Kuhn’s ‘5th Law of Thermodynamics’: Measurement, Data, and Anomalies

In Kuhn’s The Structure of Scientific Revolutions at 60. Cambridge University Press (forthcoming)
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A central component of Thomas Kuhn’s philosophy of measurement is what he calls the fifth law of thermodynamics. According to this “law,” there will always be discrepancies between experimental results and scientists’ prior expectations, whether those expectations arise from theory or from other experimental data. These discrepancies often take the form of what Kuhn calls quantitative anomalies, and they play a central role in both normal and revolutionary science. Whether the effort to resolve these anomalies is taken to be a part of normal or revolutionary science depends in part on the ever-evolving and context-dependent standards of what Kuhn calls reasonable agreement. In The Structure of Scientific Revolutions, Kuhn identifies as one of the most important types of experiments those aimed at determining the values of the fundamental physical constants. Why would he emphasize this seemingly obscure class of experiments? The answer, we argue, requires paying closer attention to, first, the historical context of a prominent research program in the Physics Department at Berkeley when Kuhn arrived in the 1950s, and second, Kuhn’s broader philosophy of measurement and data. As we show, the fifth law of thermodynamics and the failure of reasonable agreement played a fundamental role in both. In Section 2, we reconstruct Kuhn's philosophy of measurement and philosophy of data, as laid out primarily in his 1961 paper "The Function of Measurement in Modern Physical Science," where he introduces this fifth law. We discuss the important role of quantitative anomalies in Kuhn’s philosophy, noting his emphasis on the iterative process of improving reasonable agreement. Section 3 turns to the historical context at Berkeley and the research program initiated by the long-time physics chair, Raymond T. Birge, who first called attention to the widespread discrepancies and inconsistencies in the experimental data on fundamental constants. We illustrate the quantitative anomalies uncovered in this research on constants, using the example of the speed of light (c), for which there were many different (and inconsistent!) experimentally determined values measured during the Birge-Kuhn era. We follow this important research program forward in time in Section 4, highlighting Kuhnian elements taken up by the metrology institution subsequently charged with periodically adjusting the values of the fundamental constants, known as Committee on Data for Science and Technology (CODATA). In particular, we identify three striking points of similarity: First, like Kuhn, these metrologists emphasize the iterative and ever-changing standards of reasonable agreement, prioritizing the identification of quantitative anomalies. Second, the metrology community also expresses a fundamental skepticism about scientists’ ability to ever know the “true value” of a fundamental constant. Third, in the absence of any access to the true values of the constants, these metrologists emphasize the values of consistency and coherence as the only arbiters in deciding what numerical value to adopt. We connect these points to the ongoing effort to determine the value of the gravitational constant (G), which is the fundamental constant that Kuhn emphasizes as being particularly problematic in the Structure. In Section 5, we discuss Kuhn’s later reflections on the formative role that his earlier work on the philosophy of measurement and data had for the development of his views in the Structure. By paying closer attention to Kuhn’s work on the philosophy of measurement we are also able to recover a key notion of scientific progress in Kuhn’s thinking that goes beyond the increase in puzzle-solving ability later identified in the Postscript to the Structure. We conclude by reflecting on the continuing relevance of Kuhn’s views for the philosophy of metrology and philosophy of data today.

Author Profiles

Alisa Bokulich
Boston University
Federica Bocchi
Boston University


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