In response to a question about why opium puts patients to sleep, Bachelerius, a prospective doctor of medicine in Molière’s Le Malade Imaginaire, says that “there is a dormitive virtue in it, whose nature it is to make the senses drowsy.” This answer, given by Bachelerius in his viva voce examination, is received enthusiastically by his examiners, much to the amusement of the audience.
Bachelerius’ humorously bad explanation seems to turn on paraphrasing the explanandum—opium’s ability to put patients to sleep—as dormitive virtue, which is then said to be part of the nature of opium. But it does not suffice as an explanation of why opium puts people to sleep to be told that it is in the nature of opium to put people to sleep. The purported explanation appears to just tell us what we already know, albeit phrased slightly differently.
CDE succumbs to a similar explanatory pitfall—laws/M-relations are said to constitute the essences of properties, and properties are said to explain the laws of nature. So, for example, in response to the question “why do charged objects interact in accordance with Coulomb’s law?”, the CDE answer would be (roughly) “because Coulomb’s law is part of the essence of the property charge”. But an explanation of laws in terms of properties according to which it is part of the essence of properties that those laws hold seems as dissatisfying as Bachelerius’ “explanation” of opium’s ability to make a patient sleep in terms of its dormitive virtue.
In this section, I’ll precisify this worry with an argument to the conclusion that CDE laws and properties symmetrically ground each other, which makes the explanation of laws in terms of properties circular. I’ll explain how QDE does better by breaking this symmetry and providing a properly reductive picture. I’ll also argue (in 4.2) that DE’s explanatory aspirations cannot be satisfied just by identifying laws with regularities (the point holds whether regularities are understood as things in the world or descriptions) as opposed to M-relations, i.e., problems remain for the combination of a structuralist view of properties and a BSA account of laws.
Symmetrically grounded laws and properties in CDE
As discussed in Sect. 2.1, CDE posits a structure of M-relations. One question that we may ask is what (if anything) grounds this structure? Yates (2018) talks about properties, on the structuralist conception, as composing a structure:
[Structuralism]Footnote 10 require[s] that entities can be individuated by their places in a structure composed by the entities themselves. (Yates 2018, 4543).
In [structuralism], powers are fully individuated by their places in a type-casual structure fully composed of powers. (Yates 2018, 4544).
Granting that properties compose the structure, and that composition is a grounding relation, it follows that properties ground the structure.
However, one might object to the idea that properties ground structure given that the option remains to posit the structure as an ungrounded primitive entity. The main precedent for this idea is ontic structural realism (OSR). According to OSR, individuals are eliminated from the ontology in favour of an ontologically primitive relational structure (e.g., French and Ladyman 2003; Ladyman et al. 2007). Prima facie talk about individuals is then understood as merely abstracting from the fundamental relational structure. Since, on this view, structure is all there is, it certainly is not the case that the structure ontologically depends on anything else. Perhaps, then, the structuralist about properties could say something similar, namely, that a relational structure is all there is to properties, in which case it would be false to say that this structure ontologically depends on properties, or anything else. However, this interpretation of structuralism about properties shares with OSR a commitment to relations without relata, which is something that many have found objectionable (e.g., Chakravartty 1998, 2003b; Psillos 2006a); according to Chakravartty “one cannot intelligibly subscribe to the reality of relations unless one is also committed to the fact that some things are related” (1998, 399). In the interest of avoiding such controversies, it would seem reasonable to follow Yates’ understanding of structure as ontologically dependent upon the properties that “compose” it—CDE properties ground the structure.
Recall that, according to property structuralism, the structure, S, at a world, w, grounds the properties at w because it metaphysically individuates them. Hence, properties and structure symmetrically ground each other.Footnote 11 Odd as this may sound, things get worse for CDE because, as I shall now show, it follows that properties and laws symmetrically ground each other, which directly threatens CDE’s aspirations to (asymmetrically) explain laws in terms of properties.
In Sect. 2.2, it was argued that CDE laws are identified with M-relations. Now, if you fix the M-relations (that is the laws, according to CDE) at a world, w, you fix the property structure at w. If we let [M] denote the plurality of M-relations/laws at a world, w, and let S denote the property structure at w, then we may ask the following question: what is the relationship between [M] and S? Answer: identity. The plurality of M-relations at a world, w, just is the structure at w.
