Abstract
Philosophers of science have developed several accounts of how consideration of scientific models can prompt learning about real-world targets. In recent years, various authors advocated the thesis that consideration of so-called minimal models can prompt learning about such targets. In this paper, I draw on the philosophical literature on scientific modelling and on widely cited illustrations from economics and biology to argue that this thesis fails to withstand scrutiny. More specifically, I criticize leading proponents of such thesis for failing to explicate in virtue of what properties or features minimal models supposedly prompt learning and for substantially overstating the epistemic import of minimal models. I then examine and refute several arguments one may put forward to demonstrate that consideration of minimal models can prompt learning about real-world targets. In doing so, I illustrate the implications of my critique for the wider debate on the epistemology of scientific modelling.
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Notes
I employ the expression ‘possible worlds’ broadly to indicate the hypothetical, imaginary, or counterfactual scenarios and states of affairs that are posited by specific models. My broad use of this expression covers what other authors (e.g. Morgan 2001; Sugden 2000) have called ‘model worlds’ and ‘worlds of the model’. Also, I speak of ‘properties’ and ‘features’—as opposed to ‘property’ and ‘feature’—to allow for the possibility that distinct properties and features enable learning in different modelling contexts. I shall comment on this context-dependency and its implications for the merits of LMM in Sect. 2.
I shall occasionally state that minimal models ‘are assumed to lack any similarity, isomorphism, resemblance, etc. relation’ to real-world targets as an abbreviation for the characterization of ‘minimal models’ reported in the text. The proponents of LMM (e.g. Grüne-Yanoff 2009, 84) occasionally hint at a broader characterization of ‘minimal model’, according to which the set of minimal models includes both models that actually lack any similarity, isomorphism, resemblance, etc. relation to real-world targets and models for which no relation of similarity, isomorphism, resemblance, etc. to specific real-world targets has been determined by modellers. I shall expand in Sect. 2 on the differences between distinct characterizations of ‘minimal model’ and the implications of such differences for the merits of LMM. For now, I rely on the narrower characterization reported in the text both because the proponents of LMM repeatedly employ this characterization to single out minimal models (see e.g. Grüne-Yanoff 2009, 81–83) and because adopting the broader characterization would trivialize the issue whether we can learn from minimal models in the sense I explicate in Sect. 2.
I am not concerned here with assessing the merits of this supposition. For present purposes, I note that not all scientific modellers speak of learning in the sense indicated by LMM. In particular, several authors (e.g. Morgan 1999) regard learning as more akin to acquiring novel information about one’s targets than to justifiably changing confidence in specific necessity or impossibility hypotheses about such targets. In what follows, I bracket these definitional concerns and examine what we can learn from minimal models in the sense indicated by LMM. I expand on different ways in which consideration of minimal models can allegedly prompt learning in Sect. 4.
Some authors claim that learning from minimal models may go beyond undermining specific necessity or impossibility hypotheses (see e.g. Casini 2014, on the alleged provision of mechanistic insights about the examined targets). However, these authors typically adopt less restrictive characterizations of ‘minimal model’ than the characterization underlying LMM, since they allow that some world-linking relation may hold between what they call ‘minimal models’ and real-world targets (see e.g. Casini 2014, 660–662). For present purposes, I focus on the thesis that consideration of models that are minimal in the sense indicated by LMM can justifiably affect confidence in necessity or impossibility hypotheses.
Indeed, one might question whether many scientific models qualify as minimal in the sense indicated by LMM. After all, the thought would be, given a model and a putative target, one can almost invariably find some sort of similarity, isomorphism, resemblance, etc. between such model and target. I am not concerned here with assessing the cogency of this supposition. For the purpose of my critique, it suffices to note that if no model qualified as minimal in the sense indicated by LMM, then LMM would reduce to the vacuous conditional statement that if there were minimal models, then we could learn from such models. In this respect, the challenge for the proponents of LMM is to provide a reformulation of LMM that is neither vacuous in this sense nor trivial in the sense specified in the text (see my remarks on LMM* and LMM** below).
I am not aware of authors who explicitly relinquish LMM to advocate LMM*. Grüne-Yanoff might be taken to speak in favour of LMM* when he observes (2009, 98) that minimal models do not support hypotheses about particular real-world situations without empirical information about the world (see also Grüne-Yanoff 2013a).
