Abstract
In this essay, I shall show that the so-called inferential (Suárez 2003 and 2004) and interpretational (Contessa 2007) accounts of scientific representation are respectively unsatisfactory and too weak to account for scientific representation (pars destruens). Along the way, I shall also argue that the pragmatic similarity (Giere 2004 and Giere 2010) and the partial isomorphism (da Costa and French 2003 and French 2003) accounts are unable to single out scientific representation. In the pars construens I spell out a limiting case account which has explanatory surplus vis à vis the approaches which I have previously reviewed. My account offers an adequate treatment of scientific representation, or so I shall try to argue. Central to my account is the notion of a pragmatic limiting case, which will be characterized in due course.
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Notes
All I need to assume here is that in scientific representation providing descriptions or explanations of natural phenomena is the dominant pragmatic constraint.
In Sect. 5 I shall provide additional support of the claims made here.
In this context, Suárez refers to Giere 1988, 1999; van Fraassen 1980 as defences of [sim] and [iso], respectively (Suárez 2003, p. 227).
Suárez notes that he has “little to say about what makes one representation more accurate than another” (Suárez 2003, p. 226). Suárez explicitly deals with the constitution question of scientific representation and not with the normative question of scientific representation.
This argument against [iso] and [sim] is taken over in Frigg (2006).
I consider [iso], similarity qua form, as a specific version of [sim].
Others have also endorsed pragmatic [sim] (Teller 2001; Bailer-Jones 2003. According to Teller, what counts as similarity will depend on the level of accuracy one requires: “if the aim is prediction or explanation of quantitative detail one will need to specify the interests of the model users in more detail” (Teller 2001, p. 401 [emphasis added]). Moreover, he notes that because of the context-sensitivity involved in scientific representation, no general account of relevant similarity is required: “No general account is needed precisely because it is the specifics of any case at hand which provide the basis for saying what counts as relevant similarity. In other words, the very facts which make this demand impossible to meet also show that the demand was misguided to begin with.” (ibid.). Daniela Bailer-Jones also endorsed pragmatic [sim], for she stressed that the users of models should agree upon the function for which a model is intended, decide which allowances are made for the model not to fit the data or the laws of nature, and select the aspects of a phenomenon which a model represents (Bailer-Jones 2003, p. 72).
Note that ‘vehicle’ and ‘model’ are used interchangeably by Contessa.
As the arguments against (pragmatic) homomorphism are analogous to those against (pragmatic) similarity, I will omit further discussion of homomorphism in what follows.
Note that in the limiting case, where R 3 is empty, a partial structure becomes a total structure.
In what follows I shall focus on idealization and abstraction. An idealization refers to a conceptual scheme which deliberately distorts certain properties of a physical system when modelling it; an abstraction on the other hand refers to a conceptual scheme which omits certain properties of a physical system when modelling it (Cartwright 1989, p. 185–198).
In Pincock 2005, pp. 1253–1255 related concerns are raised against partial isomorphism.
That a model is a pragmatic limiting case of its target means that: (1) M provides a ceteris paribus and ceteris absentibus conceptualization of its target—i.e. it treats its target in a highly abstracted and idealized way, as it cuts loose from the complexity of the empirical world and deliberately distorts it—and (2) M allows for the inference of certain relations which are not inferable from the target itself, but which hold approximately for the target relative to a purpose P.
Another way of representing it is as an ensemble of changing pure states |ψ(t)› with probability distribution Pr(ψ(t)).
In the opposite limit, one assumes that the system is only determined by its environment so that the Hamiltonians can be ignored and only the Lindblads remain.
The formal criteria for transitivity are: if A → B and B → C then A → C. When the arrow denotes the relation ‘is a limiting case of,’ then we have: if Model1 → Target1 and Target1 → Model2 then Model1 → Model2. However, as the semantics of the limiting case approach rules out that Target1 → Model2 and Model1 → Model2, transitivity cannot obtain.
The quotation marks indicate that my proposal is neutral with respect to the realism-instrumentalism debate. It is highly desirable that an account of the normative problem of scientific representation is independent from the realism-instrumentalism debate—and equally so for an account of the constitution problem of scientific representation: for both realists and instrumentalists models represent scientifically.
Adam Morton has nicely discussed this idea in the context of atmospheric models (Morton 1993, p. 660–662).
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Ducheyne, S. Scientific Representations as Limiting Cases. Erkenn 76, 73–89 (2012). https://doi.org/10.1007/s10670-011-9309-8
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DOI: https://doi.org/10.1007/s10670-011-9309-8