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Exploratory Uses of Scientific Models

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How to Do Science with Models

Part of the book series: SpringerBriefs in Philosophy ((BRIEFSPHILOSOPH))

Abstract

This chapter discusses a variety of closely related uses of models which are best described collectively as ‘exploratory modeling’. The importance of exploration to science has recently been emphasized by a number of historians and philosophers of science writing on scientific experimentation, and the chapter begins by reviewing this lively debate. Following a clarification of the meaning of ‘exploration’ by distinguishing between a ‘convergent’ and a ‘divergent’ sense, the concept is then applied to the case of scientific models. In particular, four different functions of exploratory models are distinguished: they may function as a starting point for future inquiry, feature in proof-of-principle demonstrations, generate potential explanations of observed (types of) phenomena, and may lead to reassessments of the suitability of the target. These functions are neither mutually exclusive, nor are they thought to exhaust the spectrum of possible exploratory uses to which models may be put. Examples for each of the four types of exploratory uses are provided and range from models in sociodynamics (traffic flow models) to proposed mechanisms of molecular rearrangements in physical organic chemistry. The chapter closes with a discussion of the prospects and limitations of exploratory modeling and concludes that exploration deserves a place alongside explanation and prediction as one of the core functions of scientific modeling.

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Notes

  1. 1.

    For recent collections of papers on the problem of scientific understanding, see [57, 60].

  2. 2.

    It is worth keeping in mind that the term ‘model’, as discussed in Chap. 1 (Sect. 1.2), used to have a more restrictive meaning, referring primarily to mechanical models, with other models commonly referred to as ‘analogies’.

  3. 3.

    For a discussion of mature symbol systems as a form of ‘“cognitive scaffolding”, which allow their users to “offload” or “externalize” cognitive load’, see [33, p. 59].

  4. 4.

    This is one of the reasons why experimentation and exploration are not mutually exclusive; drawing a contrast between ‘the experimental’ and ‘the explorative’ gives rise to a number of false dichotomies, of the sort found in [59, p. 191].

  5. 5.

    Quoted after [48, p. 351]. The French original is: ‘…elle est dans l'hypothèse de Coulomb sur la nature de l'action magnétique; on croyait à cette hypothèse comme à un fait; elle écartait absolument toute idée d'action entre l'électricité et les prétendus fils magnétiques’ [49].

  6. 6.

    Both experiments were exploratory, insofar as no firm theoretical foundation was available at the time; therefore, an alternative interpretation might consider the first experiment—which aimed at demonstrating the existence of a causal link—an instance of ‘convergent’ exploration, whereas the second experiment, with its simultaneous variation of different parameters, might be considered as a case of ‘divergent’ exploration.

  7. 7.

    Whereas early minimal models tend to derive their dynamics from system-level equations, modern synthetic models in contemporary theoretical ecology tend to be ‘bottom-up, representing many small spatial units or individuals and their behavior’, with their ‘system dynamics emerg[ing] from the interaction of the components’ [36, p. 367].

  8. 8.

    Hausman’s account of modeling as a form of conceptual exploration, however, is weaker than what I have in mind: as Uskali Mäki observes, on Hausman’s account, ‘a model as such contains no truth claims about the world, it is rather a definition of a predicate given by the assumptions of the model’ [56, p. 15]; only theoretical hypotheses about the applicability of model to particular situation are truth-valued. I agree with Mäki that this insulates models too much from potential challenges arising from the realist concern with truth.

  9. 9.

    Michael Redhead seems to entertain a similar idea when he suggests that, ‘[b]y exploring models […] for a theory T we can probe how approximations A M to the model M […] misrepresent M and the true behaviour of M as opposed to A M can now be used as a guide how to T behaves’ [54, p. 153].

  10. 10.

    On this point, see [58, p. 119]. While Bailer-Jones is one of the few philosophers of science to explicitly state that models provide ‘material for exploration’ (ibid.), she appears to regard exploration as mainly associated with an understanding of models as metaphors; this, it seems to me, does not do justice to the specific character of model-based exploration discussed in the present chapter.

  11. 11.

    For a detailed account of the evolution and timeline of traffic flow models, see [50].

  12. 12.

    The Lotka-Volterra equations do, in fact, permit for an equilibrium solution; however, the equilibrium point is unstable, so that any perturbation—however small—suffices to trigger the oscillatory behaviour.

  13. 13.

    My discussion of this example draws heavily on [40].

  14. 14.

    Quoted after [44, p. 222].

  15. 15.

    For a discussion of Ingold’s system of classifications, see [45].

  16. 16.

    Quoted after [40, p. 567].

  17. 17.

    Quoted after [40, p. 571].

  18. 18.

    The notion of a ‘how-possibly’ question goes back to the philosopher of history William Herbert Dray who had argued that ‘the demand for explanation is, in some contexts, satisfactorily met if what happened is merely shown to have been possible; there is no need to go on to show that it was necessary as well’ [46, p. 157] That is, how-possibly explanations are offered as genuine and complete explanations of particular phenomena without pretending to subsume them under general laws or generalizations (see [55] for a more recent discussion).

  19. 19.

    Something like this seems to be Jordi Cat’s point in [51], though he appears to think that scientists and philosophers alike have tended to overlook the importance of initial and boundary conditions.

  20. 20.

    The difficulty of stabilizing phenomena in the absence of agreed-upon criteria for what counts as a successful experiment is known as the ‘experimenter’s regress’; for a discussion of its analogue in the case of scientific models and simulations (‘simulationist’s regress’), see [52].

  21. 21.

    Quoted after [47, p. 140].

  22. 22.

    The same holds for other many-body models such as the Hubbard model, discussed in Chap. 3 (Sect. 3.3). As I have noted elsewhere, often ‘the “exploratory” phase of understanding a proposed many-body model and cultivating intuitions about the interplay of themicroscopic mechanisms it is designed to represent is drawn out over many years; whether the model will in the end match an empirical phenomenon in many cases remains an open question’ [53, p. 263].

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    Axel Gelfert

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Gelfert, A. (2016). Exploratory Uses of Scientific Models. In: How to Do Science with Models. SpringerBriefs in Philosophy. Springer, Cham. https://doi.org/10.1007/978-3-319-27954-1_4

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