Several philosophers have argued that “constraints” constrain (and thereby explain) by virtue of being modally stronger than ordinary laws of nature. In this way, a constraint applies to all possible systems in a broader (i.e., more inclusive) sense of “possible” than the sense in play when we say that the ordinary laws of nature apply to all physically possible systems. Explanations by constraint are thus more general, more broadly unifying, than ordinary causal explanations. Putative examples of constraints are often drawn from physics. The great conservation laws (of energy, mass, momentum, etc.) are posited as being constraints because they are modally stronger than the various particular force laws they govern. This greater modal strength is reflected in the truth of various counterfactual conditionals according to which the conservation laws would still have held even if there had been different (or additional) forces. The conservation laws thereby explain why there are no perpetual motion machines, for instance. When we look at what explains the conservation laws, we find further constraints, such as the symmetry principles that (in a Hamiltonian dynamical framework) entail and are entailed by the conservation laws. As constraints (i.e., as meta-laws), the symmetry principles are modally stronger than the first-order laws, and their greater modal strength is again manifested in the truth of various counterfactual conditionals. For instance, the first-order laws would still have been symmetric under temporal translation even if there had been additional kinds of forces. All of these examples are drawn from physics. This raises the question of whether constraints, meta-laws, non-causal explanations by constraint, and so forth are plausibly present in the social sciences as well. I will argue that they are. I will look at some potential examples from linguistics and other human sciences and see whether they are analogous to the examples that I have just mentioned from physics. On this view, there are no languages of certain sorts because no such language is possible–in a broader sense of “possible” than a causal explanation could underwrite.

The function of many biological systems is made possible by a network along which items of interest whether nutrients, goods, or information–can be routed. The human brain is a notable example. It is comprised of regions that perform specific functions and engage in particular computations. Those regions are interconnected by large white matter tracts. Each tract is a bundle of neuronal axons along which information-bearing electrical signals can propagate. Collectively, the tracts evince a pattern of connectivity–or network–that constrains the passage of information. In turn, that pattern of information flow determines the sorts of functions that the brain can support. Understanding structural network constraints is hence key to understanding healthy human brain function and its alteration in disease. Recent efforts have expanded the investigation of structural constraints in several ways. First, non-invasive measurements of white matter tracts using diffusion-weighted magnetic resonance imaging techniques have become increasingly sensitive to microstructural integrity and provided estimates of tract locations at finer spatial resolutions. These gains are made possible by an increase in the scan time (from 10 minutes to 1 hour), and in the number of diffusion directions acquired (from 30 to 720). Second, data-informed computational models have been developed to quantitatively assess how the particular network architecture these tracts comprise affects the brain’s dynamical repertoire. One such model that has proven particularly promising is the network control model, which draws upon and extends theoretical work in systems engineering. Third, a conceptual shift has expanded the types of explanations we use for cognitive processes from activity-based to structurally-based. For example, the hallmark of adult mental function–cognitive control–is now being studied not only as a regional activation state or computation but also as a dynamical process constrained by the structural network connecting the regions involved. Collectively, these measurement, modeling, and conceptual expansions are providing a richer understanding of structural constraints on human brain function. To better highlight the importance of structural network constraints upon neural dynamics, I will focus on a simple example. Cognitive effort has long been an important explanatory factor in the study of human behavior in health and disease. Yet, the biophysical nature of cognitive effort remains far from understood. Here, I will cast cognitive effort in the framework of network control theory, which describes how much energy is required to move the brain from one activity state to another when that activity is constrained to pass along physical pathways in a network. I will then turn to empirical studies that link this theoretical notion of energy with cognitive effort in a behaviorally demanding task. Finally, I will ask how this structurally-constrained activity flow can provide us with insights about the brain’s non-equilibrium nature. Using a general tool for quantifying entropy production in macroscopic systems, I will provide evidence to suggest that states of marked cognitive effort are also states of greater entropy production. Collectively, the work I discuss offers a complementary view of cognitive effort as a dynamical process structurally constrained by an underlying network.

Lange (2017) has done groundbreaking work on the explanatory role of constraints. However, besides having an explanatory role, some constraints, such as perspectival ones, can also have a pragmatic role in explanation. In this talk, I develop an account of perspectival constraints based on erotetic reasoning. Erotetic reasoning relies on the inferential patterns which determine both the questions and the space of possible answers to them. According to this view, questions can be conclusions in arguments that show how a question arises from certain contexts (Hintikka 1981; Winiewski 1996). For example, we can start from a set of propositions and derive questions based on the syntax and semantics of those statements: (1) If the city of Königsberg has a layout of landmasses and bridges such that they form a connected graph with a topological property p, then Königsberg cannot be traversed by crossing each bridge exactly once (an Eulerian path is impossible). (2) Königsberg has a layout of landmasses and bridges with a topological property p’. (3) Is an Eulerian path possible in the city of Königsberg? In this example, the erotetic argument starts with a statement about what it is for an arrangement to have a certain topological property p. From this, a relevant counterfactual that grounds an explanation could be derived: Had Königsberg’s layout had a topological property p, an Eulerian path in the city would have been possible. The inferential pattern in this toy example makes it intelligible why appealing to topological properties counts as an explanation of why the Eulerian path is impossible, but also why appealing to actual walking through the city does not (Lange 2018; Kostic and Khalifa 2021). To show how this analysis can be generalized from toy examples to actual explanations in science, I discuss an account of topological explanation (Kostic 2020) which outlines perspectival constraints for using the counterfactual information in two explanatory modes, i.e., a horizontal or a vertical explanatory mode. In the horizontal mode counterfactual dependency holds between properties at the same level, whereas in the vertical mode it holds between properties at different levels. The horizontal and vertical modes emerge from different question-asking contexts, thus by using erotetic reasoning I show how perspectival constraints enhance intelligibility of explanation, rather than relativizing it.

Recent philosophical work on explanation explores the notion of “constraints” and the role they play in scientific explanation. An influential account of “explanation by constraint” is provided by Lange (2017), who considers these topics in the context of the physical sciences. Lange’s account contains two main features. First, he suggests that constraints explain by exhibiting a strong form of necessity that makes the explanatory target inevitable. Second, he claims that constraints provide a type of non-causal explanation, because they necessitate their outcomes in a way that is stronger than standard causal laws. This non-causal claim is supported by other work in the field (Green and Jones 2016) and it has helped advance accounts of non-causal explanation. While Lange’s work focuses on constraints in physics, this talk explores constraints in a broader set of scientific fields, namely, biology, neuroscience, and the social sciences. In these domains, scientists discuss developmental, anatomical, and structural constraints, respectively. I argue that these examples capture a type of causal constraint, which figures in a common type of causal explanation in science. I provide an analysis of (1) what it means for an explanatory factor to quality as a constraint and (2) how we know whether such factors are causal or not. Although Lange’s account does not include causal constraints, I clarify how this work is motivated by and shares similarities to his account. In particular, this work suggests that causal constraints explain the restriction of an outcome, exhibit a strong form of explanatory influence, and figure in impossibility explanations. Work on explanatory constraints contributes to the philosophical literature in a variety of ways. First, this work helps shed light on the diverse types of explanatory patterns that we find in science. This provides a more realistic picture of scientific explanation and the methods, strategies, 5 and reasoning it involves. Second, appreciating that some explanatory constraints are causal has implications for attributing causal responsibility to parts of a system and for suggesting potential interventions that allow for control. In the context of the social sciences, for example, this has implications for holding social structural factors accountable for outcomes and for suggesting policy-level interventions that bring about desired change.