Joshua Eisenthal

A well known conception of axiomatization has it that an axiomatized theory must be interpreted, or otherwise coordinated with reality, in order to acquire empirical content. An early version of this account is often ascribed to key figures in the logical empiricist movement, and to central figures in the early “formalist” tradition in mathematics as well. In this context, Reichenbach’s “coordinative definitions” are regarded as investing abstract propositions with empirical significance. We argue that over-emphasis on the abstract elements of this approach fails to appreciate a rich tradition of empirical axiomatization in the late nineteenth and early twentieth centuries, evident in particular in the work of Moritz Pasch, Heinrich Hertz, David Hilbert, and Reichenbach himself. We claim that such over-emphasis leads to a misunderstanding of the role of empirical facts in Reichenbach’s approach to the axiomatization of a physical theory, and of the role of Reichenbach’s coordinative definitions in particular.

A central issue in the philosophical debates over general relativity concerns the status of the metric field: should it be regarded as part of the background arena in which physical fields evolve, or as a physical field itself? In this paper, we approach this debate through its relationship to the so-called "Problem of Space": the problem of determining which abstract, mathematical geometries are candidate descriptions of physical space. In particular, we explore the way that Hermann Weyl tackled the Problem of Space in the wake of general relativity, and argue that Weyl’s proposed solution reveals a “middle way” between bare-manifold and manifold-plus-metric accounts of spacetime.

At the time of Heinrich Hertz's premature death in 1894, he was regarded as one of the leading scientists of his generation. However, the posthumous publication of his treatise in the foundations of physics, "Principles of Mechanics", presents a curious historical situation. Although Hertz's book was widely praised and admired, it was also met with a general sense of dissatisfaction. Almost all of Hertz's contemporaries criticized "Principles" for the lack of any plausible way to construct a mechanism from the hidden masses that are particularly characteristic of Hertz's framework. This issue seemed especially glaring given the expectation that Hertz's work might lead to a model of the underlying workings of the ether. In this paper I seek an explanation for why Hertz seemed so unperturbed by the difficulties of constructing such a mechanism. In arriving at this explanation, I explore how the development of Hertz's image-theory of representation framed the project of "Principles". The image-theory brings with it an austere view of the essential content of mechanics, only requiring a kind of structural isomorphism between symbolic representations and target phenomena. I argue that bringing this into view makes clear why Hertz felt no need to work out the kinds of mechanisms that many of his readers looked for. Furthermore, I argue that a crucial role of Hertz's hypothesis of hidden masses has been widely overlooked. Far from acting as a proposal for the underlying structure of the ether, I show that Hertz's hypothesis ruled out knowledge of such underlying structure.

I claim that Wittgenstein’s reference to Hertz’s “dynamical models” at 4.04 in the Tractatus provides evidence for the view that the Tractatus does not explain the sense of propositions by offering an account of the fundamental structure of reality. Just as Hertz’s dynamical models capture what all mechanical descriptions of the same system have in common, so Tractarian analysis captures what all propositions that express the same sense have in common, and in neither case is there a need to appeal to an underlying ontology.

Heinrich Hertz dedicated the last four years of his life to a systematic reformulation of mechanics. One of the main issues that troubled Hertz in the customary formulation of mechanics was a "logical obscurity" in the notion of force. However, it is unclear what this logical obscurity was, hence it is unclear how Hertz took himself to have avoided it. In this paper, I argue that a subtle ambiguity in Newton's original laws of motion lay at the basis of Hertz's concerns; an ambiguity which led to the development of two slightly different notions of force. I then show how Hertz avoided this ambiguity by deriving a unitary notion of force, thus dispelling the obscurity that lurked in the customary representation of mechanics.