1. Introduction

The last three decades have witnessed the rise of the so-called new mechanical philosophy (NMP) in philosophy of science. The emergence of this NMP was largely motivated by philosophers’ realization that, in contrast with the physical sciences in which natural laws play a central role in offering explanation, prediction, and understanding, the life sciences are best characterized as a hodgepodge of subdisciplines that focus on discovering and investigating mechanisms. Another motive for the NMP’s arising is related to the shift from the focus on scientific theories to scientific practice.

Advocates of the NMP provide philosophers with a new framework for reexamining many pivotal problems in philosophy of science: scientific explanation, causation, the autonomy of the special sciences, to name just a few. However, even though the NMP has significantly reshaped the landscape of philosophy of science, there is still a long way to go. Recently, many authors have realized that the framework has serious limitations (Brigandt Reference Brigandt2013; Levy and Bechtel Reference Levy and Bechtel2013, Reference Levy and Bechtel2016). At the heart of these limitations is the fact that previous work tends to center on qualitative aspects of mechanisms and draws on examples primarily from textbooks in cell and molecular biology, while it neglects quantitative/dynamic aspects of mechanisms that are reflected in real scientific practice.

Given these limitations, Levy and Bechtel (Reference Levy and Bechtel2016) call for an extended conception of mechanisms and mechanistic explanation, the so-called mechanism 2.0.Footnote ¹ Although Levy and Bechtel, among others (e.g., Kaplan and Bechtel Reference Kaplan and Bechtel2011; Brigandt Reference Brigandt2013), point in the right direction (or so I suppose) and highlight several crucial points regarding what the extended philosophy would look like, they have not yet fully developed their proposal. So, I here, following in their footsteps, take up the mission of developing one version of such an extended philosophy and call it ‘mechanism 2.1’. My approach, largely inspired by neuroscientific practice, is capable of capturing both the qualitative and quantitative aspects of mechanisms, and it dovetails well with scientific practice.

The essay unfolds as follows. Section 2 briefly describes the NMP, followed by section 3 where Levy and Bechtel’s proposal for mechanism 2.0 is introduced. Section 4 proposes a dynamic causal approach to characterizing mechanisms, and section 5 discusses what philosophical implications it has.

2. The New Mechanical Philosophy

The NMP represents a bundle of closely connected but slightly different ideas proposed by a number of philosophers concentrating primarily on practice in the life sciences (Bechtel and Richardson Reference Bechtel and Richardson1993; Machamer, Darden, and Craver Reference Machamer, Darden and Craver2000; Glennan Reference Glennan2002; Bechtel Reference Bechtel2006; Darden Reference Darden2006; Craver Reference Craver2007). These philosophers all agree that we place mechanisms on center stage when examining those traditional philosophical questions (e.g., explanation, causation), even though they have not yet reached a consensus on how to philosophically specify the notion of mechanisms. According to one commonly cited characterization, “Mechanisms are entities and activities organized such that they are productive of regular changes from start or set-up to finish or termination conditions” (Machamer et al. Reference Machamer, Darden and Craver2000, 3). In characterizing mechanisms, different authors employ different terminologies that reflect their distinct ontological commitments.Footnote ² Setting aside these ontological disputes, nevertheless, they all seem to agree that a mechanism involves four elements: a phenomenon/behavior, components/parts/entities, interactions/activities/operations, and spatiotemporal organization/structure. Another element, not clearly shown, is also worth mentioning: multilevel hierarchy.

The multilevel hierarchy is manifested by the fact that the component of a mechanism may constitute a submechanism by itself and that the mechanism may constitute a component of an even bigger mechanism. This also implies that a mechanism’s identification hinges on what target phenomenon/behavior is under question. In other words, there is no mechanism simpliciter but only a mechanism for a particular phenomenon/behavior. With respect to components and interactions—in terms of Craver’s (Reference Craver2007) constitutively relevant criterion—only those that contribute to producing a particular phenomenon/behavior of the mechanism count as the components and interactions of the mechanism.

