Rethinking the explanatory power of dynamical models in cognitive science

ABSTRACT

In this paper I offer an interventionist perspective on the explanatory structure and explanatory power of (some) dynamical models in cognitive science: I argue that some “pure” dynamical models – ones that do not refer to mechanisms at all – in cognitive science are “contextualized causal models” and that this explanatory structure gives such models genuine explanatory power. I contrast this view with several other perspectives on the explanatory power of “pure” dynamical models. One of the main results is that dynamical models need not refer to underlying mechanisms in order to be explanatory. I defend and illustrate this position in terms of dynamical models of the A-not-B error in developmental psychology as elaborated by Thelen and colleagues, and dynamical models of unintentional interpersonal coordination developed by Richardson and colleagues.

KEYWORDS:

• Causal explanation
• cognitive science
• dynamical model
• explanatory power
• mechanism

Acknowledgements

I thank Raoul Gervais for useful comments. I am particularly indebted to two referees who provided very constructive feedback on previous versions of this paper. I also wish to thank Bill Bechtel for relevant suggestions.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1. Stepp and colleagues (2011) advance multiple criteria for the explanatory power of dynamical models, namely predictive power, counterfactual support, and unification. In Section 2.2, I argue that this is not enough to secure the explanatory power of such models.

2. Let me note that I restrict my account to the explanatory value of dynamical models in cognitive science. Furthermore, I purposely claim that most extant defenses of the explanatory power of pure dynamical models in cognitive science fall short of securing the explanatory value of such models. If one is willing to count systems neuroscience as part of cognitive science then, by my lights, there are some promising accounts available as regards the explanatory power of pure dynamical models. In the context of systems neuroscience, I take several authors to have convincingly argued that non-mechanistic dynamical models also can have explanatory force in virtue of these models being minimal models in the sense discussed by Batterman (2002) and Batterman and Rice (2014) (Chirimuuta, 2017; Ross, 2015; Woodward, 2017). That said, these accounts differ in a crucial respect from the one elaborated here: they treat dynamical models as non-causal ones. In contrast, the account advanced in this paper is explicitly causal. I briefly contrast my account with minimal model interpretations of dynamical models in Section 6. One of the important insights that derive from this comparison is that the explanatory power of non-mechanistic dynamical models can be secured along both causal and non-causal lines.

3. One of the reasons for assessing the model of the A-not-B error in detail is that its explanatory structure (and thus its explanatory power) has been misrepresented in the literature. For instance, while some take the model to be an instance of covering law explanation (Walmsley, 2008), others interpret the model in mechanistic fashion (Zednik, 2011). Yet others have been silent about its structure and power while invoking the model as a paradigmatic case of dynamical explanation (Van Gelder, 2006). Another reason is historical: it is considered one of the flagship cases of successful dynamical explanation in cognitive science. I also discuss more recent work on dynamical explanation in cognitive science in order to show that the “contextualized causal model” interpretation advanced in this paper is not restricted to the model of the A-not-B error, but applies more broadly to dynamical explanations in cognitive science.

4. As said, I take constraints to refer to task conditions and differentiate between internal and external constraints. External constraints refer to specific characteristics or properties of the task environment (e.g., the ambiguity of the task input in the A-not-B task) under which a task is (to-be) performed by subjects (e.g., infants in the A-not-B task). Internal constraints refer to specific restrictions on the behaviors (e.g., the specific delay between looking and reaching in the A-not-B task) that subjects (e.g., infants in the A-not-B task) (are to) execute during the task. These constraints are represented as parameters (and not as variables) in the dynamical models considered in this paper.

5. Of course, in Woodward’s account explanation also involves predictive elements: answering what-if-things-had-been-different questions also concerns predicting what would happen in counterfactual scenarios. As will become clear in this section, the claim that prediction does not provide sufficient grounds for explanatory power concerns the idea that law-like regularities, while having predictive credentials, by themselves need not be explanatory. The claim is not made in reference to Woodward’s account, in which a variety of additional constraints are imposed on generalizations being truly explanatory.

6. Parameters refer to conditions that affect or constrain how dynamical behavior unfolds in real time, for example, how motor memory of previous reaches impacts perseverative reaching. Dynamical behavior, such as perseverative reaching behavior, is captured by means of variables that are assigned values which change from one time step to the next, for example, the hand reaching trajectory of an infant during the A-not-B task.

