Constitution, Non-Causal Explanation, and Demarcation

1. Introduction

The core question to be answered in Carl Craver’s influential book Explaining the Brain (2007), according to its blurb, is: “What distinguishes good explanations in neuroscience from bad?” The answer, in short, is that neuroscientific explanations are constitutive and good constitutive explanations “describe all and only the component entities, activities, properties, and organizational features that are relevant to the multifaceted phenomenon to be explained” (Craver 2007: 111). The explanatory heavy-lifting in such explanations is done by the relation of constitution or constitutive relevance,¹ of which Craver’s book offers a widely received account, viz. the Mutual Manipulability theory (MM). MM states, in essence, that a phenomenon’s constituents are the activities of those of its spatio-temporal parts that can be changed by ideal interventions on the phenomenon as a whole and that can change the phenomenon if they are themselves changed by ideal interventions.

MM establishes constitution as a relevance relation between wholes and their parts, different from causation, and it is intended to demarcate between constituents and non-constituents. On the basis of these demarcations, the quality of a neuroscientific explanation can then be cashed out in terms of the degree to which it successfully identifies all and only the explanandum’s constituents. But MM has been exposed to severe criticism (e.g., Baumgartner & Gebharter 2016; Baumgartner & Casini 2017; Harbecke 2010; Harinen 2018; Leuridan 2012; Romero 2015). Craver et al. (2021) acknowledge that MM has certain problems. They insist, however, that a lot of the criticism is unfounded because critics fail to properly distinguish between metaphysical and epistemological aspects of constitution. In response, they develop a new theory stating that, metaphysically, constituents are characterized by being causally between a phenomenon’s input and output conditions and that, epistemologically, constituents can be discovered by “a novel ‘matched interlevel experiments’ (MIE) criterion that retains the spirit of MM without conceptual confusion” (8809).

This new theory is currently gaining considerable traction in various fields. In the philosophy of medicine, for example, Varga (2023: 13) advocates it as a means of clarifying how to generate biomedical understanding by keeping separate “a horizontal (causal) dimension and a vertical (part-whole) dimension” in difference-making relationships. In the philosophy of biology, it has been endorsed by Weber (2022) and, in the literature on mechanistic explanation, by Krickel et al. (2023). Moreover, the new theory has been widely adopted in the literature on extended cognition and mind. Parise et al. (2023: 5) maintain that MIE is helpful in planning experiments determining the boundaries of cognitive processes. Smart (2022) argues that MIE establishes that a wearable holographic device and the holograms it produces are constituents of the human cognitive process of protein structure prediction. Gillett et al. (2022: 7) contend that the “reformulated version of MM works in practise and can be used effectively to determine the boundaries of cognition” and they “urge proponents and opponents of [extended cognition] to use this modified version of MM in other putative cases to continue to push the debate forward.”

The first part of our paper critically assesses the merits of the new theory relative to the core question Craver set out to answer in his (2007). On the one hand, we find that it does not retain the spirit of MM. Contrary to MM, the new theory does not establish constitution as a relevance relation different from causation; rather, it yields that constitutive explanation just is (a kind of) causal explanation. In addition, MIE does not demarcate between constituents and non-constituents, as it remains entirely silent about non-constituents. Unlike MM, therefore, it provides no basis for distinguishing good from bad constitutive explanations either. On the other hand, we argue that the new theory is not without conceptual confusion, for it is inherently unclear what Craver et al. (2021) mean by “being causally between” a phenomenon’s input and output conditions. We distinguish three possible interpretations of that metaphysical thesis and find that none of them combines coherently with MIE. Overall, this critical part of the paper demonstrates that all attempts to distinguish between causal and non-causal difference-making relations or to demarcate mechanisms—cognitive or other—based on MIE are futile, and it rebuts the value of MIE for generating mechanistic understanding or explanations in the philosophy of medicine, biology, and elsewhere.

The paper’s second part then shows that the upshot of these negative findings is not that any attempt to explicate constitution as a distinctly non-causal relation in a way that demarcates between constituents and non-constituents necessarily falls prey to conceptual problems like MM or MIE. We demonstrate that there does in fact exist a theory of constitution that successfully achieves these objectives, viz. the No De-Coupling theory (NDC; see Baumgartner & Casini 2017).

2. Mutual Manipulability

According to the new mechanist literature (Machamer et al. 2000; Glennan 2002; Bechtel & Abrahamsen 2005; Craver 2007), a mechanistic explanation describes how the joint operation of lower-level entities and activities is responsible for an upper-level phenomenon. This responsibility has several dimensions—spatio-temporal, causal, and hierarchical. In contrast to previous accounts of explanation, which gave a dominant role to causation (cf. Lewis 1986; Salmon 1984; Woodward 2003), causation is but one explanatory dimension among others for mechanists. A phenomenon is mechanistically explained by the hierarchical arrangement of its component entities and activities with respect to the phenomenon and its behaviour as well as by the spatio-temporal configuration of these components and their causal interactions. Hierarchy is the dimension of a mechanistic explanation that is theoretically least understood.

Craver (2007) famously spelled the hierarchical component of an explanation out in terms of the relation of constitution or constitutive relevance. He conceives of constitution as a relevance relation that obtains between an upper-level activity ${\displaystyle \mathrm{\Psi }}$ of a system ${\displaystyle S}$, ${\displaystyle S}$⁠’s ${\displaystyle \mathrm{\Psi }}$⁠-ing, and a lower-level activity ${\displaystyle \mathrm{\Phi }}$ of a spatio-temporal part ${\displaystyle X}$ of ${\displaystyle S}$, ${\displaystyle X}$⁠’s ${\displaystyle \mathrm{\Phi }}$⁠-ing. Craver analyzes that relation in his Mutual Manipulability theory (MM) of constitutive relevance. The following passage provides the most explicit formulation of MM:

In sum, I conjecture that to establish that ${\displaystyle X}$⁠’s ${\displaystyle \mathrm{\Phi }}$⁠-ing is relevant to ${\displaystyle S}$⁠’s ${\displaystyle \mathrm{\Psi }}$⁠-ing it is sufficient that one be able to manipulate ${\displaystyle S}$⁠’s ${\displaystyle \mathrm{\Psi }}$⁠-ing by intervening to change ${\displaystyle X}$⁠’s ${\displaystyle \mathrm{\Phi }}$⁠-ing (by stimulating or inhibiting) and that one be able to manipulate ${\displaystyle X}$⁠’s ${\displaystyle \mathrm{\Phi }}$⁠-ing by manipulating ${\displaystyle S}$⁠’s ${\displaystyle \mathrm{\Psi }}$⁠-ing. To establish that a component is irrelevant, it is sufficient to show that one cannot manipulate ${\displaystyle S}$⁠’s ${\displaystyle \mathrm{\Psi }}$⁠-ing by intervening to change ${\displaystyle X}$⁠’s ${\displaystyle \mathrm{\Phi }}$⁠-ing and that one cannot manipulate ${\displaystyle X}$⁠’s ${\displaystyle \mathrm{\Phi }}$⁠-ing by manipulating ${\displaystyle S}$⁠’s ${\displaystyle \mathrm{\Psi }}$⁠-ing. (Craver 2007: 159)

There are (at least) two reasons why MM is attractive to many. First, it establishes constitution as a relevance relation different from causation. Causation obtains between spatio-temporally non-overlapping entities and it is a one-directional dependence relation, meaning that effects depend on causes but not vice versa. By contrast, according to MM, constitution obtains between spatio-temporally overlapping entities and is a bi-directional dependence relation such that phenomena and constituents mutually depend on each other. Hence, MM grounds a distinctive non-causal type of explanation, which Craver claims to be important and widespread in many sciences, including neuroscience.² Second, MM aims to demarcate between constituents and non-constituents by echoing experimental practice in neuroscience, as reconstructed by Craver (2007: 60, 105, 131, 144). He argues that neuroscientists tend to combine “top-down” and “bottom-up” experiments, which, respectively, manipulate the upper-level phenomenon and measure its lower-level effects, and manipulate a phenomenon’s parts and measure their upper-level effects.

