Abstract
This paper provides a conceptual framework that allows for distinguishing between different kinds of generalisation and applicability. It is argued that generalising models may bring epistemic benefits. They do so if they show that restrictive and unrealistic assumptions do not threaten the credibility of results derived from models. There are two different notions of applicability, generic and specific, which give rise to three different kinds of generalizations. Only generalising a result brings epistemic benefits concerning the truth of model components or results. Abstracting the model and applying the model into new systems are not intrinsically epistemically beneficial in this way. The Dixit-Stiglitz model of monopolistic competition is used as an illustration.
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Notes
Abstracting the model and generalising results thus differ with respect to ‘expressive power’. The differences are complex, and they cannot be dealt with in this paper due to limitations of space. I develop the notions of expressive power and of abstraction in a companion paper ‘The epistemic benefits of generalisation in modelling II: expressive power and abstraction’ that focusses on the details of model descriptions in generalisations.
Weisberg (2004) argues that the precision of model descriptions determine the number of ‘models’ picked out by those descriptions. If these ‘models’ then correspond to the possible systems, Weisberg’s solution is consistent with what I say in the text. The ‘models’ that Weisberg discusses here are abstract structures or points in state space (see e.g., 2013, p. 42). Weisberg shows that generality may increase if the model descriptions pick out a proper superset of models (qua abstract structures), and the models must then apply to a larger number of possible systems. I do not need to assume that the possible systems correspond to models qua abstract structures or to model systems, nor that such abstract structures or model systems even exist. My account may thus be more palatable to philosophers who think that such things either do not exist or are epistemically suspect or unnecessary for understanding modelling (e.g., Levy, 2015; Odenbaugh, 2018). However, I do not need to deny the existence of abstract structures either, as long as at least some kinds of generality and applicability are conceptualised as having to do with the relationship between model descriptions and systems rather than models qua abstract structures and systems.
See ‘The epistemic benefits of generalisation in modelling II: expressive power and abstraction’.
Increasing each good by a constant amount λ in a homothetic utility function does not affect the elasticity of substitution between commodities: U (x0, V(λx1, λx2,…, λxn)) = U (x0, λV(x1, x2,…, xn)).
Lest this formulation leads the readers astray, generality is not a matter of the number of model descriptions. After all, as already discussed, Krugman’s simpler formulation U is a special case of the more complicated DSP. I argue in the companion paper ‘The epistemic benefits of generalisation in modelling II: Expressive power and abstraction’, that epistemically beneficial assumptions typically decrease the number of assumptions in a model.
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Acknowledgements
This paper started as a result of a set of events that transpired when Caterina Marchionni wrote a draft which pointed out how the epistemic benefits of generalisation are similar to those obtained by showing that a result is robust. I thought she was right, and I asked to join her in writing the paper. The paper was then re-written and its title was adopted while she was still a co-author. As time passed, however, we came to somewhat different views about how to develop the paper and I continued writing it alone. Due to the unusually central influence of one scholar in helping the writing process, I find it inappropriate to mention any others here, despite the fact that I can think of a few names. The anonymous reviewers have also been highly helpful. The usual disclaimer applies. The research was partly funded by a Nankai University Arts and Humanities Development Funds, grant no. ZB21BZ0218.
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Lehtinen, A. The epistemic benefits of generalisation in modelling I: Systems and applicability. Synthese 199, 10343–10370 (2021). https://doi.org/10.1007/s11229-021-03250-0
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DOI: https://doi.org/10.1007/s11229-021-03250-0