Mechanistic explanations are widespread in the cognitive sciences (Bechtel and Richardson, 1993; Machamer et al., 2000; Craver, 2007; Illari and Williamson, 2010; Glennan, 2017; Craver and Tabery, 2019). Despite extensive discussion in the philosophical literature, there is no consensus on the proper characterization of mechanisms or how exactly they figure in mechanistic explanations.³ For our purposes, we illustrate basic features of mechanistic explanations by focusing on Glennan’s (2017, p. 17) minimal conception of mechanisms:

This intentionally broad proposal captures a widely held consensus among philosophers about conditions that are necessary for something to be a mechanism. Where they disagree is about further details, such as the nature and role of causation, regularities, and levels of analysis involved in mechanisms. At a minimum, mechanistic explanations account for the phenomenon to be explained (the explanandum) by identifying the organized entities, activities, and interactions responsible for it.

Consider the case of the action potential. A mechanistic explanation of this phenomenon specifies parts such as voltage-gated sodium and potassium channels. It describes how activities of the parts, like influx and efflux of ions through the channels, underlie the rapid changes in membrane potential. It shows how these activities are organized such that they are responsible for the characteristic phases of action potentials. For example, the fact that depolarization precedes hyperpolarization is explained in part by the fact that sodium channels open faster than potassium channels. In short, mechanistic explanations spell out the relevant physical details.

Importantly, not all theoretical achievements in neuroscience are mechanistic explanations. As a point of contrast, compare Hodgkin and Huxley’s (1952) groundbreaking model of the action potential. With their mathematical model worked out, they were able to predict properties of action potentials and neatly summarize empirical data from their voltage clamp experiments. However, as Hodgkin and Huxley (1952) explicitly pointed out, their equations lacked a physical basis. There is some disagreement among philosophers about how we should interpret the explanatory merits of the model (Levy, 2014; Craver and Kaplan, 2020; Favela, 2020a), but what is clear is that the Hodgkin and Huxley model is a major achievement that is not a mechanistic explanation of the action potential. We return to issues such as these below.

Mechanistic explanations are sometimes contrasted with other kinds of explanation. In the philosophical literature, computational explanations are perhaps the most prominent alternative. Computational explanations are frequently considered a subset of functional explanations. The latter explain phenomena by appealing to their function and the functional organization of their parts (Fodor, 1968; Cummins, 1975, 1983, 2000). Insofar as computational explanations are distinct from other kinds of functional explanations, it is because the functions to which they appeal involve information processing. Hereafter, we focus on computational explanations.

In computational explanations, a phenomenon is explained in terms of a system performing a computation. A computation involves the processing of input information according to a series of specified operations that results in output information. While many computational explanations describe the object of computation as having representational content, some challenge this as a universal constraint on computational explanations (Piccinini, 2015; Dewhurst, 2018; Fresco and Miłkowski, 2021). We will use “information” broadly, such that we remain silent on this issue. Here, “operations” refer to logical or mathematical manipulations on information such as addition, subtraction, equation (setting a value equal to something), “AND,” etc. For example, calculating n! involves taking in input n and calculating the product of all natural numbers less than or equal to n and then outputting said product. Thus, we can explain why pressing “5,” “!,” “=”, in sequence on a calculator results in the display reading “120”; the calculator computes the factorial.

More detailed computational explanations of this procedure are possible. For example, the calculator performs this computation by storing n and iteratively multiplying the stored variable by one less than the previous iteration from n to 1. In this case, the operations being used are equation, multiplication, and subtraction. The information upon which those operations are being performed are the inputted value for n and the stored variable for the value of the factorial at that iteration.

In topological or “network” explanations, a phenomenon is explained by appeal to graph-theoretic properties. Scientists infer a network’s structure from data, and then apply various graph-theoretic algorithms to measure its topological properties. For instance, clustering coefficients measure degrees of interconnectedness among nodes in the same neighborhood. Here, a node’s neighborhood is defined as the set of nodes to which it is directly connected. An individual node’s local clustering coefficient is the proportion of edges within its neighborhood divided by the number of edges that could possibly exist between the members of its neighborhood. By contrast, a network’s global clustering coefficient is the ratio of closed triplets to the total number of triplets in a graph. A triplet of nodes is any three nodes that are connected by at least two edges. An open triplet is connected by exactly two edges; a closed triplet, by three. Another topological property, average (or “characteristic”) path length, measures the mean number of edges needed to connect any two nodes in the network.