Neuroscientists use these experiments to establish which parts are components in a mechanism and which are not, that is, to distinguish relevant components from mere constitutive correlates, […] sterile effects, and background conditions. (144)

But Craver (2007) does not merely want MM to reflect actual experimental practice, which is error prone and not ideal, rather he wants MM’s demarcations to be normatively adequate (106-107). Therefore, he requires that experimental manipulations meet the standards of ideal interventions as defined by Woodward (2003).³ Ideal interventions on ${\displaystyle S}$⁠’s ${\displaystyle \mathrm{\Psi }}$⁠-ing with respect to ${\displaystyle X}$⁠’s ${\displaystyle \mathrm{\Phi }}$⁠-ing must surgically cause ${\displaystyle S}$⁠’s ${\displaystyle \mathrm{\Psi }}$⁠-ing, such that all causal influence on ${\displaystyle X}$⁠’s ${\displaystyle \mathrm{\Phi }}$⁠-ing, if any, goes via ${\displaystyle S}$⁠’s ${\displaystyle \mathrm{\Psi }}$⁠-ing—and analogously for ideal interventions on ${\displaystyle X}$⁠’s ${\displaystyle \mathrm{\Phi }}$⁠-ing (see Figure 1a). However, recent literature has shown that such ideal interventions on ${\displaystyle S}$⁠’s ${\displaystyle \mathrm{\Psi }}$⁠-ing are impossible. Since ${\displaystyle S}$⁠’s ${\displaystyle \mathrm{\Psi }}$⁠-ing supervenes on its lower-level constituents, all changes in ${\displaystyle S}$⁠’s ${\displaystyle \mathrm{\Psi }}$⁠-ing must be associated with changes in some constituent or other. Hence, manipulations causing changes in ${\displaystyle S}$⁠’s ${\displaystyle \mathrm{\Psi }}$⁠-ing also cause changes on the lower level. If we assume—with Craver (2007) and many others—that constitution is a non-causal relation and that phenomena are not reducible to their constituents, it follows that all manipulations of ${\displaystyle S}$⁠’s ${\displaystyle \mathrm{\Psi }}$⁠-ing are connected to the lower level on causal paths not going through ${\displaystyle S}$⁠’s ${\displaystyle \mathrm{\Psi }}$⁠-ing, in violation of surgicality. Therefore, only non-ideal interventions on phenomena, as in Figure 1b, are possible (Baumgartner & Gebharter 2016). This, in turn, depending on the logical form MM is taken to have, either reduces MM to absurdity or renders it vacuous (Baumgartner & Casini 2017).

Figure 1: Mechanistic diagrams adapted from Craver (2007). Specific variables (e.g., ${\displaystyle \mathrm{\Psi }}(S)$) represent entities’ activities (e.g., $S$⁠’s ${\displaystyle \mathrm{\Psi }}$⁠-ing). Dotted lines stand for spatio-temporal overlap and dashed lines for constitutive relevance. Surgical interventions as in (a) are required by MM, but only non-surgical manipulations as in (b) are possible.

3. The New Proposal

Craver et al. (2021: 8809) acknowledge that the critics of MM “identify some key obstacles in the way of a coherent and systematic understanding of both the metaphysics and the epistemology of constitutive relevance and interlevel experiments,” and they set out to separately clarify epistemological and metaphysical issues with constitutive relevance. They suggest that the problems with MM stem from misrepresentations in diagrams as the ones in Figure 1a. The crisp boundary of the upper-level ellipsis is misleading because phenomena often do not involve a well-defined localized entity ${\displaystyle S}$, rather, “there only is ${\displaystyle \mathrm{\Psi }}$⁠-ing” (8811). Moreover, these diagrams conflate “synchronous spatial inclusion relations between entities and their parts (i.e., between ${\displaystyle S}$ and the ${\displaystyle X}$⁠s), and temporal inclusion relations between mechanistic processes and their parts (i.e., between ${\displaystyle \mathrm{\Psi }}$⁠-ing and ${\displaystyle \mathrm{\Phi }}$⁠-ing)” (8812).

To avoid these problems, Craver et al. replace diagrams as in Figure 1 by diagrams as in Figure 2.

Here, ${\displaystyle \mathrm{\Psi }}$⁠-ing is represented as a process beginning with an input, ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$, and terminating with an output, ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$. Between these temporal endpoints, and a mechanistic level down, is a temporally sequenced causal chain of events, involving the ${\displaystyle X_i}$ and their various ${\displaystyle {\mathrm{\Phi }}_i}$. [Figure 2a] makes clear that the problem of constitutive relevance is that of identifying the components of the process bridging ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ and ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ […] (Craver et al. 2021: 8812)

Figure 2: Revised mechanistic diagrams adapted from Craver et al. (2021).

Contrary to constituents, which Craver et al. still conceive of as activities ${\displaystyle {\mathrm{\Phi }}_i}$ of entities ${\displaystyle X_i}$, phenomena are newly conceptualized as mere input-output relations (without acting entities). The phenomenon ${\displaystyle \mathrm{\Psi }}$⁠-ing is defined by its input and output variables, ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ and ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$.⁴ It is a dependence relation between values of ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ and values of ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$. In between, there is a causal process, or sequence of events instantiating ${\displaystyle X_1}$⁠’s ${\displaystyle {\mathrm{\Phi }}_1}$⁠-ing, ${\displaystyle X_2}$⁠’s ${\displaystyle {\mathrm{\Phi }}_2}$⁠-ing, …, ${\displaystyle X_n}$⁠’s ${\displaystyle {\mathrm{\Phi }}_n}$⁠-ing, each of which may be a complex object, often involving not only the activity of single components but also interactions among multiple components (8812). For notational convenience, we will henceforth abstain from explicitly relativizing variables ${\displaystyle {\mathrm{\Phi }}_i}$ to their acting entities ${\displaystyle X_i}$ and simply write “${\displaystyle {\mathrm{\Phi }}_i}$” instead of “${\displaystyle {\mathrm{\Phi }}_i(X_i)}$” and “${\displaystyle X_i}$⁠’s ${\displaystyle {\mathrm{\Phi }}_i}$⁠-ing.”

Against that background, Craver et al. propose a new theory of constitutive relevance with an epistemological and a metaphysical component. The former provides a sufficient condition to identify constituents. Reconceptualizing phenomena as input-output relations renders ideal interventions on phenomena no more problematic than they are in ordinary causal modeling contexts, because the surgicality requirement only has to be imposed on the variables in the causal structure connecting ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ and ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ (cf. Figure 2b). An ideal intervention on the phenomenon ${\displaystyle \mathrm{\Psi }}$⁠-ing is simply a surgical cause of ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$. Craver et al. contend that three types of ideal interventions and a ‘matching’ condition are jointly sufficient to establish that some ${\displaystyle \mathrm{\Phi }}$ is part of the causal structure connecting ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ to ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ and, thereby, constitutively relevant to ${\displaystyle \mathrm{\Psi }}$⁠-ing. The result is the matched interlevel experiments (MIE) criterion (Craver et al. 2021: 8822, adjusted to our notational convention):

(MIE) To establish that ${\displaystyle \mathrm{\Phi }}$ is constitutively relevant to a mechanism that ${\displaystyle \mathrm{\Psi }}$⁠s, the following experimental results and matching condition are jointly sufficient:

• (CR1i) If an experiment initiates conditions ${\displaystyle {\mathrm{\Psi }}_{\mathrm{\text{in}}}}$ while a bottom-up intervention, ${\displaystyle \mathcal{I}}$, prevents or inhibits ${\displaystyle \mathrm{\Phi }}$, alterations to or prevention of ${\displaystyle \mathrm{\Psi }}$⁠’s terminal conditions, ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$, are detected.