Now, if the collection of M-relations, [M], at a world, w, and the property structure, S, at w are identical, then anything true of S must be true of [M] too. According to property structuralism, the structure, S, at w grounds the properties at w because it metaphysically individuates them. But if S grounds the properties at w then [M] must ground properties at w too, since S and [M] are identical. But M-relations, I have argued, just are the laws, according to CDE. Thus, the collection of M-relations at w, [M], just is a collection of laws. To say that [M] grounds properties, then, is just to say that laws ground properties, given CDE. To be clear, the argument runs as follows:
-
(i)
S = [M].
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(ii)
[M] is a collection of laws (from the CDE account of laws).
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(iii)
S grounds properties(from the CDE account of properties).
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(iv)
[M] grounds properties (from i, iii and Leibniz’s Law).
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(v)
Laws ground properties (from ii and iv).
The conclusion that laws ground properties is antagonistic to CDE’s aspiration to explain laws in terms of properties. Grounding is plausibly understood as an explanatory relation distinct from, but analogous to causation (Fine 2012, Sect. 1), see also Schaffer (2016); just as one may explain some fact A by saying that some temporally prior fact B caused it, one may explain A in terms of B by saying that B grounds A. An explanation of A in terms of B will not do, however, if in order to explain B, we must appeal to A—this kind of circularity of explanation is vicious. The type of explanation of the laws that the dispositional essentialist should seek to provide is a grounding explanation whereby properties ground laws. But if laws ground properties too, then the explanation is circular and thus fails to satisfy a key motivation for dispositional essentialism, which was to explain laws in terms of properties, not vice versa.Footnote 12
Another way of seeing the problem is as follows: according to CDE, M-relations constitute the essences of properties, and M-relations are laws. Structuralist DE thus builds laws into the essences of properties and then seeks to explain the laws of nature in terms of those very property essences (c.f. Jaag (2014)). But this looks a lot like explaining the fact that opium induces sleep in terms of opium’s dormitive nature.
A further problem highlighted by the above argument is that CDE multiplies the number of fundamental entities. Dispositional essentialism, at least on the face of it, promised an attractively reductive picture; at the fundamental level we just have physical properties which ground the laws of nature. What the above argument shows, however, is that according to CDE, properties cannot be more fundamental than laws because each grounds the other. The picture presented, then, is one of properties and laws as equifundamental, which is a far less parsimonious picture than one according to which it is just properties at the fundamental level.
QDE breaks the symmetry by denying that properties are in any way ontologically dependent upon the structure of M-relations. Properties, according to QDE, are self-individuating qualities that asymmetrically ground a structure of M-relations. And laws, according to QDE, are axioms of the best deductive systematization of all actual and possible property distributions. QDE is thus preferable to CDE in two significant respects: it avoids symmetrically grounded properties and laws and hence avoids any Molière-type concerns, it also avoids positing both properties and laws at the fundamental level.
Laws as regularities?
Perhaps the obvious response to the symmetrical grounding problem for CDE is to maintain that laws are universal generalizations, or regularities, of the form ∀x(Fx → Gx), as opposed to M-relations, viz., arcs in the property structure. Indeed, Bird himself considers this optionFootnote 13:
According to the regularity version of dispositional essentialism about laws, laws are those regularities whose truth is guaranteed by the essentially dispositional nature of […] properties. (2007, 46–47, my emphasis).
The idea, then, is that M-relations do the work of guaranteeing the truth of, or grounding (depending on whether regularities are understood as linguistic entities or entities in the world) and hence explaining, nomic regularities. But surely no M-relation is identical with any regularity, in which case premise ii. in the symmetrical grounding argument of the previous subsection can be rejected and the circularity concern is blocked. While properties cannot explain laws qua M-relations, properties can explain laws qua regularities, or so one might think.
But how, exactly, are we to understand the claim that properties explain regularities? According to an argument from Barker and Smart (2012), the property structuralist component of CDE cannot achieve even this.
According to the property structuralist, there is nothing more to the essence of a property than the M-relations in which it stands to other properties—all properties have their essences exhausted by M-relations. Hence, all that the property structuralist may appeal to in answering the question about how properties, F and G, say, explain the regularity ∀x(Fx → Gx) are the M-relations in which F and G stand to other properties (Tugby 2012, 725, highlights this nicely). To clarify the point, it will help to introduce some abbreviations:
M(F, G) = the fact that the M-relation holds between F and G.
R = the fact that if x is F then x is disposed to manifest G.
