Howard Nye, David Plunkett, Jonathan Schaffer, Allie Scott, all the members of the Claremont Colleges works-in-progress group, the participants in “Metaphysics: Aristotelian, Scholastic, Analytic” 2010, and the Rackham Graduate School at the University of Michigan for a grant to travel to the philosophy departments at the University of Sydney and the Australian National University, to whom I also owe a large debt of gratitude.
I use the term ‘property’ to include not only one-place properties but many-place relations as well. I also include quantities (e.g., mass) as well as qualities (e.g., quark colors).
I use the phrases ‘quiddistic fact’ and ‘quiddistic realization’ with precisely the meaning I here stipulate them to have. As we will see below, there is an ambiguity in the terms ‘quiddities’ and ‘quidditism’. The stipulations that I make here should be taken to block these ambiguities from infecting the phrases ‘quiddistic fact’ and ‘quiddistic realization’.
Lewis (1975) discusses the latter sort of facts and why he thinks that they are beyond the reach of science.
Property structuralists include Swoyer (1982), Shoemaker (1984, 1998), and Kistler (2002). Shoemaker, however, holds that properties are individuated by their causal roles, not nomological roles. This distinction is not idle, as a property’s nomological role may sometimes come apart from its causal role. Nonetheless, everything I say here should be taken to apply mutatis mutandis to Shoemaker’s view.
We use ‘Ramsification’ to make the notion of a nomological role precise. Suppose that we live in a Newtonian world, a world where there are two fundamental laws in which the property mass figures. First, there is the law of gravitation: between any two individuals with mass, there is an attractive force proportional to the product of their masses divided by the square of the distance between them. Second, there is Newton’s Second Law of Motion: the net force on an object is equal to the product of its mass and its rate of acceleration. Now we conjoin these laws and replace each occurrence of ‘mass’ with a variable: between any two individuals with x, there is an attractive force proportional to the product of their respective amounts of x divided by the square of the distance between them, and the net force on an object with x is equal to the product of its amount of x and its rate of acceleration. This open-sentence defines a second-order property possessed by the first-order property mass. This second-order property is what we call mass’s nomological role, and to ‘realize this role’ is simply to have this second-order property.
Robinson (1993, p. 19).
Schaffer (2005, note 2).
Please see footnote 5.
Ramsey (1929).
As stated in the introduction, we are here setting aside anti-realism about properties.
A special thanks to Amy Kind for suggesting the name ‘austere quidditism’.
Does austere quidditism imply QR? Not without the help of a principle of recombination. Please see the Appendix.
Dispositionalism seems to have had its heyday in and around the 1970s. Mellor (1974, 1982) endorsed dispositionalism, and Harre and Madden (1975) did as well, provided that we count ‘causal powers’ as dispositions. More recently, Ellis and Lierse (1994) flirt with dispositionalism, but they do not go as far as to argue that scientific explanations deal exclusively in dispositions. Similarly, Molnar (2003) holds that most but not all properties found in fundamental science are dispositions (or, more accurately, ‘powers’). Perhaps one of the few remaining dispositionalists (‘dispositional monists’, to use his phrase) is Bird (2007).
Ellis and Lierse’s (1994, p. 32)
Armstrong (1997, p. 80).
Lowe (2010, notes 19, 20).
Is this circularity really vicious? Unfortunately, no one has yet proposed non-controversial necessary and sufficient conditions for when a circularity is vicious. Note however that the circularity which I am pointing to is not of the type that was once thought to be vicious but is now widely regarded as legitimate—the kind of circularity involved in impredicative definitions. An impredicative definition is one that involves quantification over a domain of entities that includes the entity the definition picks out. But if we are to identify mass with a certain disposition, we need to explicitly define this disposition in terms of ‘mass’ and not just quantify over a domain of entities one of which is the entity that our definition picks out. That, it would seem, is a vicious circularity.
The structuralist account of mass is circular only in the sense that all impredicative definitions are circular. As mentioned in the previous footnote, such definitions are now widely regarded as legitimate. In any case, I grant this much on behalf of the structuralist.