• (CR1e) If a bottom-up intervention, ${\displaystyle \mathcal{I}}$, stimulates ${\displaystyle \mathrm{\Phi }}$, ${\displaystyle \mathrm{\Psi }}$⁠’s terminal conditions, ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ are detected.

• (CR2*) If a top-down experiment initiates conditions ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ and detects ${\displaystyle \mathrm{\Psi }}$⁠’s terminal conditions ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$, ${\displaystyle \mathrm{\Phi }}$ is also detected.

• (Matching) The activities ${\displaystyle {\mathrm{\Phi }}_i}$ activated or inhibited in bottom-up experiments (CR1i and CR1e) must be of the same kind as, and occur within quantitatively overlapping ranges with, the activities ${\displaystyle {\mathrm{\Phi }}_i}$ detected in top-down experiments (CR2*).

The sufficiency of MIE for constitutive relevance is grounded in the metaphysical component of the new theory, which stipulates that constitutive relevance is causal betweenness (8807). Causal betweenness is “the truth-maker for claims about constitutive relevance” (8810). Craver et al. (2021: 8819-8820) take inspiration from Harinen (2018), who views a phenomenon as a causal path ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}⟶{\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ and the problem of constitutive discovery as that of experimentally finding intermediate variables on that path, using experiments as described by (CR1i), (CR1e), and (CR2*).

Before we turn to assessing the merits of Craver et al.’s new theory, one of its features deserves separate emphasis. MIE is sufficient but not necessary for the constitutive nature of ${\displaystyle \mathrm{\Phi }}$, because Craver et al. contend that there are constituents for which not both of (CR1i) and (CR1e) are satisfiable. They illustrate failures of (CR1i) with a redundant mechanism: “humans have two kidneys, each one of which can regulate plasma osmolality on its own” (8824). Even though both kidneys are constitutively relevant to the osmolality phenomenon, (CR1i)-experiments removing one kidney have no effect because the other kidney compensates. Failures of (CR1e) are illustrated with the bottom bracket of a bicycle, which holds the spindle connecting the two arms of the pedal crank system. Craver et al. allege (8824) that the bracket is constitutively relevant to the biking phenomenon even though it cannot be stimulated such that the bicycle moves, that is, even though (CR1e)-experiments are impossible.

4. MIE and the Spirit of MM

Craver et al. (2021: 8809) claim that MIE retains the spirit of MM. Whether that is true, of course, depends on what exactly MM’s spirit is. We cannot provide an exhaustive analysis of that notion here, but it seems clear that the core objectives MM serves in Craver’s (2007) book are core elements of its spirit: first, to establish constitution as a relevance relation that is different from causation; and second, to demarcate between constituents and non-constituents. In what follows, we argue that MIE meets neither of these objectives.

Contrary to MM, MIE does not construe a phenomenon ${\displaystyle \mathrm{\Psi }}$⁠-ing and its constituent ${\displaystyle \mathrm{\Phi }}$ as mereologically related entities that bi-directionally depend on one another. Instead, ${\displaystyle \mathrm{\Phi }}$ (one-directionally) depends on ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$, and ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ depends on ${\displaystyle \mathrm{\Phi }}$, but the phenomenon itself—the input-output relation—is no longer part of the dependence structure. Manipulating ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ may induce changes in ${\displaystyle \mathrm{\Phi }}$ and manipulating ${\displaystyle \mathrm{\Phi }}$ may induce changes in ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$. However, changes in ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ and in ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ are not changes in the input-output relation, that is, in the phenomenon, as this would require changing the mapping of values of ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ onto values of ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$, which in turn would amount to altering the causal structure itself. To illustrate with Craver et al.’s leading example, the input to the locomotion phenomenon in C. elegans can be manipulated by, say, tapping the worm on its head, whereas manipulating the locomotion phenomenon itself requires, for instance, changing the wiring of the worm’s brain. Yet, manipulations of the phenomenon are irrelevant for MIE. Without mutual or bi-directional dependence, what we are left with is ordinary causal dependence among mereologically independent entities. Correspondingly, the problem of constitutive inference for MIE is nothing other than the problem of finding the causal structure between ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ and ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$, for which the literature on causal discovery provides various ready-made solutions. This is incompatible with MM’s objective of establishing a new type of explanation. For MIE, constitutive explanation just is (a kind of) causal explanation.⁵

The second core objective of MM is to demarcate between those spatio-temporal parts of a phenomenon that are constitutively relevant and those that are not. To this end, MM must ground the inference to both constitutive relevance and irrelevance; in other words, it must furnish both a sufficient and a necessary condition for constitution. Indeed, the passage most explicitly stating MM, which we quoted in §2, does exactly that: it introduces a sufficient condition for constitutive relevance and a sufficient condition for constitutive irrelevance, which, taken jointly, yields a sufficient as well as a necessary condition for constitution. Unfortunately, though, there are other passages where Craver says that MM offers only a sufficient condition for constitution and he formulates the account with a mere “if” (e.g., Craver 2007: 141, 154).

While the passages explicitly addressing the logical strength of MM are difficult to interpret consistently, the argumentative use Craver (2007) actually makes of MM leaves no room for interpretation. If MM were only sufficient, it could only be used to identify constituents but not non-constituents, because if a phenomenon and one of its parts fail to be mutually manipulable, MM, understood as a mere sufficient condition, entails nothing on the constitutive nature of that part. Yet, Craver unequivocally uses MM to identify non-constituents, too. Violation of MM is repeatedly taken to warrant an inference to a part of a phenomenon being a sterile effect, an isolated part, or a mere correlate (Craver 2007: 149, 156, 259). An exemplary passage is the following:

One can exclude sterile effects and other mere correlates by requiring that the experiment satisfy CR1 [i.e., the bottom-up manipulability component of MM]. […] Performance of cognitive tasks, for example, is routinely correlated with hemodynamic changes, but this does not mean that the hemodynamic changes are part of the mechanism involved in task performance (as all MRI researchers know). Hemodynamic changes can be ruled out as components of the mechanism on the grounds that intervening to prevent the increase in blood flow during a task will not prevent one from performing the task. (156)

What is more, Craver is very clear that he wants his theory to demarcate constituents from non-constituents (Craver 2007: 60, 105, 112, 144) and to demarcate the boundaries of mechanisms (Craver 2007: 141, 259). These demarcations are then used for assessing to what degree neuroscientific explanations mention all and only constituents of the explanandum (Craver 2007: 111, 259), which, in turn, is Craver’s quality criterion for these explanations. Of course, only an account that furnishes a sufficient as well as a necessary condition can deliver demarcations and identify all and only constituents.

