Abstract
In this paper, a modest version of the Semantic View is motivated as both tenable and potentially fruitful for philosophy of science. An analysis is proposed in which the Semantic View is characterized by three main claims. For each of these claims, a distinction is made between stronger and more modest interpretations. It is argued that the criticisms recently leveled against the Semantic View hold only under the stronger interpretations of these claims. However, if one only commits to the modest interpretation for all the claims, then the view obtained, the Modest Semantic View, is tenable and fruitful for the philosophy of science.
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Notes
Major developments of the Semantic View are in Suppes (1960, 1962, 1967), Suppe (1974, 1977a, 1979, 1989), Giere (1979, 1988, 1999), and van Fraassen (1972, 1980, 1989, 1991, 2008). In their subsequent works, all these authors typically remained in favor of the Semantic View broadly speaking, even if they each developed particular versions of it, and never formed a unified view. A much more unified view has been initiated by Sneed (1971), and developed in Europe and especially in Germany thanks to the work by Wolfgang Stegmüller (1976, 1979a, b, 1986), C. U. Moulines (1975a, b, 1982, 1991, 2002) and Wolfgang Balzer (1978, 1982, 1985), among others. The view associated with these authors has been called the “non-statement view” but it is now known as the “structuralist program”. One classic work associated with the structuralist program is Balzer et al. (1987). Though this article is devoted to the Anglo-Saxon tradition of the Semantic View, we shall point out some obvious affinities and differences between our view and the structuralist program on various occasions in what follows.
See for example Cartwright (1983, 1989, 1999), Cartwright et al. (1995), Ereshefsky (1991), Downes (1992), Morrison (1999), Suárez (2003), Thomson-Jones (2006), Frigg (2006), Morrison (2007), Suárez and Cartwright (2008), and Krause and Bueno (2008). Even if not explicitly directed against the Semantic View, Redhead (1980) is an important background contribution to the debate.
What follows is a conceptual reconstruction of the Semantic View. No pretension is made to give a historically adequate account of how the Semantic View developed. Note also that the differences between the set-theoretical approach of Suppes, the state–space approach of van Fraassen and the relational system approach of Suppe are irrelevant here. We agree with Suppe (1989, p. 4) and da Costa and French (2003, p. 23) that van Fraassen’s and Suppe’s approaches can be conceived within Suppes’ set-theoretical framework.
To conceive of scientific theories as set of laws or of axioms was part of what has been labeled the “received view” by Putnam in his (1962). It is not clear that the label refers to a single unified view rather than to a variety of positions taken at different times by various authors (for a presentation of the historical development of the received view, see for example Friedman 1999 or Parrini et al. 2003). That said, the view is generally taken to be as presented in Carnap (1966) and Hempel (1963).
Suppe (1977a, pp. 62–66) provides an analysis of what counts as a fruitful axiomatization.
It is well known that there are various kinds of ‘scientific models’. In this paper, no stance is taken as to any particular mode of representation (structural, analogous, iconic etc.) by which scientific models represent the world. For a synthesis of the notions of model in science, see Frigg and Hartman (2006). The relationships between the notions of scientific models (as representing phenomena in the world) and logical models will be discussed in Section 3.
Or, as it is often easier, from the scientific literature in the field. Note that, in doing so, one avoids the problem of having to define what is the theory before being able to consider the models used by the scientists to represent the world. The class of models that the semanticist sets himself to study is simply the class of models that are used to represent a certain class of phenomena.
This distinction between the modest and the stronger interpretation of (Models) is related, but not identical to the distinctions between intrinsic and extrinsic characterization of theories by Suppes (1967, pp. 60–62, and 2002), and between representational and constitutional role of models by da Costa and French (2003, p. 34).
Whether or not this claim holds for structuralist program as well is an interesting question. Clearly, in spirit, and just like the proponents of the Semantic View, the structuralists appear not to adopt the stronger interpretation of (Models), since their “theory-elements”—roughly, elements of what is commonly called a theory—contain, in addition to sets of models, other components, including, among others, the intended domain of application of the theory and the necessary approximations associated with such application. See Schmidt (2008) for a short exposition of the notion of theory-element, and for more details, see Balzer et al. (1987). The question of whether or not the structuralists systematically make the distinction explicit and reject the first interpretation of (Models) requires a detailed investigation that falls beyond the scope of this paper.
Our modest interpretation of (Models) is similar to Downes’ “Deflationary Semantic View” as described in his (1992), which is constituted by the claim that “model construction is an important part of scientific theorizing”, while rejecting the claim that “all scientific theories are simply families of models” (p. 151). That said, the Modest Semantic View defended here differs from Downes’ version of the Semantic View, because it contains, in addition to the modest interpretation of (Models), the modest interpretations of (Scientific=Logical) and of (→ Adequacy), as described in the following two sections.
The common claim that the received view demands that scientific theories be axiomatized in first order logic has been recently challenged in the literature (see Lutz 2010).
