Abstract
The incommensurability thesis, as introduced by T.S. Kuhn and P.K. Feyerabend, states that incommensurable theories are conceptually incompatible theories which share a common domain of application. Such claim has often been regarded as incoherent, since it has been understood that the determination of a common domain of application at least requires a certain degree of conceptual compatibility between the theories. The purpose of this work is to contribute to the defense of the notion of local or gradual incommensurability, as proposed by late Kuhn. The application of this notion would allow to render the incommensurability thesis coherent. To support this view, a typical example of incommensurability will be formally analyzed by applying the structuralist metatheory developed, among others by W. Balzer, C.U. Moulines and J.D. Sneed. The structural reconstruction of the relation between the phlogiston theory and the oxygen theory offered here will reveal that they are locally incommensurable, and will even make possible to determine the ontological reduction relation that they also exemplify.
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Notes
Cf. Kuhn (1983).
Besides the structuralist approach, there are other highly sophisticated and interesting approaches for tacking the problem of incommensurability. Among these, three are worthy of special mention: the cognitivist computational treatment of Thagard (1992); the treatment of Laudan, the inaugurator of the so-called ‘problem-solving approach’, which is characterized in (1977); and the proposal of Niiniluoto in the setting of his critical scientific realism, which he expounds in (1980).
“I shall use a quite modern formulation for my purpose, and I shall disregard completely the fact that chemists in the eighteen century were not able to express their ideas in the same way. I still think that I do not miss the point by my anachronistic account. Furthermore I do not try to do justice to the historical facts. I just want to formulate a phlogiston theory which is the best I can think of and which explains as many chemical facts as possible. After all the problem at issue is not only an historical one but also a problem of logical analysis”, Kamlah (1984, p. 223). Kamlah’s anachronistic treatment of the relation between the phlogiston theory and the oxygen theory essentially relies on concepts like those of molecular or atomic weights, that were not available until John Dalton developed his atomic theory at the beginning of the nineteenth century. Described in these terms, the relation between the above rival theories may seem structurally closer than it actually was, since more information than that available at the time is being employed in redefining the theoretical concepts of one theory in those of the other. But let us not forget that, in order to understand the reasons why the transition from the phlogiston theory to the oxygen theory finally happened, it is crucial to provide a historically faithful description of both rival theories. In making use of anachronistic notions, Kamlah implicitly introduces an experimental background clearly beyond the experimental possibilities available for identifying substances during Pristley’s and Lavoisier’s historical period. In particular, the chemical distinction between atoms and molecules was not drawn until Amedeo Avogadro, by experimentally determining the density of gases under different temperature and pressure conditions, extensively developed the Daltonian atomic theory. Furthermore, Kamlah’s conclusion that the phlogiston theory is reducible to a restricted oxygen theory, even despite their discrepancies relative to ontological postulates, only holds if we accept as the standard version of the former theory that according to which phlogiston is ascribed a negative atomic weight (cf. ibid., p. 227). This, however, does not seem right, for ascribing a negative weight to phlogiston is commonly understood as an ad hoc hypothesis that emerged only once the phlogiston theory was already in crisis.
Cf. Balzer et al. (1987, pp. 167–177).
In structuralist literature, the notion of a theory-net is defined by establishing two conditions: (1) that there should exist a finite non-empty set of theory-elements TE and a specialization relation σ; (2) that the specialization relation be restricted to the set TE. By adding new conditions to the two aforementioned one, it is possible to define a more restricted theory-net. This is a theoretical tree network or theoretical tree, the specific characteristics of which are as follows: (1) the connection between the theory-elements that belong to TE, such that for any pair of different theory-elements belonging to TE it is held that either both are specialization of some other common theory-element, or that both have some specialization in common; (2) the existence, within this set, of a single basic theory-element, i.e. of a single theory-element that is not a specialization of any other element of the aforementioned set. Given that the definition of a theory-net presupposes that of specialisation, the principle defining features of this should be mentioned, even if in passing. They are as follows: (a) equality between the classes of potential models and partially potential models of the respective related theory-elements; and, (b) the inclusion of the current class of models, the class of constraints, the class of links and that of intentional applications of the theory that it specializes, respectively, in the class of actual models, the class of constraints, the class of links, and that of the intentional applications of the theory that is specialized. Expressed in other terms, two theory-elements that are related by means of a specialization relation will share their conceptual apparatus, while they will diverge with regard to the scope of their laws and, consequently, with regard to the extension of their classes of intentional applications, since the theory-element that specializes restricts the laws and the empirical scope of the specialized theory-element.
As will be clear from the reconstructions, both theory-elements diverge, particularly with that concerning its dependence (PHLO) or not (OXG) on the theory of principles, and consequently, on a theory of the qualitative chemical composition. Neither of the theories studies constitutes a theory-net as it has not been necessary to establish more specific laws to account for the different types of specific cases of combustion, nor is it the case that both theories specialize the same theory. Nor do they constitute part of a theory-net given they do not satisfy any of the conditions that must be fulfilled for all specialization; i.e. neither do the laws nor either of the two theory-elements restrict any fundamental law established in the other, nor do its corresponding classes of potential and partially potential models coincide with any other theory-element. As will be seen in the reconstructions, P and Q, for example determine Mp of PHLO and of OXG, respectively, but not Mp of the Cameralist theory of elements (on which both depend). In the same manner, the relation of equal or lesser respirability, R, does not determine Mpp of either the theory of principles, or of composition or reactions, while it does determine Mpp of the theories of combustion.
