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Moving parts: the natural alliance between dynamical and mechanistic modeling approaches

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Abstract

Recently, it has been provocatively claimed that dynamical modeling approaches signal the emergence of a new explanatory framework distinct from that of mechanistic explanation. This paper rejects this proposal and argues that dynamical explanations are fully compatible with, even naturally construed as, instances of mechanistic explanations. Specifically, it is argued that the mathematical framework of dynamics provides a powerful descriptive scheme for revealing temporal features of activities in mechanisms and plays an explanatory role to the extent it is deployed for this purpose. It is also suggested that more attention should be paid to the distinctive methodological contributions of the dynamical framework including its usefulness as a heuristic for mechanism discovery and hypothesis generation in contemporary neuroscience and biology.

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Notes

  1. Although Clark’s (1997) characterization emphasizes the novelty of DST, it is important to acknowledge that the conclusions he ultimately defends about the nature of dynamical explanation differ markedly from those targeted in this paper. In fact, Clark emphasizes the need for a rapprochement of mechanistic (what he calls “componential”) and dynamical approaches, much as the current paper does.

  2. There is a large philosophical literature addressing how to understand the explanatory import of the HH model. Craver (2006, 2007, 2008) argues that, at least in its original form, the HH model is a partial or incomplete mechanistic explanation. More specifically, he argues the model is an explanatorily deficient mechanism sketch because it does not reveal critical parts—ion channels—in the mechanism underlying the observed conductances. Kaplan (2011) defends a similar view. Bogen (2005) offers a different, although compatible, interpretation of the HH model that highlights the non-explanatory but nonetheless important descriptive and predictive roles it plays. Levy (2014) rejects the idea that the original HH model is incomplete, and instead argues that abstraction from mechanistic detail is its primary explanatory virtue. According to Levy, models such as the HH model require a new “analytical category” within the mechanistic perspective to cover cases in which abstraction from certain kinds of underlying structural detail is an intentional strategy (see also, Levy and Bechtel 2013). Critically, despite their disagreements, both Craver and Levy maintain that the HH model instantiates a kind of mechanistic explanation. Others such as Weber (2008) embrace a covering-law interpretation of the model according to which its real explanatory weight is carried by implicit physical laws such as Ohm’s law, the Nernst equation, and Coulomb’s law. On this view, the mechanistic details merely serve to specify the relevant background or initial conditions for application of the laws. This view has played a less central role in subsequent debates, and Craver (2008) provides a powerful rejection of this view. Although it is inessential to the argument being made in the present paper, mechanistic interpretations of the HH model are undeniably widespread in recent philosophy of science.

  3. It is worth digressing momentarily to note how the predictive power of the HKB model and other dynamical models helps to allay the worry that they are merely descriptive. The objection proceeds as follows. For any given data set, an equation can always be constructed that fits a curve connecting each data point in that set (given the standard provisos about the tradeoffs between model generalization and overfitting). This kind of ad hoc, curve-fitting exercise results in a model or equation that, at best, provides a compact summary or redescription of the data and not an explanation of the phenomenon responsible for generating the data. Given this background, the objection continues, perhaps dynamical systems models are purely descriptive, curve-fitting models of this kind (Rosenbaum 1998; van Gelder 1998; Walmsley 2008). The natural dynamicist response is to state that dynamical models frequently go beyond merely describing the data for which they were constructed in the specific sense that they are capable of making quantitative predictions about how a system will behave in untested conditions. This, however, does not suffice to establish a dynamical model’s explanatory credentials, since predictive force is not equivalent to explanatory force (Kaplan and Craver 2011).

  4. These two views are not exhaustive of the range of possible positions. For instance, another logically weaker view one might defend is that some dynamical explanations are mechanistic, while others are non-mechanistic. This seems to be the view embraced by Zednik (2011). He maintains that some explanatory dynamical models are mechanistic, whereas others instantiate covering-law explanations. For reasons discussed shortly, this view is not tenable.

  5. Hempel recognized this to be a serious barrier to his own account. Hempel (1965) considers a number of standard criteria for lawhood and comes to the conclusion that none are completely satisfactory. Salmon (1989/2006) and Woodward (2003) arrive at similarly pessimistic conclusions.