That is, in order to make sense of a maximally large portion of Craver’s discussion of constitution and neuroscientific explanation, MM must be interpreted to deliver a sufficient and a necessary condition for constitutive relevance, which, correspondingly, is the interpretation adopted by many commentators (e.g., Baumgartner & Gebharter 2016; Baumgartner & Casini 2017; Krickel, 2018a: 98; Krickel, 2018b; Harbecke 2010: 271). This interpretation is confirmed by Craver et al. (2021: fn 8) who say, in formal explicitness, that MM entails that the conjunction of non-manipulability from the top down and of non-manipulability from the bottom up is sufficient for constitutive irrelevance, which is equivalent to the disjunction of top-down and bottom-up manipulability being necessary for constitutive relevance.⁶

By contrast, it is clear that MIE only furnishes a sufficient condition for constitutive relevance and no sufficient condition for irrelevance, that is, no necessary condition for constitutive relevance. MIE allows to identify constituents but remains silent about non-constituents. If ${\displaystyle \mathrm{\Phi }}$ violates one of (CR1i), (CR1e), (CR2*), and (Matching), nothing follows on its constitutive nature. Correspondingly, if a scientist explains a phenomenon ${\displaystyle \mathrm{\Psi }}$⁠-ing with recourse to some ${\displaystyle {\mathrm{\Phi }}_i}$ that does not satisfy all conditions of MIE, it does not follow that the explanation is bad, because ${\displaystyle {\mathrm{\Phi }}_i}$ might still be a constituent, yet one that cannot be recovered by the experiments described in MIE. Contrary to MM, MIE provides no inferential leverage to demarcate between constituents and sterile effects, isolated parts, fictional posits, etc.⁷ Whether constitutive explanations contain all and only the constituents of phenomena cannot be determined based on MIE. In replacing MM by MIE, the primary purpose Craver’s theory of constitution was designed to serve is given up: to distinguish good constitutive explanations (in neuroscience) from bad ones.

In sum, whatever the full spirit of MM might be, a theory like Craver et al.’s new proposal, which treats constitution as a form of causation and provides no handle for demarcation, is undoubtedly not in the spirit of MM.

5. Causal Betweenness and Conceptual Confusion

Not following the spirit of a predecessor theory is not itself problematic for a new theory, if that theory turns out to be valuable in its own right. Unfortunately, Craver et al.’s new proposal raises more questions than it answers. In fact, despite avoiding MM’s reliance on impossible interventions, it still fails to provide a coherent account of constitution. The source of the problem is that it is unclear how exactly to interpret the metaphysical thesis that constitution is causal betweenness. There is textual support for three different interpretations, each being problematic for different reasons.

5.1. The Path Interpretation

According to the first and most straightforward interpretation, a constituent ${\displaystyle \mathrm{\Phi }}$ being causally between a phenomenon’s input and output conditions, ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ and ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$, simply means that ${\displaystyle \mathrm{\Phi }}$ is on a directed causal path from ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ to ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$. This interpretation is supported by all of Craver et al.’s (2021) diagrams and by the fact that they follow Harinen’s (2018) understanding of the three experimental procedures in MIE (8819). Harinen endorses the “path” interpretation of causal betweenness (as already emphasized by Weinberger 2019) and views the goal of those procedures to be to experimentally find intermediate variables on the causal path ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}⟶{\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$. It is thus plausible that Craver et al. interpret betweenness in the same way.

The path interpretation is in line with Craver et al.’s claim that MIE is sufficient for constitution, because (CR1i), (CR1e), and (CR2*), jointly, indeed suffice to infer a path ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}⟶\mathrm{\Phi }⟶{\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$. To see this, consider Figure 3, which collects the causal structures compatible with the evidence generated by the experiments in (CR1i), (CR1e), and (CR2*). The result of (CR1i) can be accounted for by one or more paths from ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ to ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$, at least one via ${\displaystyle \mathrm{\Phi }}$, or by a collider at ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$. Experiment (CR1e) establishes a path from ${\displaystyle \mathrm{\Phi }}$ to ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$, while remaining silent about ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$. The result of (CR2*) is compatible with there being at least one path from ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ to ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ via ${\displaystyle \mathrm{\Phi }}$ or a common cause structure. It follows that any model compatible with the evidence produced by all experiments must feature at least one path ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}⟶\mathrm{\Phi }⟶{\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$.

Figure 3: Causal structures compatible with the data generated by the experiments described in (CRi1), (CR1e), and (CR2*), respectively. ${\mathcal{I}}_1$ to ${\mathcal{I}}_4$ represent the interventions required by those experiments.

However, Figure 3 also shows that this conclusion does not require all of (CR1i), (CR1e), and (CR2*). Either one of (CR1i) and (CR1e) establishes a path ${\displaystyle \mathrm{\Phi }⟶{\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$, while (CR2*) alone demonstrates that there is a path ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}⟶\mathrm{\Phi }}$, which, jointly, yields a path ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}⟶\mathrm{\Phi }⟶{\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$. Hence, if Craver et al. (2021) really have the path interpretation of causal betweenness in mind, their list of experiments contains a redundancy. Choosing either the combination of (CR1e) & (CR2*) or the combination of (CR1i) & (CR2*) would be sufficient to establish a path. And MIE contains yet another condition: (Matching). Relative to the path interpretation, it is mysterious why Craver et al. impose (Matching), as there is no work left for that condition. All that matters for the existence of a path is that some value of ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ makes a difference to some value of ${\displaystyle \mathrm{\Phi }}$, and that some value of ${\displaystyle \mathrm{\Phi }}$, not necessarily the same one, makes a difference to some value of ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$. That Craver et al. explicitly require (Matching) on top of three experiments, two of which would already suffice, suggests that they might not interpret causal betweenness in terms of being on a directed path from ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ to ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ after all.

5.2. The Process Interpretation

A second interpretation can be derived from what Craver et al. say about their preferred theory of causation. Although MIE exclusively draws on inference tools from a causal modeling tradition that understands causation in difference-making terms, Craver et al. (2021) do not subscribe to a difference-making theory of causation. Instead, they express a preference for a production theory of causation (e.g. Glennan 2017). They contend that a “causal dependence requires a productive process between an effect and its cause” (8823). There is a large and diverse literature on causal processes (Russell 1948; Salmon 1984; Dowe 2000; Steel 2007). Processes are widely understood as relations between events or states (or chains thereof) rather than variables. While Craver et al. do not provide a full-blown analysis of productivity, they do say that they “understand productivity in a way that allows for productive continuity” (8823). They stipulate that for “B to lie causally between A and C, there must be a process by which A contributes to the production of B, and a process by which B contributes to the production of C” (8823).

In this second interpretation, ${\displaystyle \mathrm{\Phi }}$ being causally between ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ and ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ could mean that events represented by a value ${\displaystyle {\psi }_{\mathrm{i}\mathrm{n}}^i}$ of ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$, a value ${\displaystyle {\varphi }^j}$ of ${\displaystyle \mathrm{\Phi }}$ and a value ${\displaystyle {\psi }_{\mathrm{o}\mathrm{u}\mathrm{t}}^k}$ of ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$, respectively, can be connected by a process with productive continuity. Adopting the notational convention that “${\displaystyle {\varphi }^j}$”⁠ is ⁠short⁠ for⁠ “${\displaystyle \mathrm{\Phi }={\varphi }^j}$,” a process can be modeled as an ordered sequence of events, or “stages” (8819), ${\displaystyle \langle {\psi }_{\mathrm{i}\mathrm{n}}^i,\dots ,{\varphi }^j,\dots ,{\psi }_{\mathrm{o}\mathrm{u}\mathrm{t}}^k\rangle }$, where a change at each stage—alone or jointly with other background conditions—makes a difference to its successor.

Variables may well be connected by a directed causal path via mediators without there being a process connecting concrete values of these variables. An example of such a scenario is due to Neapolitan (2004: 49, 111): finasteride (${\displaystyle F}$) is a drug that lowers testosterone levels (${\displaystyle T}$), and testosterone levels below some threshold ${\displaystyle \theta }$ cause hair growth (${\displaystyle G}$); meaning there is a directed path ${\displaystyle F⟶T⟶G}$. Yet, if finasteride cannot lower testosterone below ${\displaystyle \theta }$, then ${\displaystyle F}$, ${\displaystyle T}$, and ${\displaystyle G}$ have no values ${\displaystyle f^i}$, ${\displaystyle t^j}$, and ${\displaystyle g^k}$ that could be connected by a process ${\displaystyle \langle f^i,t^j,g^k\rangle }$. That is, even though there is a directed path from ${\displaystyle F}$ to ${\displaystyle G}$, no value of ${\displaystyle F}$ can make a difference to ${\displaystyle G}$ because of a threshold effect at the mediating link.