Cf. ibid., pp. 386–423, and Díez and Moulines (1999, p. 365).
Cf. Balzer et al. (1987, p. 390).
Below, the theory of phlogiston will be represented by the abbreviation ‘PHLO’, and the theory of oxygen by ‘OXG’.
The principal historiographic sources used in the reconstructions of the theories of phlogiston and oxygen are those mentioned in Sect. 3.1.
Adhering to the method of presentation used in An Architectonic for Science, I shall include the set of numbers among the constituents of the models.
The reduced respirability of the surrounding air is not explicable by any law of PHLO, thus it is possible to identify the combustion on the basis of other properties.
For the same reasons, the inclusion of the theoretical-OXG O sub-domain in the non-theoretical OXG domain S does not imply the necessary theoretical-OXG determination of S.
The axioms given in π(RBM, 1, 2, 5) are in keeping with those established in Balzer et al. (1987, p. 269), where the class of potential models for rigid body mechanics is defined.
The informal analysis that follows is based on the historical study of chemistry by Brock (1992, pp. 43–86).
Cf. ibid., pp. 66, 75.
Balzer et al. (1987, pp. 53–54).
Cf. ibid., p. 49.
Cf. ibid., p. 59.
Cf. ibid., p. 51.
Cf. ibid., pp. 51, 71–72.
Cf. ibid., pp. 55, 75.
Kuhn expresses this concern in (1983, p. 673).
Cf. Brock, op. cit., pp. 124–127.
Cf. Díez and Moulines (1999) op. cit., p. 459.
Dieter Mayr anticipated this notion of reduction by establishing the explanation of anomalies as a criterion for reduction between incompatible successive theories (cf. Mayr 1976, pp. 275–294).
The relevant sources to this respect are mentioned in Moulines (1984, pp. 69–70). The author refers there to numerous pairs of theories related by ontological reduction, being plausible to assume that this relation would imply some sort of translation between the partial potential models of these theories (at least for the case of homogeneous ontological reduction, which will be discussed below). Among the pairs of theories mentioned by Moulines are the following: Kepler's Planetary Theory and Newtonian Particle Mechanics, Geometric Optics and Ondulatory Optics, Simple Equilibrium Thermodynamics and Kinetic Theory of Gases, Newtonian Particle Mechanics and Quantum Mechanics, Mendelian Genetics and Molecular Biology (cf. pp. 61–62).
Cf. Stegmüller (1976, § 11); Moulines, Exploraciones Metacientíficas, cit., p. 207.
The definition of theoretical suplantation with incommensurability is established in Díez and Moulines (1999, pp. 456–460). The reason why the definition of incommensurability given in Balzer et al. (1987, pp. 306–320) is not given here has to do with its lesser interest for the analysis of this case in particular. In the present study the case requires a definition of incommensurability that may be independent of the theoretical reduction and, in that manner, it may comply with all possible cases of incommensurability, among them, these that are not susceptible to theoretical reduction, such as the one dealt with herein. There is a more recent and suited structuralist proposal for defining the relation of incommensurability. Its character is more global, it allows the substitution of highly specific but not very illuminating conclusions for the present case to be substituted by other more general and revealing ones. In particular, it makes it possible to do without the prerequisite of the reduction relation, resorting to the T-non-theoretical relation
to establish a sufficiently significant relation between the theories.Díez and Moulines (1999, p. 459).
Cf. Balzer et al. (1987, pp. 275–279).
As shall be reiterated at a later point, this condition appears in Díez and Moulines (1999, p. 459), as one of the defining conditions of the relation of incommensurability.
Cf. Balzer et al. (1987, pp. 250–251, 278–279).
Cf. ibid., p. 277.
This work is included in the compilation Reduction in Science, cit., pp. 51–70.
“Conexiones ontológicas en la reducción de teorías”, cit., pp. 364–374.
Cf. Balzer et al. (1987, pp. 317–320).
Ibid., pp. 6–7.
Moulines (1991, p. 266).
Spector (1978).
This article appears in Poznan Studies in the Philosophy of the Sciences and the Humanities (Moulines 2000).
Moulines provides a formalization relative to theory-nets (ibid., p. 190), the one offered here, relative to theory-elements, amounts to a simplified version of the former.
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Acknowledgments
I am indebted to Jose Antonio Diez Calzada for his extremely insightful revisions to many previous versions of this paper. I am also thankful to Ulises Moulines for providing me clear guidelines on different intricate matters related to the structuralist treatment of the phlogiston case. This work was financially supported by the Spanish Ministry of Education.
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Caamaño, M. A Structural Analysis of the Phlogiston Case. Erkenn 70, 331–364 (2009). https://doi.org/10.1007/s10670-008-9141-y
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DOI: https://doi.org/10.1007/s10670-008-9141-y