It is important that the move to structuralism here is not the ‘appeal to structure’ that Lowe (2010) considers and rejects. (Lowe is explicitly discussing the view that all properties are powers, but I take the distinction between such a view and dispositionalism, if there is a distinction, to be tangential to the present discussion.) The appeal to structure that Lowe has in mind is an attempt to defend dispositionalism (proper) against by appeal to certain structural facts that exist between token dispositions. The move that I have in mind is the abandonment of dispositionalism for another view altogether—the view I am calling ‘structuralism’.
Shoemaker (1998, p. 59) appears to endorse such a view when he claims that ‘properties sharing all of their causal features are identical’. (As stated in footnote 4, everything I say in this paper about nomic structuralism is to be taken to apply mutatis mutandis to causal structuralism.)
This appears to be the view endorsed by both Swoyer (1982) who claims that ‘a property is what it is in virtue of its lawful relations to other properties’ (p. 214) and Kistler (2002) who claims that ‘the identity of a universal is entirely determined by its lawful relations to other properties’ (p. 57).
Consider two distinct possibilities in each of which there are two distinct properties symmetrically related to one another exactly as P and N are in the earlier example. In that case, structuralism as a theory of inter-world identity implies that each of the properties in one of the worlds is identical with each of the properties in the other world. By the transitivity of identity, each property is then identical with its world-mate. This contradicts the supposition that each of these worlds contains two distinct properties.
By a ‘de re modal claim’, I simply mean a claim about what must have, might have, or would have been true of a given entity.
Hawthorne notes that the structuralist can allow some context sensitivity in de re modal representation: she need not hold that a property must always share the exact nomological role of another in order to de re represent it. As far as I can see, there is no need to adjust the arguments of the present paper in light of this qualification.
Please see footnotes 22 and 24.
How many properties they must share, and which properties they must share, is for Lewis a matter of context. But the basic point remains: they are qualitatively similar in virtue of sharing (enough of the right sort of) properties.
Importantly, the two most commonly endorsed arguments for counterpart theory for individuals—Lewis’s (1986) argument from accidental intrinsics and Gibbard’s (1975) argument from spatiotemporal coincidence—are no good as arguments for counterpart theory for properties. Without going into details, the reasons, respectively, are that properties do not have accidental intrinsics, and properties are perfectly capable of being non-identical and yet occupants of precisely the same spatiotemporal region.
Black (2000) offers an argument squarely directed at the view I am calling ‘austere quidditism’. Unfortunately, I do not have space to deal with this argument here. However, no philosopher seems to have taken the argument very seriously, not even Black himself (p. 92). Nonetheless, if the main argument of the present paper is correct—that austere quidditism is a coherent alternative to structuralism—those interested in the structuralism/quidditism debate ought to turn their attention to arguments such as Black’s.
It should go without saying that I have not provided a positive reason to accept QR. My aim has merely been to defend QR against what many would take to be the best reason to reject it. However, I have taken a step towards providing a positive argument in favor of QR. The less modest conclusion of Sect. 6 is that we have a reason to accept austere quidditism over structuralism. Although austere quidditism does not itself imply QR, it does imply QR when combined with a certain principle of recombination. In the appendix I explain how this works. It is, however, beyond the spatial limitations of this paper to provide you with a reason to accept the needed principle of recombination.
Hence the foreign dash notation.
Unfortunately, Lewis never gives an exact formulation of the recombination principle. He begins with the principle that ‘anything can coexist with anything else’, but ultimately rejects this principle because he sees it as incompatible with his view that one individual never exists in more than one possible world. Nevertheless, Lewis’s subsequent discussion (especially on p. 163) makes it clear that the principle he implicitly endorses implies that possibility is preserved under permutation of properties with respect to their spatiotemporal distributions. See Efird and Stoneham (2008) for a thorough discussion of Lewis’s principle of recombination.