On the question of whether the received view and the Semantic View are equivalent due to the Completeness Theorem, see the reviews on van Fraassen (1980) by Friedman (1982) and by Worrall (1984) along with van Fraassen’s answers in van Fraassen (1985, p. 301 sq.) and van Fraassen (1989, p. 211 sq.), which we believe are satisfactory. The discussion is summarized in da Costa and French (2003, pp. 30–31). On the question of wether the Semantic View—using first order model theory—is no better off than the received view—using first order logic plus identity, see French and Ladyman (1999) and references therein.
Rigorously speaking, the interpretation is a domain along with a function assigning extensions to non-logical terms.
It should be clear that “truth” is used here in the weak sense of “satisfaction”, or “truth within an interpretation”.
It is important to note that scientific models do not have to be mathematical structures. It suffices that scientific models possesses a structure (roughly, a domain and relations between the members of this domain). Any structure, whether or not this structure is captured by nice mathematical equations, can be considered from an abstract point of view. This leaves room for an account of structures within the sciences in which nice mathematical equations are not often possible to obtain.
A distinction between at least between three kinds of approximation arises from the literature: (1) Aristotelian abstractions consist in choosing the relevant parameters and variables of the system at hand—cf. Cartwright (1989, chap. 5); (2) Galilean idealizations consist in neglecting some parameters and variables that are clearly relevant the situation studied—cf. McMullin (1985); and (3) mathematical impoverishments consist in radically modifying the original equations such that solutions be tractable—cf. Redhead (1980).
This is true at least within the Anglo-Saxon tradition of the Semantic View. The structuralist program also developed, using the notion of a theory–net, a more subtle view of the complexities of the relationships between theories, models, and the data models. In a theory–net, various more “specialized” theories branch from a core theory-element. For more details on such an account, see Balzer et al. (1987, chap. IV).
It should be noted that Lloyd’s analysis does not include the assumption that population genetics is all there is to evolutionary theory. Rather, she aims at giving an account of the structure of evolutionary theory in a broader sense, including issues about species formation and extinction, group selection, and the tempo and mode of selection (1994, chap. 1, note 4 and chap. 3) [1988].
Morrisson (1999) is often cited for posing the criticism of the Semantic View along these lines. That said, Cartwright (1983, 1989) has been developing similar views over the past twenty years. More recently, Thomson-Jones (2006) gives an analysis of the relation between logical models and scientific models, the former being characterized by their truth making function, and the latter by their representational function. Brading and Landry (2006) and Frigg (2006) gives also a systematic analysis of the problem. It should be noted that van Fraassen presents the same problem in his (2006), and offers an extended discussion of it in his (2008, chap. 11), where he defends his “empiricist structuralism”.
This applies to the structuralist treatment of the “empirical claims” associated with a theory as well. See Balzer at al. (1987, chap. II) for more details.
Note also that model theory is useless when it comes to addressing the question of whether theories represent the features of the world that are not captured by the data models—a question on which the realist and the empiricist depart from one another. More on this point later.
It should be noted that Balzer et al. (1987, VII.2.2) manage to formally characterize a set of necessary (but not sufficient) conditions for an approximation to be “admissible”. For example, they formalize the rather intuitive notion that a given admissible approximation should remain so if one changes only “purely theoretical” aspects of the models associated with it. They also clearly recognize, however, that some strong pragmatic components of model construction are not formally explicable.
The exegesis of van Fraassen’s thought, and in particular, the study of the difference between constructive empiricism and empiricist structuralism falls outside of the scope of this paper.
See for example Da Costa and French (2003) for a systematic treatment of their view.
Note that this is not contradictory to our claim that the tools offered by the Semantic View are useless when it comes to solve the fundamental problem of representation. French and Ladyman are well aware of this and commit only to the claim that the Semantic Approach allows us to give an account of the relationships between the various models in the hierarchy of models as described in Section 2 (see note 12, p. 119, in their 1999). This remains true within Ladyman’s most recent ontic structural realism as exposed in Ladyman and Ross (2007). There, Ladyman and Ross explain that formal methods are good for representing and investigating “the relationships between theoretical models and models of the phenomena” (p. 117), but not for explaining how what they call “structures”, which “are to be understood as mathematical models”, can represent “real patterns” in the world (pp. 118–120). This holds true also for the accounts of evidence by Suppes, of confirmation by Lloyd, and of empirical grounding by van Fraassen in his (2008).
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Acknowledgements
I am extremely grateful to Armond Duwell for extensive discussions on earlier versions of this paper. I also wish to thank Michael Dickson for perceptive comments, as well as Leah McClimans for pressing on the notion of adequacy in the last section. Finally, I wish to express my gratitude to two anonymous referees for pointing out the affinities between the views of the structuralist program and my own.
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Le Bihan, S. Defending the Semantic View: what it takes. Euro Jnl Phil Sci 2, 249–274 (2012). https://doi.org/10.1007/s13194-011-0026-6
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DOI: https://doi.org/10.1007/s13194-011-0026-6