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Guest Post by Joshua Eisenthal (CalTech, The Einstein Papers Project)

Models and Multiplicities

Joshua Eisenthal. Journal of the History of Philosophy. Volume 60, Number 2, April 2022.

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Although Heinrich Hertz is best known for his groundbreaking experimental detection of electric waves, his most significant impact on philosophy stemmed from his theoretical treatise, Principles of Mechanics. This text had a far-reaching influence on Wittgenstein in particular, and in the Tractatus there are two explicit (but obscure) references to Hertz’s work. In my paper, “Models and Multiplicities”, I take up the task of interpreting Wittgenstein’s first reference to Principles:

4.04 There must be just as much as is distinguishable in a proposition as in the situation that it represents. 
The two must possess the same logical (mathematical) multiplicity. (Compare Hertz’s Mechanics on dynamical models.).

My central claim in this paper is that a satisfactory interpretation of this remark has a direct impact on the debate between “ontologically oriented” and “logically oriented” interpretations of the Tractatus — a debate that has persisted for at least the last fifty years. The central question in this debate is whether Wittgenstein presents an account of the fundamental structure of reality in order to explain the meaningfulness of ordinary sentences. On an ontologically oriented view, it is because reality ultimately consists of simple objects (and sentences with sense can ultimately be analyzed into names of such objects) that language is able to describe the world. In contrast, on a logically oriented view, the Tractatus offers no such ontological underpinning of the meaningfulness of our language. Indeed, on a logically oriented view the Tractarian ‘ontology’ does not have any significance if considered in isolation from the logical analysis of ordinary sentences, an analysis that is carried out entirely for the sake of avoiding certain philosophical confusions.

The overarching goal of my paper is to argue that Wittgenstein’s reference to Hertz’s dynamical models provides significant evidence in favor of a logically oriented interpretation. The crux of this argument draws on the parallels between Wittgenstein’s analysis of sentences and Hertz’s analysis of mechanical systems. Wittgenstein brings this parallel to our attention by prompting us to look to Hertz’s dynamical models in order to understand why a proposition and the situation it represents must have the same “multiplicity”. In Principles, a dynamical model does not capture the ontological constitution of the target system; rather, it captures that system’s degrees of freedom — the information that is necessary and sufficient for writing down appropriate equations of motion. This is the essential content of a mechanical description, what all descriptions of a given system have in common. In a similar vein, Tractarian analysis captures the essential content of a proposition, what all sentences which express the same sense have in common. According to the Tractatus, two sentences express the same sense just in case they have the same set of logical relationships with other propositions. (As Wittgenstein puts it at 5.141, “If p follows from q and q from p, then they are one and the same proposition.”) I argue that, on this point, the parallel with Hertz is especially illuminating. In particular, I argue that, for both Hertz and Wittgenstein, analysis does not lead to a specification of ultimate ontological constitution.

I thus claim that a satisfactory interpretation of Wittgenstein’s reference to dynamical models provides clear evidence for a logically oriented interpretation of the Tractatus as a whole. I also suggest that this interpretation points to a way in which Hertz influenced Wittgenstein’s approach to philosophy much more broadly. For Hertz, a major motivation to reformulate mechanics arose from the persistent questioning of the “essence” (Wesen) of force; he complains of “the statements which one hears with wearisome frequency, that the essence of force is still a mystery, that one of the chief problems of physics is the investigation of the nature of force, and son on” (Hertz 1899 p.7). On Hertz’s view, a question concerning something’s essence is intrinsically confused: “Can we by our conceptions, by our words, completely represent the essence of any thing? Certainly not.” (Ibid.) Hence one of the overarching goals of Principles is to clarify the structure of mechanics so that such confused questions no longer arise. Although it would be uncontentious to recognize a similar methodology in Wittgenstein’s later work, the presence of this Hertzian influence in Wittgenstein’s earlier work is much less widely appreciated. One question we are left with, then, is the extent to which Hertz’s influence informs Wittgenstein’s overarching approach to philosophy already in the Tractatus.

Link to Joshua Eisenthal's website.

Click here to read the papers appearing in a new Topical Collection in Synthese.

Theme of the Topical Collection. From the Call for Papers by Erik Curiel and Flavia Padovani:

"Hans Reichenbach is among the most important philosophers of science of the Twentieth Century and without doubt one of the most prominent philosophers of physics of the first half of the past century.  His work has ramified in fundamental ways into virtually every major debate in the philosophy of science and physics.  While Reichenbach's philosophical project is no longer seen as viable as a whole, his work continues to be influential often in unnoticed but deep ways.  Although many of his ideas still retain their interest and are discussed in current philosophy of science, he remains, in fact, one of the least understood and least carefully studied philosophical thinkers of his time.  Because his own work has not been well understood, his influence is not widely recognized. 

The primary aim of this collection is to fill this gap by illuminating Reichenbach's contributions to advances in many fields in philosophy, and his legacy in the context of current philosophical research across the discipline as a whole.  The theme of the collection, therefore, will be an investigation of his work both in its own context and in its continuing contemporary influence in current philosophy. This collection aims, moreover, at reviving the tradition of inter-disciplinary collaboration that was at the heart of Reichenbach's vision for intellectual work, promoting the cross-pollination of ideas that discussion across traditional disciplinary boundaries can create and so exploring ways in which his insights can continue to be valuable in current scientific and formal approaches to philosophy.  It is, in that spirit, a sequel to the conference "All Things Reichenbach" that took place at the Munich Center for Mathematical Philosophy (LMU Munich) in July 2019."

If you are interested in doing more research on Hans Reichenbach, the resources below are recommended.

Reichenbach's Experience and Prediction is well known for its analysis of the contexts of discovery and justification. See Revisiting Discovery and Justification, edited by Friedrich Steinle and Jutta Schickore.

The Hans Reichenbach Papers (1884-1972) are held at the University of Pittsburgh. Guide to the Hans Reichenbach Papers.

Sander Verhaegh, "Coming to America: Carnap, Reichenbach, and the Great Intellectual Migration. Part II: Hans Reichenbach." Journal for the History of Analytical Philosophy.

Flavia Padovani, "From Physical Possibility to Probability and Back: Reichenbach’s Account of Coordination." Ch. 14 in Logical Empiricism and the Physical Sciences, ed. Sebastian Lutz and Adam Tamas Tuboly. Routledge.