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Appendix: Lewis on quidditism, recombination, and QR
Appendix: Lewis on quidditism, recombination, and QR
In ‘Ramseyan Humility’ (2008), Lewis gives three arguments to the effect that quidditism, together with a principle of recombination, implies QR. These three arguments might be called ‘the argument from permutation’, ‘the argument from aliens’, and ‘the argument from idlers’. Here I will focus exclusively on the argument from permutation, and I will address two issues: first, exactly what sort of principle of recombination is required, and second, exactly which form of quidditism does Lewis have in mind? My answers, respectively, are ‘it depends’ and ‘austere quidditism’.
First, we’ll need to introduce some of Lewis’s terminology. Let T be the complete and true theory about which nomological roles are realized at our world. T is equivalent to one (infinitely) long existentially-quantified sentence: there exist properties x1, x2,…, xn such that x1, x2,…, xn have such and such relationships to one another. Call the n-tuple of properties that actually satisfies T ‘the actual realization of T’. In rough terms, QR says that the world might have been just like it actually is with respect to which roles are realized, and yet different with respect to which properties realized those roles. In Lewis’s terminology, QR says that T might have been realized without being realized by the n-tuple that actually realizes T.
Here is Lewis’s argument from permutation for QR:
Suppose we have the actual realization of T. Maybe some members of the n-tuple that realizes T are not fundamental properties, or maybe some belong to single-membered categories [e.g., perhaps there is only one property that is a 2-place quantity]. Hold those ones fixed. Permute the rest within their categories to obtain a new n-tuple. It too would realize T. (2008, p. 208)
Why does Lewis think that such a permutation is a possible realization of T? He goes on to say that
Possibility is governed by a combinatorial principle [here Lewis cites Lewis (1986, §1.8) and Armstrong (1989)]. We can take apart the distinct elements of a possibility and rearrange them. We can remove some of them altogether. We can reduplicate some or all of them. We can replace an element of one possibility with an element of another. When we do, since there is no necessary connection between distinct existences, the result will itself be a possibility. How much this means depends on what we take the distinct elements to be. Here, let us take them to include not only spatiotemporal parts, but also abstract parts—specifically, the fundamental properties…
Combinatorialism tells us that possibility is preserved under permutations of items—at least if they are items from the same category. If it is possible that –A–B–C–, and if A, B, and C, are, say, all-or-nothing monadic properties, then it is also possible that –C–A–B–. The actual realization of T is a possible realization; we permute items within more-than-one-member categories; and what we get is also a possible realization of T. (pp. 208–209)
Lewis then asks whether this possibility—the existence of which is guaranteed by the recombination principle—is different from the actual realization of T. Here is his answer:
Quidditism is the premise that tells us that the permutation is indeed a different possibility [here Lewis cites Black (2000)]. Two different possibilities can differ just by a permutation of fundamental properties. They do not differ in whether T is realized…
Quidditism is to properties as haecceitism is to individuals. If we start with a possibility and permute individuals, combinatorialism says that we get a possibility; haecceitism says that it is a different possibility. (p. 209)
Again, our two questions are (1) what principle of recombination does the argument require? And (2) what form of quidditism does Lewis have in mind? There is reason to think that the two questions cannot be answered independently: the required form of quidditism will depend on what it is we are recombining, which will in turn affect which principle of recombination is in play. So let us then begin by asking: what precisely is being recombined when we move between possibilities in Lewis’s argument?
Lewis says that the principle of recombination implies that ‘if it is possible that –A–B–C–, and if A, B, and C, are, say, all-or-nothing monadic properties, then it is also possible that –C–A–B–.’ Clearly, it is properties that are being recombined here. That part is easy. But how, exactly, are they being recombined? Answer: by permutation. Yes, but permutation with respect to what—in other words, what do the dashes in Lewis’s text represent? I think there are two main possibilities here: first, Lewis may intend to be permuting A, B, and C with respect to their spatiotemporal distributions; second, Lewis may intend to be permuting A, B, and C with respect to how these properties realize T—that is, with respect to their nomological roles.