7. This skill-based account of understanding originates from the contextual theory of understanding, which was originally developed by De Regt and Dieks (2005) in the context of scientific theories in physics. Gervais (2015) applies the account to Voss’ dynamical model.

8. Smith and Thelen (2003) speak about “multiple causes”; I prefer to speak about a core causal factor (i.e., motor memory) and internal and external constraints that affect whether or not the core causal factor is a difference maker for perseverative reaching. This re-characterization more precisely captures what goes on in the experimental investigations and is in line with the repeated emphasis on motor memory as cause of the A-not-B error.

9. Whereas Craver (2007) stresses ideal interventions that induce changes in one level by inducing changes in the other, Baumgartner and Casini (2017) argue that such ideal interventions, as defined by Craver (2007), are impossible in principle when the relation between micro and macro levels is one of constitution. In their view, micro and macro levels, in the case of constitution, can only be manipulated via fat-handed interventions that cause changes at both levels via separate causal paths. These differences, although intriguing, need not concern us here.

10. A similar argument can be run as regards internal constraints: since these refer to restrictions on subjects’ behaviors that are (to be) executed during tasks (e.g., the specific delay between looking and reaching in the A-not-B task) and not to such behaviors themselves, such task conditions are also not constituents of mechanisms. I focus the discussion on external constraints since I take their non-constitutive (and non-causal) nature to be especially salient and establishing that suffices for my purposes here, namely demonstrating that mechanistic and contextualized causal models are importantly different.

11. Contextualized causal models are (also) different from mechanistic models as construed by Woodward (2013). Woodward considers mechanisms to be sets of (modular) causal relationships. That is, he takes mechanisms to consist of components/parts that can be characterized by variables, where these variables stand in causal (i.e., difference making) relationships to one another, and in which these relationships are viewed as intermediate or intervening links along the causal paths connecting mechanisms’ overall input to their overall output (these overall input-output relationships characterize the overall behavior of mechanisms, i.e., their phenomena). Mechanistic models represent such sets of (modular) causal relationships. Now, Woodward says much more about features of mechanisms and models thereof (in particular, with respect to stability, modularity, and sensitivity to organization), but this brief sketch suffices to see that mechanistic models as understood by Woodward are not to be equated with contextualized causal models: the latter do not represent sets of (modular) causal relationships. As said in Section 3.1, internal and external constraints listed in contextualized causal models are not to be thought of as causal factors on a causal (directed) path from constraint to core causal factor to explanandum phenomenon (effect), or directly from constraint to explanandum phenomenon (effect). For instance, constraints like body posture or ambiguity of the task input do not cause a specific value of motor memory of previous reaches, of course. Cued reaches to specific locations is what causes memory of these reaches. And neither do constraints directly cause perseverative reaching. For that to occur, memory of previous reaches has to be in place. These constraints rather set the context within which a core causal factor is a difference maker or not. So, contextualized causal models articulate contextual dependencies between constraints and core causal factors, not causal relationships between them (the causal relationship holds between core causal factors and target explananda, relative to these constraints).

12. I am not inclined to stretch the concept of mechanistic model further to also include external constraints. There then would be little distinctive left about such models; they may then include virtually anything. One needs to draw the line somewhere.

13. Schöner and co-workers have, since Thelen and colleagues’ (2001) publication, focused a lot on dynamic field models understood as dynamic neural field models in which “the different factors that impact on behavior are conceived of as ‘forces’ in neural dynamics, ranging from intrinsic factors that reflect the neural circuitry to environmental factors that act through sensory input. The joint effect of these forces is the emergence of a stable state that becomes visible as overt behavior” (Maruyama, Dineva, Spencer, & Schöner, 2014). The dynamic neural field model, in the context of the A-not-B task, represents reaching directions in terms of activation levels of neurons, that is, in terms of the distribution of neural activation in the field. Such neural activation distributions results from perceptual inputs (specifics of the task input) and recent motor memory traces. This might suggest that the dynamic neural field model captures all the features of the original dynamic field model of the A-not-B error in terms of characterizations of neural activations. This is not the case, however. The model only articulates reaching directions and motor memory traces in terms of characterizations of neural activations. Specifics of the task environment (i.e., the external constraints) are considered key to infant perseverative reaching and are viewed as “forces” providing input to these neural activations, but are not themselves considered to be neural activation patterns and neither are they represented as such (Maruyama et al., 2014). In light of this, it would be a mistake to consider dynamic neural field models of the A-not-B error to be merely mechanistic models of neural mechanisms underlying the A-not-B error, for external constraints are assigned key importance. What it does show is that since the 2001 formulation, work has been done on the neural underpinnings of the internal operations listed in the 2001 model, thus conferring plausibility on the dynamics specified in the 2001 model (see also Section 4).