This NMP has significant implications for a number of philosophical issues (e.g., explanation). This philosophy advocates a new account of explanation (i.e., mechanistic explanation). According to this account, explaining a phenomenon/behavior (at least in the life sciences) lies in uncovering a mechanism, that is, uncovering how the various components interact with one another in a spatiotemporally orchestrated manner to produce the phenomenon of interest. Obviously, there is no role for laws to play, and explanation does not proceed in a manner suggested by the covering-law model of scientific explanation.

No doubt, this philosophy’s attractiveness essentially comes down to the fact that it goes in concert with practice in the life sciences. Yet, as many philosophers have pointed out, although this framework has come very close to practice, it does not come close enough.

3. Mechanism 2.0: Call for an Extension

Recently, many philosophers have cast doubt on the adequacy of the NMP (Bechtel and Abrahamsen Reference Bechtel and Abrahamsen2010, Reference Bechtel and Abrahamsen2013; Brigandt Reference Brigandt2013; Levy and Bechtel Reference Levy and Bechtel2013, Reference Levy and Bechtel2016). According to these philosophers, the NMP has the following limitations. First, the NMP treats a mechanism as if it is composed of a linear causal sequence. However, scientists have recognized that a mechanism can be a very complex network of interacting components that possesses feedback/feedforward loops, whose interactions are typically nonlinear and nonsequential. Second, the NMP routinely concentrates on the structural, organizational, and spatial aspects of a mechanism, ignoring that a mechanism is essentially a dynamic system within which the parts are changing over time. Third, these two features, linear and nondynamic thinking, are always associated with a third feature of that philosophy: qualitative thinking. This feature is clearly illustrated by the way the new mechanists qualitatively describe how a mechanism is brought about and by the simple paradigmatic examples drawn from textbooks (e.g., the lac operon of E. coli). These qualitative characterizations of mechanisms may help unravel some qualitative aspects of the mechanism but fall short of making sense of those quantitative, often more important and more complex, aspects.

Because of these limitations, an extended philosophy of mechanisms, accompanied by an updated account of mechanistic explanation, is called for (Bechtel and Abrahamsen Reference Bechtel and Abrahamsen2010; Brigandt Reference Brigandt2013; Levy and Bechtel Reference Levy and Bechtel2016). However, although Levy and Bechtel (Reference Levy and Bechtel2016), among others, have pointed out the limitations of the NMP and signposted the direction for an extension, they have not fully fleshed out what that extended philosophy would be. For the moment, let me list those key features, as singled out and agreed on by these philosophers, that an extended conception of a mechanism must be able to capture. First, the extended framework must treat a mechanism as a nonlinear, dynamic complex system that may involve feedback/feedforward loops. Second, in addition to the qualitative thinking, the extended framework must facilitate quantitative thinking. Third, as a result, the extended philosophy must come even closer to scientific practice. Given these key features, the extended framework might look as follows.

4. Mechanism 2.1: A Dynamic Causal Approach

I propose that a mechanism is a dynamic causal system that involves various components interacting, typically nonlinearly (although sometimes linearly), with one another to produce a phenomenon of interest. In agreement with the NMP, my approach also holds that a mechanism involves four elements: a phenomenon/behavior to be explained, components/parts/entities, interactions/activities/operations, and spatiotemporal organization/structure. Additionally, it considers the multilevel character of mechanisms. However, my approach differs from the NMP in two important aspects. First, it treats a mechanism as a dynamic system that may involve nonlinear interactions and feedback/feedforward loops, and second, it explicitly views a mechanism as a causal structure composed of components and their causal connections.Footnote ³