We can thus understand the property structuralist as positing a necessary connection between M(F, G) and R to explain the regularity ∀x(Fx → Gx). It is no accident, according to the property structuralist, that if M(F, G) holds then R holds, hence it is no accident that if M(F, G) holds then every x that is F will be G too. Thus, the regularity, ∀x(Fx → Gx), is explained by M(F, G)’s holding.
But now we may ask: what accounts for the necessary connection between M(F, G) and R? Why is it that in every possible world in which M(F, G) holds, every x that is F will be G? Perhaps there is some third-order relation, M*, between the relational facts M(F, G) and R, which ensures that if M(F, G) holds then R holds too. We can denote the situation like this: M*[M(F, G), R]. But now we may ask what accounts for the connection between M*[M(F, G), R], M(F, G) and R? What ensures that if M*[M(F, G), R] holds at a world, w, then if M(F, G) holds R holds too? Is there some fourth-order relational fact, M**, such that M**[M*[M(F, G), R], M(F, G), R]? We are clearly off on a regress of higher and higher order M-relations. (This is the nub of Barker and Smart’s “ultimate argument against dispositional monist accounts of laws” (2012), see also Barker (2013).Footnote 14)
Perhaps the regress can be blocked by repudiating the initial explanatory demand. The property structuralist might say that there is a brute necessary connection between the fact that the M-relation holds between F and G and the fact that for all x, if x is F then x is disposed to manifest G. That is to say, there is a brute necessary connection between M(F, G) and R such that in any world in which M(F, G) holds, R holds too. By maintaining that the necessary connection between M(F, G) and R is just brute, the property structuralist needn’t appeal to higher order relations and the regress is blocked.
However, appeal to brute necessary connections is antagonistic to the motivation for property structuralism, and CDE more generally, which was to explain patterns of property distributions, not in terms of some brute necessary connections, but in terms of powerful properties. As Tugby puts it, “One of the main intuitions behind dispositionalism is that the properties of things are not inert: they pack a powerful punch; they give a causal ‘biff’ to their possessors.” (2012, 726). But if it turns out that all the work is being done by brute necessary connections between higher-order relational facts, then this motivation for CDE seems not to have been satisfied.
The point, then, is that it will not help one with anti-Humean/dispositional essentialist sympathies, who is concerned by the symmetrical grounding problem, to identify the laws with regularities instead of M-relations. Furthermore, it doesn’t matter if the regularities in question are more sophisticated, as per the BSA. As mentioned in Sect. 3.2, the dispositional-BSA account of laws (Demarest 2017; Kimpton-Nye 2017) still wants the laws/regularities to be metaphysically explained by properties, which it achieves by maintaining that properties metaphysically explain their distributions which, in turn, metaphysically explain the BSA-laws. But what the Barker-Smart problem shows is that structuralism about properties precludes those properties from explaining regularities in property distributions, and if properties cannot metaphysically explain their own distributions, they cannot explain the BSA laws. Whether laws are M-relations, simple regularities or sophisticated BSA-regularities, a structuralist metaphysics of properties is not cut out to do the explanatory work that dispositional essentialism requires. We are thus pushed towards more radically rethinking dispositional essentialism and QDE constitutes just such a radical rethink.Footnote 15
An opacity worry for QDE
The opacity worry for QDE is a challenge to add plausibility to the claim that qualities ground dispositions. As Tugby puts it “…opponents […] might object […] that the alleged internal connection between qualities and dispositions is itself pretty opaque.” (2012, 729).Footnote 16
Schaffer defines a relevant sense of “opacity” as follows:
Opacity: It is opaque as to why the obtaining of the ground state is linked to the obtaining of the grounded state if and only if the proposition that the ground state obtains without the grounded state obtaining is [conceivable/logically possible/a priori open]. (Schaffer 2017, 4).
The worry, then, is that the purported grounding link between quality and disposition is opaque in the above sense—it is certainly conceivable, logically possible and a priori open that a quality, positive charge, say, exists in the absence of a disposition to exert an attractive force on instances of negative charge. So why think that any such grounding link exists?
Schaffer has argued, however, that a purported grounding link’s being opaque is not a good reason to reject that link out of hand. This is because Schaffer advocates an abductive methodology in metaphysics according to which metaphysical posits are justified to the extent that they are explanatorily fruitful (Schaffer forthcoming, pp. 8–9) (see also (Lewis and Lewis 1970; Paul 2012 for ideas relating to and in defence of this abductive methodology in metaphysics)).