In their seminal paper, Watts and Strogatz (1998) applied these concepts to a family of graphs and showed how a network’s topological structure determines its dynamics. First, regular graphs have both high global clustering coefficients and high average path length. By contrast, random graphs have low global clustering coefficients and low average path length. Finally, they introduced a third type of small-world graph with high clustering coefficient but low average path length.

Highlighting differences between these three types of graphs yields a powerful explanatory strategy. For example, because regular networks have larger average path lengths than small-world networks, things will “diffuse” throughout the former more slowly than the latter, largely due to the greater number of edges to be traversed. Similarly, because random networks have smaller clustering coefficients than small-world networks, things will also spread throughout the former more slowly than the latter, largely due to sparse interconnections within neighborhoods of nodes. Hence, ceteris paribus, propagation/diffusion is faster in small-world networks. This is because the fewer long-range connections between highly interconnected neighborhoods of nodes shorten the distance between neighborhoods of nodes that are otherwise very distant and enables them to behave as if they were first neighbors. For example, Watts and Strogatz showed that the nervous system of Caenorhabditi elegans is a small-world network, and subsequent researchers argued that this system’s small-world topology explains its relatively efficient information propagation (Latora and Marchiori, 2001; Bullmore and Sporns, 2012).

In dynamical explanations, phenomena are accounted for using the resources of dynamic systems theory. At root, a system is dynamical if its state space can be described using differential equations, paradigmatically of the following form:

Here, x is a vector (often describing the position of the system of interest), f is a function, t is time, and p is a fixed parameter. Thus, the equation describes the evolution of a system over time. In dynamical explanations, these equations are used to show how values of a quantity at a given time and place would uniquely determine the phenomenon of interest, which is typically treated as values of the same quantity at a subsequent time.

For example, consider dynamical explanations of why bimanual coordination—defined roughly as wagging the index fingers of both hands at the same time—is done either in- or anti-phase. Haken et al. (1985) use the following differential equation to model this phenomenon:

Here ϕ is relative phase, having a value of either 0° or 180° (representing in- and anti-phase conditions, respectively) and b/a is the coupling ratio inversely related to the oscillations’ frequency. The explanation rests on the fact that only the in- and anti-phase oscillations of the index fingers are basins of attraction.

We highlight two reasons to think that Khalifa’s account of understanding is especially promising as a basis for explanatory integration. First, as Khalifa (2019) argues, his is among the most demanding philosophical accounts of understanding. Consequently, it serves as a useful ideal to which scientists should aspire. Second, this ideal is not utopian. This is especially clear with Khalifa’s requirement that scientists evaluate their explanations relative to the best available methods and evidence. Indeed, among philosophical accounts of understanding, Khalifa’s account is uniquely sensitive to the centrality of hypothesis testing and experimental design in advancing scientific understanding (Khalifa, 2017; Khalifa, in press), and thus makes contact with workaday scientific practices. In this section, we present its three core principles.

Khalifa’s first central principle is the Explanatory Floor:

The Explanatory Floor’s underlying intuition is simple. It seems odd to understand why Y while lacking a correct answer to the question, “Why Y?” For instance, the person who lacks a correct answer to the question “Why do apples fall from trees?” does not understand why apples fall from trees. Since explanations are answers to why-questions, the Explanatory Floor appears platitudinous. Below, we provide further details about correct explanation.

The Explanatory Floor is only one of three principles comprising Khalifa’s account and imposes only a necessary condition on understanding. By contrast, the second principle, the Nexus Principle, describes how understanding can improve:

To motivate the Nexus Principle, suppose that one person can correctly identify two causes of a fire, and another person can only identify one of those causes. Ceteris paribus, the former understands why the fire occurred better than the latter. Crucially in what follows, however, “correct explanatory information” is not limited to correct explanations. The explanatory nexus also includes the relationships between correct explanations. We return to these “inter-explanatory relationships” below.