This approach does not come out of the blue. Rather, it reflects how scientists—especially neuroscientists—in practice conceptualize a mechanism (Friston, Harrison, and Penny Reference Friston, Harrison and Penny2003; Stephan et al. Reference Stephan, Harrison, Kiebel, David, Penny and Friston2007; Friston Reference Friston2009; Rubenstein et al. Reference Rubenstein, Bongers, Schölkopf and Mooij2016). To see how this approach can make sense of scientific practice and therefore offer us an extended conception of mechanisms, consider an example drawn from neuroscience. Neuroscientists wonder how human brains respond to stimuli (e.g., visual words). The question they are asking is what mechanism underlies the observed pattern regarding humans’ response to visual stimuli. To answer this question, they hypothesize a mechanism involving five components (i.e., areas) in the brain: visual areas V1 and V4, the inferior temporal gyrus (BA37), the angular gyrus (BA39), and the superior temporal gyrus (STG). The hypothesized mechanism is depicted in figure 1.

Figure 1. Schematic representation of a neuronal mechanism responsible for bringing about the observed stimuli-response pattern in humans. (Adapted from Friston et al. [Reference Friston, Harrison and Penny2003, 1275] with permission.)

Obviously, this mechanism involves feedback loops. Also, the mechanism can be interpreted as a causal structure, for all the arrows, both the one-way and the two-way arrows, denote causal connections.Footnote ⁴ These causal connections are termed effective connectivity, denoting “the influence that one neuronal system exerts over another in terms of inducing a response” (Friston et al. Reference Friston, Harrison and Penny2003, 1277). As can be seen from figure 1, there are two kinds of stimuli/inputs that influence the system: a stimulus can induce a response by either exerting direct influences over a specific region (e.g., u ₁) or exerting indirect effects by modulating the coupling (i.e., the causal connection) among regions (e.g., u ₂). Attention to a particular feature is a case of the second kind of stimulus/input, for differing degrees of attention usually can result in different strengths of the coupling between the same set of regions. In total, there are three types of interactions: (1) the direct influence of inputs on brain areas, (2) the intrinsic coupling among brain areas, and (3) the modulation of the intrinsic coupling induced by inputs.

We have not yet seen how the mechanism can be dynamic. Given figure 1, mental simulation may help us roughly understand how the mechanism works, but it offers no help in understanding the mechanism dynamically. To do so, we must be equipped with some mathematical tools. The deterministic differential equations are often the tools sought after by neuroscientists.Footnote ⁵ Now, we assign a state variable x_i to each region of the mechanism, describing some neurophysiological properties of that region (e.g., postsynaptic potentials). These state variables can interact with one another; namely, one state variable’s change relies on (the change of) at least one other state variable. The set of interactions between the state variables then can be expressed by a set of ordinary differential equations:Footnote ⁶

(1) $\begin{array}{}\text{(1)}& \frac{dx}{dt}=\left[\begin{array}{c}{f}_1\left(x_1,\dots ,x_n\right)\\ .\\ .\\ .\\ f_n\left(x_1,\dots ,x_n\right)\end{array}\right]=F\left(x\right)\mathrm{.}\end{array}$

Yet, this set of equations is insufficient to specify the mechanism. To begin with, the set of equations does not give us any information about the specific form, or the nature, of the causal relationships, f_i. Hence, a set of parameters, denoted by θ, that encodes the information about the form and strength of the causal relationships is required. The set of dependence/causal relationships, however, does define the structure/organization of the mechanism (Stephan et al. Reference Stephan, Harrison, Kiebel, David, Penny and Friston2007, 130).