It follows that, if causal betweenness is understood in terms of the “process” interpretation, establishing betweenness requires not only establishing the existence of a directed path ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}⟶\mathrm{\Phi }⟶{\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$, but also that values of these variables can be connected by a process ${\displaystyle \langle {\psi }_{\mathrm{i}\mathrm{n}}^i,{\varphi }^j,{\psi }_{\mathrm{o}\mathrm{u}\mathrm{t}}^k\rangle }$. In other words, it must be shown that there is some context—meaning some configuration of values of background conditions—where a value ${\displaystyle {\varphi }^j}$ of ${\displaystyle \mathrm{\Phi }}$ is both the effect of a value ${\displaystyle {\psi }_{\mathrm{i}\mathrm{n}}^i}$ of ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ and the cause of a value ${\displaystyle {\psi }_{\mathrm{o}\mathrm{u}\mathrm{t}}^k}$ of ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$. If that holds, the path ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}⟶\mathrm{\Phi }⟶{\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ is said to be instantiated by an active causal route (Hitchcock 2001) connecting the input to the output via the constituent. If we interpret the constraint, expressed in (Matching), that activities ${\displaystyle {\mathrm{\Phi }}_i}$ activated in bottom-up and top-down experiments must match as demanding that the same values of ${\displaystyle {\mathrm{\Phi }}_i}$ figure in both types of experiments, ensuring the existence of an active causal route can be seen to be exactly the purpose of (Matching).

Establishing the existence of an active causal route is a notoriously hard problem, since it presupposes much background knowledge about the structure in question (see below). Still, there exist well-known scientific approaches to address this problem, for instance, back-door adjustment in the graphical literature (Pearl 2009: 79), mediation analysis in the potential outcomes framework (e.g. Vanderweele et al. 2014), or tests of contributing causation in the experimental literature (e.g. Woodward 2003: 50). The latter approach—on the assumption that the existing paths between a cause and an effect are known, that interventions are surgical, and that the background conditions are stable throughout the experiment—is particularly well suited to test whether one such path can be instantiated by an active route. Craver et al. do not mention any of the existing approaches but instead attempt to develop their own. In the remainder of this subsection, however, we will argue that MIE is not sufficient to establish that there is an active causal route from ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ to ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ via ${\displaystyle \mathrm{\Phi }}$.

To demonstrate this, we introduce a concrete causal structure, in Figure 4, for which all conditions of MIE are satisfied and yet there exists no active route through ${\displaystyle \mathrm{\Phi }}$. The structure contains two paths from ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ to ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$, one via ${\displaystyle \mathrm{\Phi }}$ and one via another intermediate link ${\displaystyle \mathrm{\Omega }}$.⁸ Moreover, it features a context variable ${\displaystyle \mathrm{\Delta }}$ that represents configurations of background conditions. ${\displaystyle \mathrm{\Delta }}$ can take three values ${\displaystyle \{{\delta }^1,{\delta }^2,{\delta }^3\}}$; all other variables are binary. ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ and ${\displaystyle \mathrm{\Delta }}$ are exogenous and thus independent of one another; all other variables are endogenously determined as described in Equations (1), (2), and (3). In addition, all variables, except for the background condition ${\displaystyle \mathrm{\Delta }}$, can be altered through surgical interventions, which, for simplicity, are not explicitly modeled in the equations. Moreover, to avoid unnecessary complications, we assume that the structure is deterministic.

Figure 4: A context-sensitive, two-path structure and its governing equations. Concatenation means conjunction, “${\displaystyle \mathrm{\vee }}$” disjunction, and “${\displaystyle \mathrm{\leftrightarrow }}$” equivalence.

The property of this structure relevant to our argument is that the paths ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}⟶\mathrm{\Phi }}$ and ${\displaystyle \mathrm{\Phi }⟶{\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ can only be activated in different background contexts. According to Equation (2), ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}⟶\mathrm{\Phi }}$ is only active when ${\displaystyle \mathrm{\Delta }}$ happens to take value ${\displaystyle {\delta }^3}$, whereas (3) stipulates that ${\displaystyle \mathrm{\Phi }⟶{\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ is only active when ${\displaystyle \mathrm{\Delta }}$ takes values ${\displaystyle {\delta }^1}$ or ${\displaystyle {\delta }^2}$. That is, ${\displaystyle \mathrm{\Phi }}$ is only sensitive to changes in ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ in context ${\displaystyle {\delta }^3}$, and ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ is only sensitive to changes in ${\displaystyle \mathrm{\Phi }}$ in contexts ${\displaystyle {\delta }^1}$ and ${\displaystyle {\delta }^2}$. It follows that there exists no context where causal influence is transmitted from ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ to ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ via ${\displaystyle \mathrm{\Phi }}$.

The experiments of MIE only succeed if they happen to be conducted in backgrounds where ${\displaystyle \mathrm{\Delta }}$ takes values such that the experimental interventions on ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ and ${\displaystyle \mathrm{\Phi }}$ have the downstream effects expressed in Equations (1) to (3). If experiment (CR1i) is performed when ${\displaystyle \mathrm{\Delta }}$ takes value ${\displaystyle {\delta }^1}$, an intervention ${\displaystyle {\mathcal{I}}_1}$ first sets ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ to ${\displaystyle {\psi }_{\mathrm{i}\mathrm{n}}^1}$, which triggers ${\displaystyle {\omega }^1}$ by virtue of Equation (1). According to (2), ${\displaystyle {\delta }^1}$ causes ${\displaystyle {\varphi }^1}$ independently of ${\displaystyle {\psi }_{\mathrm{i}\mathrm{n}}^1}$, which yields ${\displaystyle {\delta }^1{\omega }^1{\varphi }^1}$ and, as per (3), causes ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ to take value ${\displaystyle {\psi }_{\mathrm{o}\mathrm{u}\mathrm{t}}^1}$. Next, an intervention ${\displaystyle {\mathcal{I}}_2}$ sets ${\displaystyle \mathrm{\Phi }}$ to ${\displaystyle {\varphi }^0}$, such that ${\displaystyle {\delta }^1{\omega }^1{\varphi }^1}$ is no longer given, meaning that ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ turns to ${\displaystyle {\psi }_{\mathrm{o}\mathrm{u}\mathrm{t}}^0}$. It follows that the conditions of (CR1i) are satisfied without an active route through ${\displaystyle \mathrm{\Phi }}$. Experiment (CR1e) is straightforward: if conducted in a context where ${\displaystyle {\delta }^2}$ is given, an intervention ${\displaystyle {\mathcal{I}}_3}$ sets ${\displaystyle \mathrm{\Phi }}$ to ${\displaystyle {\varphi }^1}$, and ${\displaystyle {\delta }^2{\varphi }^1}$ causes ${\displaystyle {\psi }_{\mathrm{o}\mathrm{u}\mathrm{t}}^1}$ subject to (3). Finally, if experiment (CR2*) is run when the background is ${\displaystyle {\delta }^3}$, an intervention ${\displaystyle {\mathcal{I}}_4}$ sets ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ to ${\displaystyle {\psi }_{\mathrm{i}\mathrm{n}}^1}$, which produces ${\displaystyle {\omega }^1}$ and ${\displaystyle {\varphi }^1}$. However, when ${\displaystyle \mathrm{\Delta }}$ takes value ${\displaystyle {\delta }^3}$, ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ is only sensitive to changes in ${\displaystyle \mathrm{\Omega }}$, not in ${\displaystyle \mathrm{\Phi }}$. That means that also the conditions in (CR2*) are satisfied without an active route through ${\displaystyle \mathrm{\Phi }}$. Moreover, the values to which ${\displaystyle \mathrm{\Phi }}$ is set in the activation and the detection experiments match, in compliance with (Matching). In sum, MIE is satisfied without causal influence ever being transmitted on an active route through ${\displaystyle \mathrm{\Phi }}$. And if there cannot be such an active route, there cannot be events instantiating the path ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}⟶\mathrm{\Phi }⟶{\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ such that they are connected by a process with productive continuity.