Furthermore, recall our earlier remark that gaps in understanding arise when one simply has an accurate representation of an explanation (or explanatory nexus) without significant cognitive ability. This leads to the last principle, the Scientific Knowledge Principle:

Once again, we may motivate this with a simple example. Consider two agents who possess the same explanatory information that nevertheless differ in understanding because of their abilities to relate that information to relevant theories, models, methods, and observations. The Scientific Knowledge Principle is intended to capture this idea. Khalifa provides a detailed account of scientific knowledge of an explanation:

The core notions here are safety and SEEing. Safety is an epistemological concept that requires an agent’s belief to not easily have been false given the way in which it was formed (Pritchard, 2009). SEEing then describes the way a belief in an explanation should be formed to promote understanding. SEEing consists of three phases:

Thus, scientific knowledge of an explanation is achieved when one’s commitment to an explanation could not easily have been false given the way that one considered and compared that explanation to plausible alternative explanations of the same phenomenon.

With our account of understanding in hand, we now argue that it provides a fruitful account of how different explanations, such as the ones discussed above, can be integrated. The Nexus Principle is the key engine of integration. As noted above, this principle states that understanding improves in proportion to the amount of explanatory information possessed. In the cognitive sciences, a multitude of factors explain a single phenomenon. According to the Nexus Principle, understanding improves not only when more of these factors are identified, but when the “inter-explanatory relationships” between these factors are also identified.

One “inter-explanatory relationship” is that of relative goodness. Some explanations are better than others, even if both are correct. For instance, the presence of oxygen is explanatorily relevant to any fire’s occurrence. However, oxygen is rarely judged as the best explanation of a fire. Per the Nexus Principle, grasping facts such as these enhances one’s understanding. Parallel points apply in the cognitive sciences. For example, it has been observed that mental simulations that involve episodic memory engage the default network significantly more than mental simulations that involve semantic memory (Parikh et al., 2018). Hence, episodic memory better explains cases in which the default network was more active during a mental simulation than does semantic memory.

However, correct explanations can stand in other relations than superiority and inferiority. For instance, the aforementioned explanation involving the default network contributes to a more encompassing computational explanation of counterfactual reasoning involving three core stages of counterfactual thought (Van Hoeck et al., 2015). First, alternative possibilities to the actual course of events are mentally simulated. Second, consequences are inferred from these simulations. Third, adaptive behavior and learning geared toward future planning and problem-solving occurs. The default network figures prominently in the explanation of (at least) the first of these processes (Figure 2).

As this example illustrates, grasping the relationships between different kinds of explanations can advance scientists’ understanding. In Figure 2, a computational account of mental simulation explains certain aspects of counterfactual reasoning, but mental simulation is then explained mechanistically: the default network consists of parts (e.g., ventral medial prefrontal cortex and posterior cingulate cortex) whose activities and interactions (anatomical connections) are organized so as to be responsible for various phenomena related to mental simulations. Quite plausibly, scientific understanding increases when the relationship between these two explanations is discovered.

Importantly, this is but an instance of an indefinite number of other structures consisting of inter-explanatory relationships (see Figure 3 for examples). In all of these structures, we assume that for all i, X_i is a correct explanation of its respective explanandum. Intuitively, a person who could not distinguish these different explanatory structures would not understand Y as well as someone who did. For instance, a person who knew that X₁ only explains Y through X₂ in Figure 3A, or that X₁ and X₂ are independent of each other in Figure 3B, or that X₃ is a common explanation or “deep determinant” of both X₁ and X₂ in Figure 3D, etc. seems to have a better understanding than a person who did not grasp these relationships. Undoubtedly, explanations can stand in other relationships that figure in the nexus.

Thus, the Nexus Principle provides useful guidelines for how different kinds of explanations should be integrated. Moreover, we have already seen that different kinds of explanations can stand in fruitful inter-explanatory relationships, and that these relationships enhance our understanding. In some cases, we may find that one and the same phenomenon is explained both mechanistically and non-mechanistically, but one of these explanations will be better than another. As noted above, “better than” and “worse than” are also inter-explanatory relationships. So, the Nexus Principle implies that knowing the relative strengths and weaknesses of different explanations enhances understanding.

The Scientific Knowledge Principle also plays a role in UBI. Suppose that X₁ and X₂ are competing explanations of Y. SEEing would largely be achieved when, through empirical testing, X₁ was found to explain significantly more of Y’s variance than X₂. This gives scientists grounds for thinking X₁ better explains Y than X₂ and thereby bolsters their understanding of Y. Importantly, SEEing is also how scientists discover other inter-explanatory relationships. An example is the aforementioned study that identified the inter-explanatory relationships between episodic memory, semantic memory, the default network, and mental simulation (Parikh et al., 2018).

