Abstract
In this paper I propose clearly to distinguish four fundamental types of intertheoretical relations that may be used to represent different types of theoretical change in empirical science. These four types can be represented formally through a refined version of the set-theoretical apparatus of structuralism. They may be described as: crystallization, theory-evolution, embedding, and replacement with partial incommensurability. They will be first explicated in intuitive, informal terms, and some historical examples will be suggested for each type. In the second part of the paper, the four types are characterized in structuralistic terms; the notions of a partial substructure and of a diachronic theory-net will play a central role.
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Notes
To be fair to Kuhn, he admitted on several occasions that the application of formal tools, especially those of structuralism, to diachronics (at least for some issues) might be possible or even desirable (see his remarks on this point in Kuhn 1976, and 2000). However, he himself never undertook this endeavor.
Under “wave optics”, respectively “Maxwell’s electrodynamics”, I understand here the formalisms of Fresnel and his immediate followers, respectively of Maxwell, together with the kinds of optical phenomena they were intended to cover—leaving aside the ontological (some would say: metaphysical) assumption of the existence of an ‘ether’. To include the ether hypothesis would probably make the analysis more complicated, but this is not a point that it is essential to decide here.
The two last examples are quite controversial as real cases of replacement with incommensurability. In spite of Kuhn’s (quite brief) argumentation in his Structure of Scientific Revolutions for this case, the detailed analyses of this example provided by several authors (e.g. by Erhard Scheibe in his Reduktion physikalischer Theorien) rather suggest that this is a case of embedding with approximation.
To simplify the exposition, I give here only a half-formal definition of diachronic theory-elements. A formally more adequate definition would require some technicalities which may be spared here without, I hope, loss of comprehension. The reader interested in the technical details may consult Architectonic, Ch. V.
The symbol “<” for the relation of historical precedence between periods is to be interpreted as a qualitative, not as a quantitative relation. This means, among other things, that two different periods standing in the relation “<” may overlap chronologically, i.e. they may share years or months.
M k is the class of actual models of T k and I k the set of intended applications of T k ; analogously for M k * and I k *.
I don’t have a formal proof of this theorem. However, it seems to me that the theorem is plausible in view of the characteristics of the notions involved. The possibility of a formal proof will essentially depend on the definition of reduction adopted, since equivalence and intertheoretical approximation may be seen as “variations” of reduction. The problem is that we still lack a consensus (either among structuralists or among non-structuralists) about the most adequate formal explication of reduction as an intertheoretical relation. This notwithstanding, if we accept that, whatever the ultimate explication might be, an essential component of the concept of reduction will be what I call “ontological reduction” (see e.g. Moulines 1984), then it seems that the proof of the theorem in question would be rather straightforward, since ontological reduction can be defined just in terms of what I call here “echelon partial substructures”.
Kuhn and Stegmüller have claimed in some of their writings that there are historical cases of “scientific revolutions” (more or less corresponding to the kind of process I call “replacement” here) where some successful intended applications of the paradigm preceding the revolution are “lost” or “forgotten” because there is no room for them in the paradigm following the revolution. (Stegmüller calls this alleged diachronic phenomenon “Kuhn-loss”.) It is a matter of controversy whether there really have been such cases in the history of science. Nevertheless, just in case this is so, I have added to condition (2) above the qualification “almost all” since, even if there were real examples of “Kuhn-losses” in a process of replacement, such losses would certainly be in small number in comparison with the surplus of successes of the replacing theory—otherwise no reasonable scientist would be ready to replace the former theory by the latter.
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Moulines, C.U. Intertheoretical Relations and the Dynamics of Science. Erkenn 79 (Suppl 8), 1505–1519 (2014). https://doi.org/10.1007/s10670-013-9580-y
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DOI: https://doi.org/10.1007/s10670-013-9580-y