This example shows that, under the process interpretation, MIE is insufficient to establish constitution, contrary to what Craver et al. claim. Ensuring that variables on a causal path are set to matching values does not ensure that this path can be instantiated by an active route. But a test of contributing causation could help out. If the paths ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}⟶\mathrm{\Omega }⟶{\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ and ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}⟶\mathrm{\Phi }⟶{\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ have been uncovered via path tests as described in the previous subsection, the existence of an active route along one of these paths can then be investigated by blocking the other path (e.g. by suppressing the middle link) in a stable background context and checking if a surgical change of ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ correlates with a change in ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$. In the case of our example, this sort of test reveals that, if we surgically intervene on ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ (by setting it to ${\displaystyle {\psi }_{\mathrm{i}\mathrm{n}}^1}$ or ${\displaystyle {\psi }_{\mathrm{i}\mathrm{n}}^0}$) and block the path ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}⟶\mathrm{\Omega }⟶{\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ by forcing ${\displaystyle \mathrm{\Omega }}$ to take the value it would take if it was not for the intervention on ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ (by fixing it to ${\displaystyle {\omega }^0}$ or ${\displaystyle {\omega }^1}$, respectively), then the intervention on ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ cannot make a difference to ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ in any of the background contexts ${\displaystyle {\delta }_1}$, ${\displaystyle {\delta }_2}$, and ${\displaystyle {\delta }_3}$. This shows that there is no active route, and thus no process, from ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ to ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ via ${\displaystyle \mathrm{\Phi }}$. By contrast, if we intervene to block ${\displaystyle \mathrm{\Phi }}$ by fixing it, say, to value ${\displaystyle {\varphi }^0}$, it is still possible for ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ to make a difference to ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ via ${\displaystyle \mathrm{\Omega }}$, namely in context ${\displaystyle {\delta }^3}$, for when ${\displaystyle \mathrm{\Delta }}$ happens to take value ${\displaystyle {\delta }^3}$, interventions on ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}}$ are associated with changes in ${\displaystyle {\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ despite ${\displaystyle \mathrm{\Phi }}$ being fixed to ${\displaystyle {\varphi }^0}$. It follows that the path ${\displaystyle {\mathrm{\Psi }}_{\mathrm{i}\mathrm{n}}⟶\mathrm{\Omega }⟶{\mathrm{\Psi }}_{\mathrm{o}\mathrm{u}\mathrm{t}}}$ can be instantiated by an active route. In sum, subject to the process interpretation, only ${\displaystyle \mathrm{\Omega }}$ is a constituent, but MIE erroneously identifies ${\displaystyle \mathrm{\Phi }}$ as a constituent as well.

6. No De-Coupling

We end this paper with a positive outlook on the prospects of meeting MM’s original objectives. The severe problems encountered by MM and MIE are not to be taken as evidence that it would be impossible to render constitution as a distinctly non-causal relation in a way that demarcates between constituents and non-constituents without falling into conceptual traps. In fact, there exists a theory of constitution that accomplishes exactly that, viz. the No De-Coupling theory (NDC; Baumgartner & Casini 2017).¹² What is more, NDC has been argued to allow for more faithful reconstructions of actual scientific practice than MM (van Eck 2019; Serban & Holm 2020). This section thus reviews the basics of NDC and shows how it meets MM’s objectives.

The main problem of MM arises from its attempt to define “${\displaystyle \mathrm{\Phi }}$ is constitutively relevant to ${\displaystyle \mathrm{\Psi }}$” in terms of the possible existence of an ideal intervention on ${\displaystyle \mathrm{\Psi }}$ that changes ${\displaystyle \mathrm{\Phi }}$. As phenomena and constituents spatio-temporally overlap and, thus, are assumed not to be causally related, all causes (i.e. intervention candidates) ${\displaystyle Z_i}$ of ${\displaystyle \mathrm{\Psi }}$ that change ${\displaystyle \mathrm{\Phi }}$ cause ${\displaystyle \mathrm{\Psi }}$ and ${\displaystyle \mathrm{\Phi }}$ on two different directed paths ${\displaystyle \langle Z_i,\mathrm{\Psi }\rangle }$ and ${\displaystyle \langle Z_i,\mathrm{\Phi }\rangle }$, where a directed path simply is an ordered ${\displaystyle n}$-tuple of variables (Spirtes et al. 2000: 7). That ${\displaystyle \langle Z_i,\mathrm{\Psi }\rangle }$ and ${\displaystyle \langle Z_i,\mathrm{\Phi }\rangle }$ are different paths follows from the fact that the ${\displaystyle n}$-tuples are different because their second elements, ${\displaystyle \mathrm{\Psi }}$ and ${\displaystyle \mathrm{\Phi }}$, are non-identical. A cause ${\displaystyle Z_i}$ with two effects ${\displaystyle \mathrm{\Psi }}$ and ${\displaystyle \mathrm{\Phi }}$ on two different paths is a common cause of ${\displaystyle \mathrm{\Psi }}$ and ${\displaystyle \mathrm{\Phi }}$ (Spirtes et al. 2000: 22).¹³ Since ${\displaystyle Z_i}$ is just a placeholder for any cause of ${\displaystyle \mathrm{\Psi }}$ that changes ${\displaystyle \mathrm{\Phi }}$, it follows that all such causes are common causes of ${\displaystyle \mathrm{\Psi }}$ and ${\displaystyle \mathrm{\Phi }}$. But common causes are not ideal interventions. Therefore, every cause of ${\displaystyle \mathrm{\Psi }}$ that changes ${\displaystyle \mathrm{\Phi }}$ fails to be an ideal intervention, meaning there cannot be any ideal interventions as required by MM (Romero 2015; Baumgartner & Gebharter 2016).

This predicament of MM is the starting point of NDC. According to NDC, the characteristic feature of constitution is not the possibility to manipulate phenomena and constituents by ideal interventions but the impossibility to do so. An upper-level phenomenon ${\displaystyle \mathrm{\Psi }}$ is realized on a lower level by a set of constituents ${\displaystyle \mathbf{\Phi }=\{{\mathrm{\Phi }}_1,\dots ,{\mathrm{\Phi }}_n\}}$. If, as is usual, ${\displaystyle \mathrm{\Psi }}$ is assumed to non-reductively supervene on ${\displaystyle \mathbf{\Phi }}$ (e.g. Glennan 1996; Eronen 2012), it follows that every change induced on ${\displaystyle \mathrm{\Psi }}$ is necessarily associated with a change in some ${\displaystyle {\mathrm{\Phi }}_i\in \mathbf{\Phi }}$. As phenomena and their constituents are not causally related, every cause inducing a change in ${\displaystyle \mathrm{\Psi }}$ is necessarily causing a change in some ${\displaystyle {\mathrm{\Phi }}_i\in \mathbf{\Phi }}$ on a different path. That is, every cause of ${\displaystyle \mathrm{\Psi }}$ necessarily is a common cause of ${\displaystyle \mathrm{\Psi }}$ and at least one ${\displaystyle {\mathrm{\Phi }}_i\in \mathbf{\Phi }}$, meaning a phenomenon and the set of its constituents are unbreakably coupled via common causes. According to NDC, this is the defining feature of constitution.

