Philosophia Mathematica 16 (1):140-144 (2007)
Philosophers unacquainted with the workings of actual scientific practice are prone to imagine that our best scientific theories deliver univocal representations of the physical world that we can use to calibrate our metaphysics and epistemology. Those few philosophers who are also scientists, like Heinrich Hertz , tend to contest this assumption. As Jesper Lützen relates in his scholarly and engaging book, Hertz's Principles of Mechanics contributed to a lively debate about the content of classical mechanics and what, if anything, this highly successful scientific theory told us about the physical world. Lützen provides an in-depth reconstruction of how Hertz reacted to the foundational problems within the physics of his day and then used these problems to motivate his influential philosophical reflections on the nature of science and scientific theorizing. While giving a thorough portrait of how Hertz brought together science and philosophy, Lützen himself offers an excellent example of the benefits of combining philosophy, the history of science, and the history of mathematics. Lützen convincingly argues that Hertz's most influential innovation was in bringing geometrical concepts to bear on mechanics in a novel and productive fashion. In his preface he motivates his book by noting that most of the work on Hertz's philosophy of science fails to engage with what Hertz does after the Introduction of his Principles. The bulk of Lützen's book, then, concerns the physical and mathematical content of Hertz's image of mechanics. This places certain demands on the reader who is otherwise unacquainted with analytic mechanics, but is sure to repay those who are willing to work carefully through the more technical details of Lützen's reconstruction.1Hertz is well known for his conception of scientific theories as images [Bilder] and for the fact that his preferred image of mechanics takes only space, …
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