  6. Although this characterization focuses on the specific challenges for explanations involving deductive subsumption under laws, it is also problematic for so-called inductive-statistical explanations involving inductive subsumption under statistical laws (Hempel 1965). Inductive-statistical explanations conform to the same general pattern, but are assessed according to whether the explanans confers high probability on the occurrence of the explanandum event. The admission of exceptions in a statistical law featured in the explanans could serve to lower the probability conferred on the explanandum, and consequently cause similar problems—albeit less severe—for inductive-statistical variants of the CL account.

  7. One may object that even though the HKB model does not apply to human locomotory behavior, it does apply to other rhythmic limb movements such as those involved in equine locomotion, and so the scope of the model is not quite as restricted as implied. Indeed, Kelso (1995) famously cites this interesting feature as a notable strength of the model. Nevertheless, this response is inadequate because a situation in which the HKB model has highly gerrymandered scope (the model applies to some but not all systems exhibiting rhythmic limb behavior) is hardly an improvement over one in which it has restricted scope.

  8. The tight connection between explanation and prediction follows as a direct consequence of the CL account. If explanations take the form of arguments, then explanations and predictions will have the same logical structure. Hempel (1965) recognized this, and argued that every adequate explanation can serve as a potential prediction. For reasons explored in detail by Hempel (1965), he did not endorse the reverse claim that every adequate prediction is a potential explanation.

  9. Of course, understanding all aspects of temporal organization is not equally important for every mechanism. For example, understanding the precise temporal transition from one state to another in a digital logic gate or transistor may be relatively unimportant as those intermediate, transitional states between on- and off-states are not critical to how the transistor performs its function.

  10. Although the action potential waveform observed in the squid axon is fairly typical, and closely resembles those recorded from myelinated axons of vertebrate motor neurons, it is important to note that the precise waveforms vary from neuron class to neuron class and from species to species.

  11. Electrochemical equilibrium is defined by the precise balancing of two opposing forces: (1) a concentration gradient, which causes ions to flow from regions of higher concentration to regions of lower concentration, and (2) an opposing electrical gradient that develops as charged ions diffuse down their concentration gradients across a permeable membrane, taking their electrical charge with them. The electrical potential generated across the membrane at electrochemical equilibrium, otherwise known as the equilibrium or reversal potential, can be computed using the Nerst equation (for a single permeant ion species) and the extended Goldman equation (for more than one permeant ion species). For further details, see Dayan and Abbott (2001).

  12. This claim is consistent with the idea that pragmatic factors might dictate that such detail is irrelevant in a given explanatory context. This does not, however, negate the fact that explanations with such gaps leave something more to be explained. Filling in those gaps comprises a kind of progress, even if that kind of progress is not relevant in a given explanatory context.

  13. At the end of their seminal 1952 paper, they state: “It was pointed out in […] this paper that certain features of our equations were capable of a physical interpretation, but the success of the equations is no evidence in favour of the mechanism of permeability change that we tentatively had in mind when formulating them. The point that we do consider to be established is that fairly simple permeability changes in response to alterations in membrane potential, of the kind deduced from the voltage clamp results, are a sufficient explanation of a wide range of phenomena that have been fitted by solutions of the equations” (Hodgkin and Huxley 1952, 541).

  14. Kaplan and Craver (2011) propose a mapping requirement on mechanistic models, which they dub the model–mechanism–mapping (3M) principle. 3M is intended to capture a central tenet of the mechanistic framework, namely, that a model carries explanatory force to the extent it reveals aspects of the causal structure of a mechanism (i.e., to the extent the model elements map onto identifiable components, activities, and organizational features of the target mechanism).

  15. For a different interpretation of the view expressed by Bechtel and Abrahamsen (2010), see Zednik (2011). Zednik puzzlingly maintains that they endorse the view that a given dynamical model “does not itself describe the […] mechanism, but instead analyzes how the mechanism behaves over time” (Zednik 2011, 248). This interpretation is, however, exceedingly difficult to reconcile with the broader framework presented by Bechtel and Abrahamsen.

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  1. Department of Cognitive Science, ARC Centre of Excellence in Cognition and its Disorders (CCD), Perception in Action Research Centre (PARC), Macquarie University, Australian Hearing Hub 3.822, 16 University Drive, Sydney, NSW, 2109, Australia

    David Michael Kaplan

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Kaplan, D.M. Moving parts: the natural alliance between dynamical and mechanistic modeling approaches. Biol Philos 30, 757–786 (2015). https://doi.org/10.1007/s10539-015-9499-6

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