According to mechanists’ assimilation strategy, many putatively non-mechanistic explanations are in fact elliptical mechanistic explanations or “mechanism sketches” (Piccinini and Craver, 2011; Zednik, 2011; Miłkowski, 2013; Piccinini, 2015; Povich, 2015, in press). Thus, when deploying the assimilation strategy, mechanists take computational, topological, and dynamical models to fall short of a (complete) mechanistic explanation, but to nevertheless provide important information about such mechanistic explanations. Mechanists have proposed two ways that putatively non-mechanistic explanations can provide mechanistic information, and thereby serve as mechanism sketches. First, putatively non-mechanistic explanations can be heuristics for discovering mechanistic explanations. Second, putatively non-mechanistic explanations can constrain the space of acceptable mechanistic explanations.

An alternative interpretation is possible. The fact that non-mechanistic models assist in the identification of mechanistic explanations does not entail that the former is a species of the latter. Consequently, putatively non-mechanistic explanations can play these two roles with respect to mechanistic explanations without being mere mechanism sketches. In other words, “genuinely” non-mechanistic explanations can guide or constrain the discovery of mechanistic explanations. Earlier explanatory pluralists (McCauley, 1986, 1996) already anticipated precursors to this idea, but did not tie it explicitly as a response to mechanists’ assimilation strategy.

Moreover, this fits comfortably with our account of SEEing and hence with UBI. Heuristics of discovery are naturally seen as advancing SEEing’s first stage of considering plausible potential explanations. Similarly, since the goal of SEEing is to identify correct explanations and their relationships, it is a consequence of UBI that different kinds of explanations of the related phenomena constrain each other. For instance, suppose that we have two computational explanations of the same phenomenon, and that the key difference between them is that only the first of these is probable given the best mechanistic explanations of that phenomenon. Then that counts as a reason to treat the first computational explanation as better than the second. Hence, SEEing entails mechanistic explanations can constrain computational explanations.

More generally, UBI can capture the same key inter-explanatory relationships that mechanists prize without assimilating putatively non-mechanistic explanations to mechanistic explanation. Indeed, like many mechanists, UBI suggests that not only do putatively non-mechanistic explanations guide and constrain the discovery of mechanistic explanations, but that the converse is also true. (The next section provides an example of this.) Parity of reasoning entails that mechanistic explanations should thereby be relegated to mere “computational, topological, and dynamical sketches” in these cases, but mechanists must resist this conclusion on pain of contradiction. Since UBI captures these important inter-explanatory relationships without broaching the more controversial question of assimilation, it need not determine which models are mere sketches of adequate explanations. Future research would evaluate whether this is a virtue or a vice.

Mechanists’ assimilation strategy becomes more plausible than the UBI-inspired alternative if there are good grounds for thinking that the criteria that pluralists use to establish putatively non-mechanistic explanations as genuine explanations are insufficient. This is the crux of the mechanists’ negative strategy. As with the assimilation strategy, we suggest that UBI provides a suggestive foil to the negative strategy.

The negative strategy’s key move is to identify a set of non-explanatory models that pluralists’ criteria would wrongly label as explanatory. Two kinds of non-explanatory models—how-possibly and phenomenological models—exemplify this mechanist argument. How-possibly models describe factors that could but do not actually produce the phenomenon to be explained. For instance, most explanations begin as conjectures or untested hypotheses. Those that turn out to be false will be how-possibly explanations. Phenomenological models, which accurately describe or predict the target phenomenon without explaining it, provide a second basis for the negative strategy. Paradigmatically, phenomenological models correctly represent non-explanatory correlations between two or more variables. Mechanists claim that pluralist criteria of explanation will wrongly classify some how-possibly and some phenomenological models as correct explanations. By contrast, since models that accurately represent mechanisms are “how-actually models,” i.e., models that cite explanatory factors responsible for the phenomenon of interest, MBI appears well-positioned to distinguish correct explanations from how-possibly and phenomenological models.

However, UBI can distinguish correct explanations from how-possibly and phenomenological models. Moreover, it can do so in two distinct ways that do not appeal to mechanisms. First, it can do so on what we call structural grounds, i.e., by identifying non-mechanistic criteria of explanation that are sufficient for funding the distinction. It can also defuse the negative strategy on what we call procedural grounds, i.e., by showing that the procedures and methods that promote understanding also distinguish correct explanations from these non-explanatory models.