Abstract
In this paper I begin with a recent challenge to the Semantic Approach and identify an underlying assumption, namely that identity conditions for theories should be provided. Drawing on previous work, I suggest that this demand should be resisted and that the Semantic Approach should be seen as a philosophical device that we may use to represent certain features of scientific practice. Focussing on the partial structures variant of that approach, I then consider a further challenge that arises from a concern with the role of idealisations in that practice. I argue that the partial structures approach is capable of meeting this challenge and I conclude with some broader observations about the role of such formal accounts within the philosophy of science.
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Notes
cf. also Frigg (2006, p. 51) and LeBihan (2012) who also refer to the Semantic Approach as the orthodox view of theories and models. And here is Suppe from the late 1980s: “The Semantic Conception of Theories today probably is the philosophical analysis of the nature of theories most widely held among philosophers of science” (Suppe 1989, p. 3).
Basically, by demonstrating how certain proposals for defining an isomorphism fail.
For further on modelling San Francisco bay, see Weisberg (2013).
Again, he frames the debate in terms ofidentifying scientific theories with objects of a certain sort, namely models and distinguishes two broad versions of the Semantic Approach: the stronger which takes a scientific theory to be a collection of models and a weaker form that takes it as ‘best thought of’ as such a collection (2006, p. 529).
Of course, things are not quite that simple; see French (2015).
It is assumed that we are working in Zermelo-Fraenkel set theory (with the axiom of choice), with its familiar first-order language.
To avoid a possible confusion between \(R_{1}\), \(R_{2}\), and \(R_{3}\) and particular occurrences of a partial relation \(R_{i}\), we will always refer to the former as \(R_{1}\)-, \(R_{2}\)- and \(R_{3}\)-components of the partial relation \(R_{i}\).
For simplicity, we are considering here only two-place relations. But the definition can, of course, be easily extended to n-place relations.
For an additional application of this framework to the idea of partial conceptual spaces, see Bueno (2016).
This set of accepted sentences P represents the accepted information about the structure’s domain. Depending on the interpretation of science that is adopted, different kinds of sentences are to be introduced in P: realists will typically include laws and theories, whereas empiricists will add mainly certain regularities and observational statements about the domain in question.
And of course it is precisely such considerations that motivate a shift from theories to ‘research programmes’.
Weisberg himself also prefers a similarity based approach but defends one based on Tversky’s contrast account (Weisberg 2013, pp. 143–155).
The other three desiderata are that on any such account a model must be maximally similar to itself and to any target that shares all of its properties; that the model-world relationship should accommodate ‘rich’ structures in terms of the kinds of properties involved and that the models should be tractable, in the sense that similarity judgments should be open to comparison and not dependent on any hidden or inaccessible features of the models concerned. All of which seem to be uncontentious requirements.
Here we are talking about models that can be ‘de-idealised’. It has been argued that there are certain idealisations—the ‘thermodynamic limit’ in statistical mechanics, for example—that cannot be dispensed with in this way and thus that play an essential explanatory role. However the nature of this role remains, at best, unclear with nothing to indicate how it can be situated in standard accounts of explanation (see Bueno and French 2012 and forthcoming).
I am not suggesting that this was the heuristic route that Schelling actually took! However, the preface to Schelling (2006/1978) does suggest that in much of his work (of which the Schelling model is only a small part) was inspired by striking examples or significant social phenomena of one kind or another.
Interestingly, Gibbard and Varian explicitly compare models to pictorial representations: econometric models—of the kind that run of computers and are used to make economic forecasts are likened to photographs (perhaps, given recent events, really bad, out of focus photographs ... of the economist’s thumb); what they call ‘approximations’, which we might term idealised models, are akin to pencil drawings and caricature models are like, well, caricatures (1978, p. 665). And as they note, a given model may evolve from a caricature to an approximation or even to an econometric model.
Thus—following on from the previous footnote— the distortion illuminates a certain feature of reality, just as a pictorial caricature does (ibid, p. 676).
Frigg and Hartmann (2012) suggest that it is controversial whether such caricature models can be regarded as informative representations of their target systems, citing Reiss (2006). However, Reiss only briefly mentions these models in the context of arguing that they cannot be used to establish the existence of Cartwrightian capacities in the domain of social science.
It also helps respond to the worry about how strictly false models, containing such idealizations, can still explain—the answer is that although false, insofar as they work, whether in an explanatory sense or otherwise, they can be regarded as partially or quasi-true (da Costa and French 1990). Whether this corresponds to an appropriate form of approximate truth is another matter. Consider the model of a solenoid in which the magnetic field is taken to extend to infinity – this is not approximate to any real life situation (thanks to James Fraser for this example). However insofar as this is so only by virtue of the fact that infinity is not approximate to any finite quantity, one might respond either by treating such as special cases, depending on one’s view of infinity (i.e. a constructivist would have very definite views on such examples!) or by noting that just as physicists talk, perhaps loosely, of bringing in a test charge ‘from infinity’ so we can talk of dialling down the field ‘from infinity’.
See Woodward (2006), who also gives a useful classification of different forms of robustness. What we have in the Schelling case would appear to fall under what he calls ‘derivational robustness’, whereby ‘...an assumption is adopted about the value of the parameter and this is used, in conjunction with other theoretical assumptions, to derive some range of observed phenomena. Investigations are then made whether, given other values of the parameter, but the same theoretical assumptions, the same conclusions can be derived’ (ibid, p. 233).
Paternotte and Grose (2017) argue that not all cases of robustness can be accommodated by Weisberg’s analysis. They use examples from evolutionary game theory to show that in such cases there is no common structure, yet robustness may be justified in cases of phenomena that follow from multiple initial conditions or are multiply instantiated.
Indeed, Pincock acknowledges this point (op. cit., p. 1253).
Weisberg suggests that many proponents of the partial structure approach are structural realists who would deny that qualitative features are relevant to scientific enquiry (ibid, p. 141). But of course one could be a structural realist with regard to the most fundamental properties, in physics say, and still accept that features of systems at ‘higher’ levels or in different domains might best be described in non-relational terms.
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Acknowledgements
I’d like to thank Otavio Bueno, Juha Saatsi and Pete Vickers for helpful discussions concerning the topics considered here. I’d also like to thank the two referees for useful comments and Dimitris Portides for the kind invitation to contribute to this special issue.
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French, S. Identity conditions, idealisations and isomorphisms: a defence of the Semantic Approach. Synthese 198 (Suppl 24), 5897–5917 (2021). https://doi.org/10.1007/s11229-017-1564-z
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DOI: https://doi.org/10.1007/s11229-017-1564-z