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Crystallizations as a Form of Scientific Semantic Change: The Case of Thermodynamics


When considering the diachronic structure of scientific disciplines, four ideal types of change in the semantic systems constituting them may be distinguished: (1) (normal) evolution; (2) (revolutionary) replacement; (3) embedding (of one conceptual system into another); and (4) (gradual) crystallization of a conceptual framework. In the literature on diachronic philosophy of science, the last type has been unduly neglected in spite of its great significance for understanding the history of science. It consists in a piecemeal but nevertheless fundamental change of the conceptual framework of a discipline during a relatively long period of time. In this paper, an attempt is made to characterize as precisely as possible what the general semantic features of crystallization are and to illustrate them by analysing the gradual emergence of phenomenological thermodynamics in the middle of the nineteenth century, in particular as due to the work of Rudolf J. Clausius between 1850 and 1854. The (formal-semantic) notion of classes of models as understood in the structuralist metatheory of science will be used for that purpose. Three different conceptual nets will formally be distinguished in Clausius’s papers corresponding to as many steps in the crystallization of what is now known as (phenomenological) thermodynamics. The reconstruction makes explicit the way Clausius’s concepts evolved during the historical period under consideration.


  • Conceptual Change
  • Equivalence Principle
  • Intended Application
  • Formal Reconstruction
  • Phenomenological Thermodynamic

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  1. 1.

    In the following, by “a (scientific) theory” I always refer only to empirical theories. Problems related to the nature of purely mathematical theories lie outside the scope of this paper.

  2. 2.

    The standard exposition of the structuralist metatheory (with several examples of application) is [1].

  3. 3.

    The detailed structuralist reconstruction of this example will be found in [1, Ch. V.].

  4. 4.

    For a structuralist reconstruction of this example see [2].

  5. 5.

    This example is dealt with in [1, Ch. VII].

  6. 6.

    For the history of the emergence of Gibbsian thermodynamics see [8].

  7. 7.

    Here, as in the rest of the paper, I translate as truthfully as I can from the original German text. The page numbers indicated in the quotations are those of the original essay.

  8. 8.

    One needs a continuous sequence of states as arguments of differentiable magnitudes. Clausius assumes throughout his text without further ado that most thermodynamic magnitudes are differentiable functions.

  9. 9.

    Clausius assumes that, according to Joule’s experiments, the value of A should be approximately 1/421. But A’s concrete value is irrelevant for the formal reconstruction of the theory.

  10. 10.

    A further interesting aspect of U should be noted: Clausius explicitly avows that he introduces this magnitude in order to formulate a differential equation that will allow for a derivation of the ideal gas law, U making sense only in the context of the equation at stake. In other words, U appears to be Cl − 1-theoretical. The same goes for the function h introduced later on—see below.

  11. 11.

    Clausius writes at the end of his paper that experimental results suggest that the actual value of a should lie “around 273”; but, again, the concrete value is unimportant for the formal reconstruction.

  12. 12.

    It is not clear in the original text whether Clausius wanted to conceive A as a positive or a negative value. In the first case, of course, he should have worded his “Equivalence Principle” slightly differently. But this is a minor point.


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Correspondence to C. Ulises Moulines .

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Moulines, C.U. (2013). Crystallizations as a Form of Scientific Semantic Change: The Case of Thermodynamics. In: Küppers, BO., Hahn, U., Artmann, S. (eds) Evolution of Semantic Systems. Springer, Berlin, Heidelberg.

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