It may be explanatorily fruitful, and hence justified, to posit the existence of a grounding link even if that link is not transparent in the sense that its existence is evident to pure reason or a priori knowable. For example, and assuming that sets exist, Schaffer suggests that we are justified in positing a grounding link (namely, set formation) between Socrates and {Socrates}. This is because, given that Socrates exists and that the set formation grounding link exists between Socrates and {Socrates}, it is no accident that {Socrates} exists given the existence of Socrates, so the link is explanatorily fruitful:
To buttress this […] claim [that a grounding link obtains between Socrates and {Socrates}], note that the theoretical role of explanation includes (i) revealing patterns, (ii) providing recipes, and (iii) allowing understanding [Schaffer 2018 ]. Seeing {Socrates} as the output of Socrates via set formation (i) reveals a unifying pattern that extends through Plato and {Plato}, Aristotle and {Aristotle}, etc.; (ii) conveys a recipe to wiggle the existence of {Socrates} by wiggling the existence of Socrates; and (iii) allows one to understand why {Socrates} exists, by revealing how sets are collected. (Schaffer forthcoming, 2).
Schaffer discusses other examples from mereology (2017, forthcoming), meta-ethics and quantum ontology (forthcoming). In each of these examples, we are justified in positing a grounding link between two entities because doing so is explanatorily fruitful in the sense that it reveals patterns, provides a recipe, and allows understanding. What’s more, the grounding link in each case is opaque in the above sense that it is conceivable/logically possible/a priori open that the ground state obtained without the obtaining of the grounded state. For example, it is conceivable that Socrates existed without the existence of {Socrates} and it is conceivable that some wood arranged table-wise existed without the existence of a table (mereological nihilism is conceivable). Nevertheless, we are justified in positing grounding links in these cases—set formation in the former and a mereological fusion principle in the latter—because doing so is explanatorily fruitful.
So, according to Schaffer, the existence of grounding links need not be evident to pure reason or knowable a priori, i.e., they need not be transparent. Rather, we can take a more holistic, abductive approach to metaphysics, according to which we are defeasibly justified in positing grounding links if they are explanatory. In this sense, Schaffer thinks that there is an important analogy between grounding and causation:
Those who would demand a priori grounding principles strike me as akin to those in the early days of the sciences who demanded a priori causal principles (“rational mechanics”). We have come to recognize the need for substantive dependence functions in concrete causal cases. I am trying to extend this insight to concrete metaphysical cases. (Schaffer 2017, 14).
According to this Schafferian line, then, it is no objection to QDE that the grounding link between quality and disposition is opaque. Indeed, we have defeasible justification for believing in grounding links between qualities and dispositions given their explanatory fruitfulness. And the point of the discussion thus far has been that QDE, “opaque” grounding links and all, is explanatorily fruitful. QDE is explanatorily superior to Humean accounts of laws and properties because it guarantees that the laws are sufficiently modally robust (see sect. 1), and it is explanatorily superior to CDE because it breaks the problematic symmetry and equifundamentality between laws and properties.
Schaffer’s argument for the explanatoriness of the set formation grounding link (see second Schaffer quote above) can be mirrored for QDE: positing a grounding link between positive charge and a disposition to exert an attractive force on negatively charged individuals (i) reveals a unifying pattern that extends through mass and a disposition to exert an attractive force on massive individuals, etc.; (ii) conveys a recipe to wiggle the existence of a disposition by wiggling the existence of a quality; and (iii) allows one to understand why certain dispositions exist by revealing how they depend on the existence of certain qualities.
QDE’s “opaque” grounding links are explanatorily fruitful—this has been the main thrust of the argument of the present section. We are thus justified in believing in the existence of these grounding links given a holistic, abductive approach to metaphysics.
Perhaps one could object that the analogy between Socrates grounding {Socrates} and qualities grounding dispositions breaks down because whereas we have independent reason to believe in the existence of Socrates, the only reason for positing qualities is to ground dispositions and laws.Footnote 17 Admittedly, qualities, in the present sense, are more “theoretical” than individuals such as Socrates—the main reason for positing qualities is the theoretical work that they can do and the theoretical work of concern here is explaining dispositions and laws. But qualities can also do other theoretical work besides accounting for dispositions and laws, such as explaining objective similarity and difference. Indeed, accounting for similarity and difference is generally a role assigned to natural properties, so one could understand the present discussion as a case in favour of understanding the metaphysics of natural properties in such a way that they can also explain laws and dispositions.