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“A Logical Obscurity” (3/17/17)

March 21, 2017

Joshua Eisenthal

Abstract: There is unambiguous evidence that Wittgenstein had a deep and life-long appreciation of Heinrich Hertz’s seminal work, Principles of Mechanics. Besides two direct references to Principles in the Tractatus (at 4.04 and 6.361), Wittgenstein also included Hertz’s name on one of the rare occasions when he directly listed his influences. Furthermore, Wittgenstein quoted a passage from Hertz’s introduction both times that he gave a programmatic address at Cambridge, and even considered using an extract from this passage as the motto for the Philosophical Investigations. However, it is not clear how this passage from Hertz’s introduction relates to the rest of Hertz’s book. This has resulted in a serious obstacle to understanding what the impact of Principles was on Wittgenstein’s philosophy. In my paper I present a detailed analysis of the context and significance of this passage from Hertz’s introduction. 

Hertz asserted that his aim in Principles was to give a ‘complete and definite presentation of the laws of mechanics’. In motivating this project, Hertz complained of a logical obscurity in the traditional Newtonian formulation of mechanics, and drew particular attention to the concern felt amongst physicists over the nature of force. It is this passage, concerning the seemingly mysterious nature of force, that so struck Wittgenstein. Of particular importance is the way the passage ends: 

‘the answer which we want is not really an answer to this question [“What is the nature of force?”]. It is not by finding out more and fresh relations and connections that it can be answered; but by removing the contradictions existing between those already known, and thus perhaps by reducing their number. When these painful contradictions are removed, the question as to the nature of force will not have been answered; but our minds, no longer vexed, will cease to ask illegitimate questions.’

Hertz’s characterization of this ‘illegitimate question’, and the way he took himself to respond to it in Principles, resonated profoundly with Wittgenstein. As Wittgenstein remarked in The Big Typescript: ‘As I do philosophy, its entire task is to shape expression in such a way that certain worries disappear. ((Hertz.))’

In order to be able to compare Hertz’s methods with Wittgenstein’s, we need an account of the context and significance of this passage from Hertz’s introduction. A fundamental difficulty in this task arises from the fact that there is no satisfactory account of the ‘logical obscurity’ that motivated Hertz to write Principles in the first place. FitzGerald suggested that Hertz had simply misunderstood Newton’s third law, but it is implausible that this would have led Hertz to spend the last four years of his life reformulating mechanics. Mach suggested that Hertz had been troubled by the fact that forces are not directly observable, but a careful reading reveals that Hertz regarded an appeal to the unobservable as necessary in scientific theorizing. No other commentators, either historical or contemporary, have offered a satisfactory account of what troubled Hertz in the traditional formulation of mechanics. 

In my paper I argue that the source of Hertz’s concerns can be traced back to tacit shifts between “bottom-up” central forces and “top-down” constraint forces. Although such shifts are pervasive they are clearly problematic from a logically rigorous point of view. In particular, the velocity dependence of constraint forces threatens to undermine a clear derivation of the conservation of energy. I argue that an appreciation of these issues reveals the tension that Hertz perceived in the Newtonian notion of force. I then show how Hertz dissolved this tension through the logically perspicuous notion of force that he derived within his own framework. Thus we have in view a precise characterization of the achievement that seems to have inspired Wittgenstein’s approach to analogous tensions in philosophy.

 

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