Abstract
In the last two sections of Structure, Thomas Kuhn first develops his famous threefold conception of the incommensurability of scientific paradigms and, subsequently, a conception of scientific progress as growth of empirical strength. The latter conception seems to be at odds with the former in that semantic incommensurability appears to imply the existence of situations where scientific progress in Kuhns sense can no longer exist. In contrast to this seeming inconsistency of Kuhns conception, we will try to show in this study that the semantic incommensurability of scientific terms appears to be fully compatible with scientific progress. Our argumentation is based on an improved version of the formalization of Kuhns conception as developed in the 1970s by Joseph Sneed and Wolfgang Stegmüller: In order to be comparable, incommensurable theories need the specification of relations that refer to the concrete ontologies of these theories and involve certain truth claims. The original structuralist account of reduction fails to provide such relations, because (1) it is too structural and (2) it is too wide. Moreover, the original structuralist account also fails to cover important cases of incommensurable theories in being too restrictive for them. In this paper, we develop an improved notion of “reduction” that allows us to avoid these shortcomings by means of a more flexible device for the formalization of (partially reductive) relations between theories. For that purpose, we use a framework of rigid logic, i.e., logic that is based on a fixed collection of objects.
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Notes
See Kuhn (1996, pp. 168 and 169).
Kuhn (1996, p. 170f).
Kuhn (1996, p. 172f).
Cf. Michael Friedman’s “neo-Kantian” interpretation of Kuhn in Friedman (2001).
Kuhn (1996, p. 169).
The canonical formulation of the structuralist account of reduction is found in Balzer et al. (1987, Chap. VI. 4). See also Sneed (1979, 1976). A review of early discussions and criticisms of that notion is presented in Rott (1987). A volume exclusively devoted to the problem is Balzer et al. (1984). See also Hoering (1984) and Niebergall (2000). Last but not least, a certain critique of the structuralist concept of reduction is the main point of criticism in Kuhn (1976).
See Balzer et al. (1987, Chaps. I and II) for the respective specifications. \(\mathbf {M_p}\) represents a class of potential models, i.e., the class of all models of many-sorted first- or higher-order logic as restricted to a certain finite vocabulary that fulfills a number of “characterizations” (e. g., a relation symbol may be associated with a certain type, and it may be required that the relation is transitive or the like). \(\mathbf {M}\) represents a class of models, as obtained from \(\mathbf {M_p}\), by the application of a number of laws. \(\mathbf {I}\) is a subclass of \(\mathbf {M_p}\)—the class of intended applications. Thus, the empirical claim of the theory is expressed by the proposition that \(\mathbf {I}\subseteq \mathbf {M}\). This conception of a theory-element is a gross simplification of the structuralist formalism because we do not consider partial potential models, constraints and links here, and we also assume that a theory is represented by a single theory-element. However, we only introduce this simplified notion here, in order to illustrate the problems of the structuralist notion of reduction. We certainly do not claim that constraints, links, and partial potential models may be dispensable. Cf. Moulines (1984), where the same simplified framework is used (for the same purpose).
This is just a special case of the structuralist notion as defined in Balzer et al. (1987, p. 277, DVI-5 and DVI-6). In the latter case, a theory is reduced, in our sense, to a specialization of another theory. However, we skip this detail here because it just leads to a notion of reduction, which is even wider.
We do not need complex examples such as they are considered in Niebergall (2000, p. 153ff). “Absurd” reductions are obtained here in a rather trivial and straightforward way.
That reduction involves a truth claim was already pointed out in Hoering (1984, p. 43f).
This example is dealt with from a structuralist point of view in Caamaño (2009) (see also the remark in the next footnote). The example of phlogiston is also one of Kuhn’s main examples of a scientific revolution. Cf. Kuhn (1996, Chap. VI and p. 107) and Kuhn (1976, p. 192). Our claims in this paper somewhat overlap with the recent discussion of phlogiston theory in Ladyman (2011), and Schurz (2011). The difference between our account and the discussions by Ladyman and Schurz is essentially that we are not concerned with the realism debate here but rather with the problem of incommensurability and with the problem of reduction in the realm of the structuralist framework. However, our conception strongly converges with Ladyman and Schurz insofar as we claim that reduction between theories has to establish a certain correspondence relation between the empirical claims of these theories.
The solution to the problem of reduction of phlogiston theory to modern chemistry as provided in Caamaño (2009) is simply to restrict reduction to the partial potential models of these two theories (i.e., the non-theoretical objects) and to identify the latter as being identical. However, this implies that the non-theoretical objects of these two theories have to be entirely theory-independent. Our conception, on the other hand, will also work in cases where even the non-theoretical concepts of a theory are “theory-infected.” Cf. Sect. 3, below.
Caamaño (1984, p. 58).
Caamaño (1984, p. 58).