To flesh this basic idea out into a full-blown theory of constitution, two further constraints and an operationalization of the notion of unbreakability are needed. First, a parthood constraint must be imposed: not all sets of variables that are coupled via common causes with the phenomenon ${\displaystyle \mathrm{\Psi }}$ are constituents but only those that contain spatio-temporal parts of ${\displaystyle \mathrm{\Psi }}$. Second, a minimality constraint is required ensuring that ${\displaystyle \mathbf{\Phi }}$ does not contain redundant variables, that is, variables that can be removed from ${\displaystyle \mathbf{\Phi }}$ such that the remaining set is still coupled via common causes with the phenomenon. Third, unbreakability can be operationalized in terms of the phenomenon ${\displaystyle \mathrm{\Psi }}$ and the elements of ${\displaystyle \mathbf{\Phi }}$ remaining coupled via common causes across all expansions of the set of analyzed variables ${\displaystyle \mathbf{V}}$. In other words, no matter what additional causes of ${\displaystyle \mathrm{\Psi }}$ are integrated into the analysis, all of these added causes of ${\displaystyle \mathrm{\Psi }}$ are common causes of ${\displaystyle \mathrm{\Psi }}$ and at least one ${\displaystyle {\mathrm{\Phi }}_i\in \mathbf{\Phi }}$—no surgical cause of ${\displaystyle \mathrm{\Psi }}$ can be found by expanding ${\displaystyle \mathbf{V}}$.

If we let a complex instance of a variable set ${\displaystyle \mathbf{\Phi }}$ designate the occurrence or process (in a particular spatio-temporal region) represented by a complex value assignment ${\displaystyle {\mathrm{\Phi }}_1={\varphi }_1,\dots ,{\mathrm{\Phi }}_n={\varphi }_n}$ to all elements of ${\displaystyle \mathbf{\Phi }}$, the No De-Coupling theory of constitution can be stated as follows (Baumgartner & Casini 2017):

(NDC) ${\displaystyle {\mathrm{\Phi }}_1}$ is constitutively relevant to ${\displaystyle \mathrm{\Psi }}$ if, and only if, there exists a variable set ${\displaystyle \mathbf{V}}$ containing ${\displaystyle \mathrm{\Psi }}$ and a proper subset ${\displaystyle \mathbf{\Phi }=\{{\mathrm{\Phi }}_1,\dots ,{\mathrm{\Phi }}_n\}}$, such that the following conditions hold:

• (Parthood) For every complex instance of ${\displaystyle \mathbf{\Phi }}$, there is an instance of ${\displaystyle \mathrm{\Psi }}$ such that the former is a spatio-temporal part of the latter.

• (Coupling) Every cause of ${\displaystyle \mathrm{\Psi }}$ in ${\displaystyle \mathbf{V}}$ is a common cause of ${\displaystyle \mathrm{\Psi }}$ and at least one ${\displaystyle {\mathrm{\Phi }}_i}$ in ${\displaystyle \mathbf{\Phi }}$.

• (Minimality) There does not exist a ${\displaystyle {\mathrm{\Phi }}_k\in \mathbf{\Phi }}$ such that ${\displaystyle \mathbf{\Phi }\backslash \{{\mathrm{\Phi }}_k\}}$ satisfies (Coupling).

• (No De-Coupling) The Coupling of ${\displaystyle \mathbf{\Phi }}$ and ${\displaystyle \mathrm{\Psi }}$ subsists in all expansions of ${\displaystyle \mathbf{V}}$.

Less formally, NDC defines a constituent to be a member of a minimal set of spatio-temporal parts of the phenomenon that is unbreakably common-cause coupled with the phenomenon.

NDC has various features setting it apart from other theories of constitution, but most of them are not relevant for our current purposes (for details see Baumgartner & Casini 2017; van Eck 2019; Serban & Holm 2020). What matters here are only those of its characteristics that need to be understood in order to see (I) that NDC does in fact establish constitution as distinctly non-causal dependence relation, (II) that it demarcates between constituents and non-constituents, and (III) that it is conceptually sound. Let us hence take these three points in turn.

(I) We begin with the non-causal nature of constitution. NDC defines constitution based on (Parthood), which requires phenomena and constituents to be mereologically related. As causation is commonly assumed to obtain among mereologically unrelated entities only, (Parthood) entails that no ${\displaystyle \mathrm{\Phi }}$ that NDC identifies as constituent of a phenomenon ${\displaystyle \mathrm{\Psi }}$ can be an ordinary cause or effect of ${\displaystyle \mathrm{\Psi }}$. However, despite being widely assumed, only few theories of causation contain explicit clauses stipulating that causes and effects must not spatio-temporally overlap. Some authors even allow for abnormal forms of causal dependence that obtain among overlapping entities (e.g. Leuridan 2012). Hence, (Parthood) does provide some, albeit not conclusive, support for the non-causal nature of NDC-defined constitution.

Further support is offered by the fact that NDC defines constitution in terms of all causes of the phenomenon, across all variable set expansions, not being interventions but common causes. That is, constitution is a universally defined relation, or alternatively, it is defined based on the non-existence of possible interventions. By contrast, theories of causation analyze causation in terms of the existence of ${\displaystyle \mathcal{P}}$, where ${\displaystyle \mathcal{P}}$, depending the theoretical framework, stands for possible interventions, for probabilistic or counterfactual difference-making scenarios, or for processes or energy transfer, etc. That is, causation is routinely rendered as existentially defined relation. This, in turn, means that the negation of causation—causal irrelevance—becomes universally defined. More specifically, if “${\displaystyle X}$ is causally relevant to ${\displaystyle Y}$” is defined via ${\displaystyle \mathrm{\exists }x\mathcal{P}x}$, then, by contraposition, “${\displaystyle X}$ is causally irrelevant to ${\displaystyle Y}$” is rendered in terms of ${\displaystyle \mathrm{\neg }\mathrm{\exists }x\mathcal{P}x}$, viz. in terms of ${\displaystyle \mathrm{\forall }x\mathrm{\neg }\mathcal{P}x}$. For example, Woodward’s (2003) interventionist theory of causation cashes out “${\displaystyle X}$ is causally irrelevant to ${\displaystyle Y}$” based on the non-existence of ideal interventions on ${\displaystyle X}$ with respect to ${\displaystyle Y}$. This is exactly how NDC defines “${\displaystyle \mathrm{\Phi }}$ is constitutively relevant to ${\displaystyle \mathrm{\Psi }}$.” Of course, NDC does not yield a notion of constitution that is co-extensional with causal irrelevance. After all, constitution is a robust dependence relation, whereas the extension of causal irrelevance encompasses many independent entities. Still, the extension of NDC-constitution is a proper subset of the extension of the notion of causal irrelevance (as commonly defined).

In addition, Baumgartner and Casini (2017) characterize NDC as an abductive theory because it reconstructs an inference to constitution as an inference to the best explanation. A phenomenon and its constituents have highly correlated behavior patterns. That strong correlation can be accounted for by the mere fact that phenomena and constituents are coupled via common causes. That is, pure causal models, which do not contain any constitutive dependencies, can faithfully reproduce the empirical data generated by mechanistic systems. But pure causal models have an important explanatory gap: they cannot explain why the coupling of phenomena and constituents cannot be broken. NDC supplies a relevance relation, different from causation, that fills precisely this explanatory gap. Models introducing NDC-constitution not only account for the empirical data relative to some given set of analyzed variables but they also explain why upper- and lower-level variables remain coupled across all expansions of analyzed variable sets.