I focus on these two models because the proponents of LMM have debated over the epistemic import of those models in great detail and have claimed such models to constitute “a good example” of how minimal models can prompt learning about real-world targets (see e.g. Grüne-Yanoff 2009, 96, on Schelling’s model). My considerations hold mutatis mutandis for other instances of putative learning from minimal models (see e.g. Batterman and Rice 2014, on Fisher’s model of the 1:1 sex ratio, and Knuuttila 2009, on Tobin’s ultra-Keynesian model).
In his works, Schelling presents several versions of the checkerboard model, which differ in various details (see e.g. Sugden 2011). I shall expand on these differences whenever they are material to my critique of LMM.
Maynard Smith and Price (1973) explore more complicated versions of the Hawk–Dove model, where individual contestants can adopt several different strategies and can modify their own behaviour in response to their opponent’s behaviour. I focus on the basic Hawk–Dove model because it constitutes a more plausible candidate minimal model than the more complicated versions explored by Maynard Smith and Price (1973).
The expression ‘how-possibly explanations’ was originally used by Dray (1957, 1968) to indicate explanations that purport to account for how events whose occurrence was previously regarded as impossible could have occurred. Here I employ such expression to designate explanations that aim to identify possible causes of the examined phenomena, irrespective of whether the occurrence of these phenomena was previously regarded as impossible (for another characterization of how-possibly explanations that drops the presumption of impossibility, see e.g. Resnik 1991; for a recent discussion of how-possibly explanations, see e.g. Bokulich 2014; Forber 2012; Reydon 2012).
Rohwer and Rice (2013, 341 and 349) put forward similar remarks concerning Maynard Smith and Parker’s (1976) Hawk–Dove model of animal conflict. However, Rohwer and Rice adopt a less restrictive characterization of ‘minimal model’ than the characterization underlying LMM, since they allow that some world-linking relation may hold between what they call ‘minimal models’ and real-world targets (see e.g. Rohwer and Rice 2013, 347). Hence, their calls for the possibility of learning from minimal models do not directly support LMM, and my critique of LMM does not directly apply to such calls (see footnote no. 13 for a similar point about Batterman and Rice 2014).
The expression that models ‘come into clusters’ has been employed in different senses by scientific modellers. Below I use this expression to indicate situations where modellers’ predictive and explanatory goals are best achieved by using a combination of structurally dissimilar models.
Batterman and Rice emphasize a similar point when they claim that minimal models can be used to explain why classes of heterogeneous target systems display the same large-scale behavior “by demonstrating that the details that distinguish the model system and [the target] systems are irrelevant” (2014, 350). However, Batterman and Rice adopt a less restrictive characterization of ‘minimal model’ than the characterization underlying LMM, since they allow that some world-linking relation may hold between what they call ‘minimal models’ and real-world targets (see e.g. Batterman and Rice 2014, 355). Hence, their calls for the possibility of learning from minimal models do not directly support LMM, and my critique of LMM does not directly apply to such calls (see footnote no. 11 for a similar point about Rohwer and Rice 2013).
As Grüne-Yanoff puts it: “if model use merely contributes to the formulation of [a] hypothesis, then no learning takes place. Learning requires that the model effects justified changes of our confidence in the hypothesis, or if the model itself gave rise to its formulation that it forces us to form a belief about this newly-formulated hypothesis based on consideration of the model itself” (2009, 85).
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Acknowledgments
I thank J. McKenzie Alexander, Jesus Zamora Bonilla, Lorenzo Casini, Till Grüne-Yanoff, Olivier Roy, Paul Teller, and Michael Weisberg for their comments on earlier versions of this paper. I also benefited from the observations of audiences at the Munich Center for Mathematical Philosophy, the 6th Models and Simulations Conference at the University of Notre Dame, and the 24th Biennial Meeting of the Philosophy of Science Association in Chicago. An earlier version of part of the paper appeared in the Proceedings of the 24th Biennial Meeting of the Philosophy of Science Association.
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Fumagalli, R. Why We Cannot Learn from Minimal Models. Erkenn 81, 433–455 (2016). https://doi.org/10.1007/s10670-015-9749-7
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DOI: https://doi.org/10.1007/s10670-015-9749-7