See Kuhn (1996, p. 107).
Kuhn (1976, p. 190).
For an overview of these varieties, see Sankey (1993).
The principal layout of the rigid framework is described with much more detail (with the inclusion of constraints, links, etc.) in Damböck (2012). In this paper we provide just a sketch of the principal framework, because our main purpose is the problem of reduction, which was not considered in Damböck (2012).
As a reviewer of this paper points out, it has to be noted here that this claim is only true for potential models but not with respect to intended applications. Whereas the classical structuralist formalism introduces the objects of a theory at the level of intended applications, we already introduce them at the level of specifications of the \(D_i\) (which are mere types in the structuralist formalism and sets in our conception). As a consequence of this formal trick, our formalism becomes more flexible. In particular, in the context of the classical framework it may appear to be extremely complicated (if not impossible) to establish the definition of reduction we develop below.
We do not use our framework for the specification of a semantic for a logic that uses the vocabulary of the theory (but only for the specification of a relation between theories in an informal model theoretic language). However, in order to keep our construct consistent, we may require here that the domain sets \(\mathfrak {S}(D_i)\) and the elements of relations, as specified below, by means of cartesian products of the form \(\{R_j\}\times \mathfrak {S}(R_j)\) be disjoint. For purposes of simplicity, we do not consider “auxiliary types” here. Cf. Balzer et al. (1987, p. 10). Functions are introduced as special cases of relations by means of “characterizations.” Cf. Balzer et al. (1987, p. 14).
For a comprehensive treatment of these crucial definitions see Damböck (2012, Sects. 2 and 4, in particular, pp. 710–11).
See Moulines (1984, p. 60).
See Balzer et al. (1987, Chap. IV. 1). The specialization-relation is intended to cover most cases of normal (non-revolutionary) development of a science.
Another example (namely, classical particle mechanics) that illustrates how to translate case studies from the classical into the rigid formalism can be found in Damböck (2012, p. 711f).
The following examples are all adopted from p. 337 of Caamaño’s paper.
A model that allows us to identify these elements of a model that are approximately true may be chosen, along the lines that were drawn out in Balzer et al. (1987, Chap. VII).
Cf. Kuhn (1996, p. 111).
Stegmüller’s attempt to close “rationality gaps” in Kuhn’s conception is formulated in Stegmüller (1976, 1976). Cf., in particular, Stegmüller (1976, p. 215): “Two points in Kuhn’s conception remain unexplained. First, how it is that the older, dislodged theory had been successful. Second, how we come to speak of progress in the case of scientific upheavals.” See also Kuhn’s reply in Kuhn (1976). For a historical treatment of the program of “Kuhn Sneedified” and the encounter between Stegmüller and Kuhn see Damböck (2014).
Cf. the remarks on p. 9, above.
See Kuhn (1976, p. 192). It may be objected here that these claims and solutions that phlogiston theory exclusively provides are not available in the context of modern chemistry simply because they are false. However, it is not the aim of this paper to defend Kuhn’s positive claims about the existence of ‘Kuhn losses’. Our argumentation is just a conditional one: if there are “Kuhn-losses” then we have a good solution for that case.
It seems to be neither necessary nor wise to identify the observable parts of a theory by means of the unique identification of a “non-theoretical vocabulary” because there may be certain properties, which sometimes express observable, and at other times non-observable facts. For example, the size of an object becomes un-observable, as soon as the object in question is “small enough.” (That is, the identification of a certain term as theoretical or non-theoretical has to be context-sensitive). For further discussions of the problems of observability and empirical adequacy, see van Fraassen (1980, Chap. 3).
Empirical data are not neutral but in their selves are formulated in the respective non-theoretical vocabulary of a theory. Of course, we may have some measurements, even in incommensurable theories, where different observational terms are associated with the same numerical values. However, it is quite obvious that this does not necessarily have to be so. On the basis of their entirely different theoretical terms, these two theories may use entirely different units that lead to entirely different numerical values for the same observable phenomenon.
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Acknowledgments
Work on this paper was supported by the Austrian Science Fund (FWF Research Grant P21750 and P24615). Earlier versions of this paper were presented at workshops in Munich (February 2012), Tilburg and Konstanz (April 2012). For comments I am grateful to Jeffrey Barrett, Hans-Joachim Dahms, Richard Dawid, Paul Hoyningen-Huene, Walter Hoering, Franz Huber, Theo Kuipers, Christoph Limbeck- Lilienau, Carlos Ulises Moulines, Michael Schorner, and Friedrich Stadler.
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Damböck, C. Kuhn’s notion of scientific progress: “Reduction” between incommensurable theories in a rigid structuralist framework. Synthese 191, 2195–2213 (2014). https://doi.org/10.1007/s11229-013-0392-z
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DOI: https://doi.org/10.1007/s11229-013-0392-z