(II) The next point is demarcation. That NDC furnishes a criterion demarcating constituents and non-constituents follows from the fact that its definiens is both sufficient and necessary for constitutive relevance. ${\displaystyle \mathrm{\Phi }}$ is constitutively relevant to ${\displaystyle \mathrm{\Psi }}$ if, and only if, there exists a variable set ${\displaystyle \mathbf{V}}$ containing ${\displaystyle \mathrm{\Psi }}$ and a subset ${\displaystyle \mathbf{\Phi }}$, such that ${\displaystyle \mathrm{\Phi }\in \mathbf{\Phi }}$ and NDC’s four conditions are satisfied. In other words, containment in a set complying with (Parthood), (Coupling), (Minimality), and (No De-Coupling) demarcates between constituents and non-constituents. According to this criterion, for example, both kidneys are constituents of the osmolality phenomenon because both of them are contained in some minimal set ${\displaystyle \mathbf{\Phi }}$—possibly not both in the same set—of unbreakably common-cause coupled parts of the phenomenon. By contrast, if we assume with Craver et al. (2021: 8824) that a bike’s bracket is a standing condition, NDC rules that it is not a constituent of the bike’s movement. As the bracket and the movement are unconditionally independent, they do not share common causes.

Of course, whether NDC’s demarcation criterion is satisfied by some ${\displaystyle \mathrm{\Phi }\in \mathbf{\Phi }}$ and a phenomenon ${\displaystyle \mathrm{\Psi }}$ can only be decided inductively. Establishing (No De-Coupling) calls for progressive expansions of analyzed variable sets by additional causes of ${\displaystyle \mathrm{\Psi }}$ and continuous testing whether these added causes break the common-cause coupling of ${\displaystyle \mathbf{\Phi }}$ and ${\displaystyle \mathrm{\Psi }}$. After a finite number of expansions and rigorous but unsuccessful attempts at breaking this coupling, the satisfaction of (No De-Coupling) can be inductively inferred. This, in turn, licenses an abductive inference to every element of ${\displaystyle \mathbf{\Phi }}$ being a constituent of ${\displaystyle \mathrm{\Psi }}$. By contrast, if variable set expansions reveal a surgical cause of ${\displaystyle \mathrm{\Psi }}$ that does not target any element of ${\displaystyle \mathbf{\Phi }}$, the common-cause coupling of ${\displaystyle \mathbf{\Phi }}$ and ${\displaystyle \mathrm{\Psi }}$ is falsified. That, however, does not entail that a particular ${\displaystyle \mathrm{\Phi }\in \mathbf{\Phi }}$ might not be contained in another set ${\displaystyle {\mathbf{\Phi }}^{\mathbf{\prime }}}$ for which common-cause coupling cannot be broken. Hence, that a particular ${\displaystyle \mathrm{\Phi }}$ is a non-constituent can likewise only be inductively corroborated, namely by means of an extended unsuccessful search for a constituting set comprising ${\displaystyle \mathrm{\Phi }}$. But its inductive nature notwithstanding, NDC furnishes a clear criterion demarcating between constituents and non-constituents.

(III) Finally, that NDC faces none of the conceptual problems of MM and MIE is apparent from the mere fact that neither the problematic notion of an ideal intervention nor that of causal betweenness play any role in NDC. Instead, the core notion based on which NDC defines constitution is that of a common cause, which is standard, unambiguous, and readily applicable to mechanistic systems. The only notion appearing in NDC that is not straightforward is that of spatio-temporal parthood; it raises certain logical and metaphysical questions commonly addressed in the field of mereology. These issues, however, are sidestepped in the literature on mechanistic explanation. Mechanists simply assume a metaphysically thin notion of parthood according to which ${\displaystyle x}$ is a part of ${\displaystyle y}$ if, and only if, ${\displaystyle x}$ occupies a spacetime region that is contained in the region occupied by ${\displaystyle y}$, and they take clarity on such parthood relations among analyzed behaviors for granted. Craver (2007) avails himself to that background assumption for MM and so do Baumgartner and Casini (2017) for NDC.

Overall, barring mereological questions concerning parthood, this section has shown that NDC indeed establishes constitution as a distinctly non-causal explanatory relation, that it provides a criterion demarcating between constituents and non-constituents, and that it accomplishes this without falling into conceptual traps.

7. Conclusion

To solve the problems of Craver’s (2007) Mutual Manipulability theory (MM), Craver et al. (2021) presented a new theory of constitution consisting of the metaphysical thesis that constitution is causal betweenness and the epistemic condition MIE, which the authors claim to be sufficient (but not necessary) to identify constituents. The main part of our paper argued that this new theory, contrary to the assertions of Craver et al., neither retains the spirit of MM nor is free of conceptual confusion.

On the one hand, contra MM, the new theory renders constitutive explanation as a form of causal explanation and it reduces the problem of finding constituents to the problem of finding the causes or the processes between a phenomenon’s input and output conditions. There exist many well-tested methodological approaches to solve this problem, but MIE attempts to develop its own solution from scratch. Moreover, whereas MM is meant to rule out, for example, that hemodynamic changes are constituents of cognitive task performance, MIE remains entirely silent about non-constituents. In consequence, MIE does not provide a basis for distinguishing between good and bad constitutive explanations.

On the other hand, the new theory’s metaphysical component is inherently ambiguous. We discussed three viable interpretations of what Craver et al. could mean by constituents being causally between input and outcome conditions of phenomena: the path, the process, and the modulation interpretation. We found that all of them are defective and none of them combines coherently with MIE. Relative to the path interpretation, MIE is indeed sufficient to identify constituents but contains two redundant conditions that serve no purpose whatsoever. By contrast, relative to the process interpretation, MIE is not sufficient for identifying constituents, contrary to what Craver et al. claim. Finally, the modulation interpretation either trivializes the notion of constitution, by allowing too many standing conditions to count as constituents, or it is forced to reintroduce defining criteria for acting upper-level entities, which—according to Craver et al.—are the very source of the problem that the new theory set out to avoid. We conclude that the new theory is not free of conceptual confusion either.

Since the flaws of MM have become a discussion point in the literature, different theories of constitution have been proposed, some of which explicitly tailored to meet the same objectives as MM. Unfortunately, Craver et al. (2021) do not engage with these alternative theories. It hence remains unclear which aspects of the available alternatives Craver et al. deem unsuitable and why they believe that yet another theory of constitution would be needed in the first place. To substantiate that there is no actual need for a new theory if the goal is to meet MM’s objectives, we reviewed the basics of the No De-Coupling theory (Baumgartner & Casini 2017) and demonstrated its ability to deliver on its promises. By defining constitution in terms of unbreakable common-cause coupling, NDC provides a distinctly non-causal relevance relation grounding a hierarchical form of explanation, which fills an important explanatory gap of pure causal models. Contrary to the latter, constitutive models are capable of explaining why behavior patterns of phenomena and their constituents cannot be de-coupled. This validates a core tenet, not only of Craver’s account of neuroscientific explanation, but of the new mechanist program more generally: constitution is a standalone explanatory dimension on a par with causation. A mechanistic explanation of a phenomenon is good if, and only if, it describes the hierarchical arrangement and causal interactions of all and only its constitutively relevant component entities and activities.

Acknowledgements

We thank two anonymous reviewers for helpful comments on an earlier draft. Moreover, we are grateful to the Trond Mohn Foundation (grant 811886 for M.B.) and the Italian Ministry of University and Research (grants 201743F9YE, 20177FX2A7, and the PRO3 grant for the project “Understanding public data: experts, decisions, epistemic values” for L.C.) for generous support of this research.