Second, since the mechanism is an open system that exchanges matter, energy, or information with its environment, the inputs into the system, denoted by the vector function $u\left(t\right)$ , should also be considered. By expanding equation (1) along these two lines, we obtain a general nonlinear state equation for the system:Footnote ⁷

(2) $\begin{array}{}\text{(2)}& \frac{dx}{dt}=F\left(x,u,\theta \right)\mathrm{.}\end{array}$

This equation describes how a state variable’s change is a function of some neurophysiological influences exerted by some state variables (including itself at an earlier time) and some inputs, and it establishes a mapping between the system dynamics and the system structure. It offers “a causal description of how system dynamics results from system structure, because it describes (i) when and where external inputs enter the system; and (ii) how the state changes induced by these inputs evolve in time depending on the system’s structure. Given a particular temporal sequence of inputs $u\left(t\right)$ and an initial state $x\left(0\right)$ , one obtains a complete description of how the dynamics of the system … results from its structure” (Stephan et al. Reference Stephan, Harrison, Kiebel, David, Penny and Friston2007, 130). The equation is general because it provides an overarching framework for representing neural systems, which can be implemented in different ways. One such an implementation, a bilinear approximation, represents the system dynamics using a bilinear differential equation:Footnote ⁸

(3) $\begin{array}{}\text{(3)}& \begin{array}{cc}\frac{dx}{dt}& =F\left(x,u,\theta \right)\\ & =Ax+\sum u_j{B}^{j}x+Cu\\ & =\left(A+\sum u_j{B}^j\right)x+Cu,\end{array}\end{array}$

where A is the connectivity matrix denoting the intrinsic coupling among brain areas when no input is present, B^j are the induced connectivity matrices denoting the change of the intrinsic coupling induced by the jth input, and C is the matrix standing for the direct influences of inputs on brain areas. Together, they constitute the parameter set $\theta =\left\{A,B^j,C\right\}$ to be estimated. With the parameter set at hand, the mechanism represented in figure 1 can be redrawn as figure 2. In this scenario, each state variable’s change, ${\dot{x}}_i$ , is a function of its own state at an earlier time, at least one other state variable, and some external inputs.

Figure 2. Schema that redepicts the mechanism in figure 1 using the differential equations. The middle panel presents the differential equations shown in the upper panel in a matrix form, which can be further simplified using the parameter matrices A, B^j , and C. (Adapted from Friston et al. [Reference Friston, Harrison and Penny2003, 1279] with permission.)

So far, we have shown in detail how a mechanism can be dynamic and how a mechanism’s dynamic character can be properly captured with certain quantitative tools. However, that is not the end of the story. To fully understand a mechanism, it is standard practice that neuroscientists look deeply into each area of the mechanism and treat each as a dynamic system (i.e., a submechanism).Footnote ⁹ More specifically, the submechanism in our example is this: changes in neuronal activity induce a vasodilatory signal that results in changes in blood flow, which in turn cause changes in blood volume and deoxyhemoglobin content. Then, blood volume and deoxyhemoglobin content nonlinearly generate measurable responses of that area. The submechanism of each area is depicted in figure 3.

Figure 3. Schema that depicts the submechanism of each area of the mechanism. (Adapted from Friston et al. [Reference Friston, Harrison and Penny2003, 1281] with permission.)

This submechanism involves four hemodynamic state variables (s, f, v, and q) and a parameter set ϑ. To understand this submechanism dynamically, we, again, need to appeal to a set of differential equations that captures the (causal) relationships between these state variables employing the parameter set ϑ.Footnote ¹⁰ Finally, we obtain a full picture of the mechanism involving two levels (the mechanism level and the component level; see fig. 4). The schematic graph in figure 4, as depicting a causal structure, together with the quantitative tools necessary to capture the nonlinear, dynamic aspects embodied in the causal structure constitute the basis for proposing that a mechanism is a dynamic causal system that involves various components interacting, typically nonlinearly, with one another to produce a phenomenon of interest.Footnote ¹¹ The next section will discuss the key features of this approach and the philosophical implication it delivers.

Figure 4. Schema that represents a mechanism and its submechanisms.

5. Discussion

6. Conclusion

Following neuroscientific practice, I have proposed a dynamic causal approach to characterizing the notion of mechanisms. This approach shares with the NMP all those insights about mechanisms but also offers an extended, updated conception that highlights the dynamic, causal aspects of mechanisms and that comes closer to real scientific practice.