I think that Lewis is being intentionally ambiguous here.Footnote 34 What Lewis ultimately wants to show, of course, is that possibility is preserved under permutation of properties with respect to their nomological roles (this, combined with quidditism, is meant to entail QR). However, Lewis does not himself have a principle of recombination that entails that possibility is preserved under permutation of properties with respect to their nomological roles. What he does have [what is endorsed in Lewis (1986, §1.8)] is a principle that entails that possibility is preserved under permutation of properties with respect to their spatiotemporal distributions.Footnote 35 Moreover, Lewis accepts a Humean theory of laws according to which the laws (and thus which properties realize which nomological roles) are determined by the spatiotemporal distribution of properties. Hence, his principle of recombination—which itself concerns spatiotemporal distributions—together with his Humean theory of laws, entails that possibility is preserved under permutation of properties with respect to their nomological roles.
But Lewis of course realizes that not everyone accepts a Humean theory of laws. Hence, he implicitly acknowledges that others may need a different principle of recombination—one that, together with their view of laws, entails that possibility is preserved under permutation of properties with respect to their nomological roles. All of this is confirmed in (2008, note 14), where Lewis writes:
If laws are suitable regularities [in the distribution of properties through spacetime], the exchange of locations of P1 and P2 will guarantee the exchange of nomological roles. If laws of nature are certain special lawmaking relations of fundamental properties, P1 and P2 will have to be exchanged also as arguments of these lawmaking relations to guarantee the exchange of nomological roles.
One of the questions with which we began this appendix was: what sort of recombination principle is required by Lewis’s argument? The answer is this: any recombination principle that, together with one’s theory of laws, entails that possibility is preserved under permutation of properties with respect to their nomological roles. More generally, we might simply say that what the argument requires is the principle that possibility is preserved under permutation of properties with respect to their nomological roles—let us call this simply ‘the permutation principle’. There are many ways to get to the permutation principle, but we need not adjudicate between them. So much for our first question. We turn now to our second question: what form of quidditism does Lewis have in mind?
It may seem that the permutation principle alone entails QR, and so the appeal to quidditism is superfluous. After all, the permutation principle implies the following:
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(1)
There is a possibility where positive charge (and not mass) realizes the nomological role that is actually realized by mass (and not positive charge).
Doesn’t (1) imply QR?
Quiddistic Realization. For at least some nomological role R realized by some property P, R might have been realized without being realized by P.
Why does Lewis appeal to quidditism?
To see why Lewis needs quidditism to get from the permutation principle to QR, we must keep in mind that, for Lewis, it is not always true that a thesis about what possibilities there are is equivalent to the corresponding thesis about what might have been. For example, because Lewis is a counterpart theorist about individuals, he allows that it might have been that Humphrey won the election, but he denies that there is a possibility where Humphrey wins the election. The latter is equivalent to the former if and only if we assume the identity theory of inter-possibility individuation for individuals, which Lewis denies.
Similarly, if structuralism is true, then (1) does not imply QR. According to structuralism, the possibility mentioned in (1) is, for the purpose of evaluating claims about what might have been, no different from actuality: (1) merely implies that the role actually realized by mass might have been realized by mass. On the other hand, given the identity theory of inter-possibility individuation for properties—that is, given austere quidditism—(1) implies that the role actually realized by mass might have instead been realized by positive charge. Hence, given austere quidditism, (1) implies QR.
Moreover, it is clear that extravagant quidditism is of no help in getting from the permutation principle to QR. The permutation principle says nothing at all about quiddities—in particular, it does not say that possibility is preserved under permutation of quiddities with respect to the nomological roles of the properties that have those quiddities. Indeed, nowhere in Lewis’s argument will you find mention of quiddities, intrinsic aspects, essential natures, or anything of the kind. I take all of this as strong evidence that Lewis preferred his quidditism without quiddities.
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Locke, D. Quidditism without quiddities. Philos Stud 160, 345–363 (2012). https://doi.org/10.1007/s11098-011-9722-5
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DOI: https://doi.org/10.1007/s11098-011-9722-5