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Cognitive dynamical models as minimal models

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Abstract

The debate over the explanatory nature of cognitive models has been waged mostly between two factions: the mechanists and the dynamical systems theorists. The former hold that cognitive models are explanatory only if they satisfy a set of mapping criteria, particularly the 3M/3M* requirement. The latter have argued, pace the mechanists, that some cognitive models are both dynamical and constitute covering-law explanations. In this paper, I provide a minimal model interpretation of dynamical cognitive models, arguing that this both provides needed clarity to the mechanist versus dynamicist divide in cognitive science and also paves the way towards further insights about scientific explanation generally.

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Fig. 1

Adapted from Keslo (1995)

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Notes

  1. As Craver points out (2006, 2007) the HH model was not explanatory by Hodgkin’s own lights since the model was compatible with a wide range of possible mechanisms.

  2. This claim by DS advocates is one that can and has been challenged (Chemero 2000). Upon closer inspection, the claim that discretization is ipso facto inadequate for the modelling of dynamical phenomena is dubious. Moreover, the question of how to model a phenomenon (discretely or continuously) may reflect more about the pragmatic decisions of the modelers rather than something about the nature of the phenomenon itself. I thank Colin Allen for drawing my attention to this point.

  3. Another response has been to embrace the charge of predictivism, maintaining that predictive success is in fact evidence for explanatory goodness (Chemero and Silberstein 2008).

  4. Many of the covering law proponents adopt something like Hempel and Oppenheim’s (1948) version of a covering law explanation (Bechtel 1998; Chemero and Silberstein 2008; Walmsley 2008). This has engendered criticism since the 1948 view is demanding, requiring strict, exceptionless or universal nomic generalizations and also that explanation of the relevant laws employed in the explanans require derivations of higher-level laws from lower-level ones (Gervais and Weber 2011). A more nuanced or sophisticated version of the DN view such as the simple instrumentalist DN approach might go some way to avoiding the problems that have dogged the covering law approach to cognitive dynamical models.

  5. A bifurcation occurs when “a parameter value is reached at which a sudden change in the qualitative type of the attractor occurs” (Norton 1995). Notice that a bifurcation occurs only in the anti-phase motion as frequency is scaled up but not in the in-phase motion which remains markedly stable in response to perturbations.

  6. Macro-scale is technically not quite correct. A minimal model explanation may also address meso-scale regularities. Thus, macro-scale should be taken to mean “non-micro-scale”.

  7. An additional example is Kugler and Turvey (2015) recreating quadri-pedal locomotive, dynamical motion with an inverted pendulum and spring.

  8. Ariew et al. (2017) provide a similar but importantly novel line of explanation as regards minimality for the observation of statistical phenomenon “reversion towards the mean” in biological populations across nature.

  9. For an insightful and informed treatment of the use of scales in engineering explanations as well as the “tyranny of the scales” issue in material physics, see chapter 5 of Wilson (2017).

  10. I thank an anonymous reviewer for stressing this point.

  11. It is worth acknowledging that the covering law proponent does not directly address this concern since, by their lights, satisfaction of the mapping requirement is not necessary for models to be explanatory. Thus, the disagreement about explanation between the mechanists and covering law proponents is more fundamental. And this partially explains the intractability of the impasse that has formed between them.

  12. This is a live issue in the scientific explanation debate (Reutlinger 2017). James Woodward himself has acknowledged the notion of non-causal counterfactual dependency and non-causal explanations in more recent work; c.f. Woodward (2018).

  13. This provides an extensive overview of the recent state of play in the scientific explanation debate.

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Acknowledgements

Thanks are owed to Andre Ariew, Mark Wilson, Robert Batterman, Colin Allen and Randall Westgren for helpful conversations and comments on the draft.

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  1. Department of Philosophy, University of Missouri, Columbia, MO, 65201, USA

    Travis Holmes

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Holmes, T. Cognitive dynamical models as minimal models. Synthese 199, 2353–2373 (2021). https://doi.org/10.1007/s11229-020-02888-6

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