14. A worthwhile follow-up project would be to assess what an application of Hitchcock and Woodward’s (2003) (comparative) account of explanatory power, which builds upon Woodward’s (2003) account of causal explanation, to contextualized causal models would look like. For Woodward (e.g., 1997, 2000, 2003), the capacity to answer what-if-things-had-been-different questions is a necessary condition for an explanation to have genuine explanatory import or explanatory power. I take the explanatory power of contextualized causal models to also reside in this ability (see Sections 2.1 and 3.2). Hitchcock and Woodward (2003) also argue that one explanation can do better than another one with respect to this capacity – that one explanation may be able to answer more what-if-things-had-been-different questions than another one and in this sense has more explanatory power than its counterpart. I also think that this is a fruitful way to assess the comparative explanatory power of contextualized causal models vis-à-vis mechanistic models. Hitchcock and Woodward (2003) cash out this idea of comparative explanatory power in terms of one explanatory generalization being more invariant under (testing) interventions than another one; the more invariant explanatory generalization will answer more what-if-things-had-been-different questions than its less invariant counterpart. In general terms, a generalization that describes a causal dependency relationship between explanans and explanandum variables is invariant if it would continue to hold – remain stable or unchanged – if various other conditions were to change. However, whereas invariance under interventions and the capacity to answer what-if-things-had-been-different questions are a package deal in Woodward and Hitchcock’s (comparative) account of explanatory power, we need to prize these features apart in the context of contextualized causal models. To see this, consider that the dependency relation articulated in Thelen and colleagues’ (2001) model between motor memory and perseverative reaching is a fragile one; whether or not motor memory is a difference maker for perseverative reaching is relative to a variety of contextual constraints – manipulate these constraints (or off path variables) and the dependency relation gets affected as well. Understanding these contextual subtleties of the A-not-B error is precisely what drove Thelen and colleagues’ (2001) research into the phenomenon. The power of the model precisely resides in this feature of making explicit a number of constraints under which motor memory is and isn’t a difference maker for perseverative reaching. So it answers relevant what-if-things-had-been-different questions by highlighting the context-sensitive – fragile – nature of the dependency relationship between motor memory and the A-not-B error. The capacity to answer what-if questions and invariance under interventions here, in a sense, pull in opposite directions.

15. Similar views can be found in Glennan (2005) and Woodward (2017) with respect to how much detail ought to be included in mechanistic models. Woodward, for instance, in discussing the Hodgkin and Huxley (HH) model of the action potential, writes: “The HH model shows that the generation of the action potential depends on (or requires at a minimum), among other things, the existence of at least two voltage gated and time dependent ion channels … given that such a structure is present and behaves appropriately, the presence of the specific mechanism by which the ion channels in the giant squid operates is not required for [explaining the] the generation of the action potential, as long as some mechanism or other that plays this role is present.” (2017, p. 28).

16. To be sure, I do think that there are a lot of explanatory contexts in the life sciences where mechanistic explanations do provide the best explanations.

17. Although the weight of a person sitting in a rocking chair decreases the chair’s natural period by elevating the center of mass of the chair, different weights of the subjects in other rocking chair experiments did not have a significant effect on movement coordination. Although weight differences were not recorded in the current experiment, given these previous outcomes, the experimenters take it that possible effects of weight differences in all likelihood are minimal.

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Dingmar van Eck

Dingmar van Eck is postdoctoral researcher in philosophy of science at the Centre for Logic and Philosophy of Science, Ghent University. Most of his current research is on issues related to scientific explanation in the life sciences and engineering sciences.