The Lever as Instrument of Reason

Technological Constructions of Knowledge around 1800

Jocelyn Holland

• Publisher: Bloomsbury Academic
• Year: 2019
• ISBN:
  9781501346064
• Edition: 1
• Topic: Literatura
• Subtopic: Crítica literaria alemana

The lever appears to be a very simple object, a tool used since ancient times for the most primitive of tasks: to lift and to balance. Why, then, were prominent intellectuals active around 1800 in areas as diverse as science, philosophy, and literature inspired to think and write about levers? In The Lever as Instrument of Reason, readers will discover the remarkable ways in which the lever is used to model the construction of knowledge and to mobilize new ideas among diverse disciplines. These acts of construction are shown to model key aspects of the human, from the more abstract processes of moral decision-making to a quite literal equation of the powerful human ego with the supposed stability and power of the fulcrum point.

One The Balance of Life /
Quantifying Kant

This concept can be extended far beyond the limits of the material world.¹

Immanuel Kant

Introduction

All too often, it is the fate of simple things to be overlooked. Such is the case of the mechanical lever. We can scarcely live an hour of the day without taking advantage of something that relies on its mechanical laws—leaving, for a moment, the levers of the body and those which function as extensions of the body entirely out of the equation. Yet the lever as such is rarely something that calls attention to itself, perhaps because, pace Archimedes, it is almost always available to us in the guise of something else. The levers that we encounter in our daily lives are better known as scissors, hammers, and bottle openers, each of which operates according to the same principle of mechanical advantage. And if that weren’t enough, the numerous metaphorical incarnations of the lever generate a different kind of clutter: from the eighteenth century onward, many objects conceptually linked to power and manipulation—in any sense of the word—were at some point metaphorically attached to a lever. The political, religious and philosophical texts of the nineteenth century are littered with ideological levers of all kinds, including the levers of reason, morality, intelligence, and the state. Clearly, there are historical trends to be observed: in our current climate of fiscal instability, there is much talk of the “economic levers” and, even more specifically, the “interest rate” levers being wielded by the monetary mechanics at the Federal Reserve. In the process of its dissemination as metaphor, however, the lever tends to lose its specificity as mechanical object, with the result that it could just as well be exchanged with other instruments of power, such as Nietzsche’s—or Heidegger’s—hammer. In the introduction to this study, I argued that the most productive approach to the lever requires thinking of it as more than just a “simple” metaphor such as one finds in the examples above. I also raised a few alternatives which, collectively, can help work toward a broader understanding of what a lever can be. In the most general sense, one can think in terms of a conceptual apparatus, given that one rarely finds the lever in isolation, but rather attached to concepts such as equilibrium, power, and advantage, each of which have their own value in disciplines such as philosophy, literature, and psychology. The lever, as I understand it, also fulfills some of the criteria for the somewhat elusive notion of an “absolute metaphor” as defined by Hans Blumenberg. For Blumenberg, an absolute metaphor has a pragmatic function as a model. It cannot be reduced to purely terminological claims, but rather, within a specific historical experience, such a metaphor provides a point of orientation and helps to structure a world.

To give a sense of the challenges faced when, around 1800, one is confronted with a lever that refuses the status of simple, rhetorical ornamentation, I would like to mention an example that will likely be familiar to many readers before shifting attention to the essay by Kant that is the focal point of this chapter. The example comes from the philosopher Georg Wilhelm Hegel’s discussion of the concept “sublation” in the Wissenschaft der Logik (Science of Logic), which can also be found in the Enzyklopädie der philosophischen Wissenschaften (Encyclopedia of the Philosophical Sciences). In these works, Hegel draws upon the theoretical language associated with the lever to explain the relationship between the real and the ideal. In the Science of Logic, when Hegel explains what it means for something to be sublated (aufgehoben) he reminds us that one of the peculiar features of this word is that it encompasses two opposed meanings in German: to preserve and to remove. To illustrate how the word aufgehoben unifies opposed meanings, Hegel turns to the lever:

Something is sublated only in so far as it has entered into unity with its opposite; in this closer determination as something reflected, it may fittingly be called a moment. In the case of the lever, “weight” and “distance from a point” are called its mechanical moments because of the sameness of their effect, in spite of the difference between something real like weight, and something idealized such as the merely spatial determination of “line.”²

With this example, Hegel points to one of the most significant theoretical features of the lever: its ability to unite two fundamentally different things—a weight and the linear measurement of its distance from a fulcrum point—using a logic of the “sameness” of effect. The lever effectively provides Hegel with a model for both illustrating and understanding the concept of sublation. We could compare the passage from The Science of Logic with Hegel’s reference to the “tragic” lever in his Lectures on Aesthetics. In the context of aesthetics, the lever’s mechanics play no role whatsoever, such that it might just as well be a pulley (though admittedly to lesser rhetorical effect). The same does not hold true for sublation: if we want to understand this concept, and the negotiation it undertakes between the real and the ideal, one needs to have some familiarity with both the lever and the concept of the mechanical moment. It is important to understand how the mechanical advantage of the lever is translated into philosophical gain. To “grasp” intuitively the peculiar state of affairs through which force is expended and, at the same time, held in abeyance, one also needs to have a sense of the powerful act of translation the lever embodies, whereby one thing (the real) is understood in terms of something else (the ideal) quite distinct from it.

As stated in the introduction, one of the tasks of this study is to call attention to the lever and thereby to defamiliarize it, to pare it down to its most basic functional relations, and to make it strange enough to become interesting again. An important first step is to divest the lever of any requirement of materiality. The levers that swing in and out of equilibrium in this chapter and the following ones are not necessarily made of wood or iron. Instead, they are often closer to what mechanical treatises refer to as “mathem atical” rather than “physical” levers, a distinction that will become clearer with reference to a few of the key mechanical handbooks from the seventeenth and eighteenth centuries. In the posthumously published Nouvelle mécanique ou statique (New Mechanics or Statics) (1725), Pierre Varignon, a French mathematician who moved in the circles of Newton, Leibniz, and the Bernoullis, writes that the lever is an “inflexible stick” (verge inflexible), with the added caveat that, for mathematical purposes, it should be considered without weight.³ Andrew Motte’s more literally minded Treatise of the Mechanical Powers (1727) only considers the physical lever. He describes it as “generally in Practice a wooden or iron Bar, when used for the lifting of Weights” and adds, with an eye for the lever’s versatility, “it comes in Use under many different Forms upon several Occasions of Life.”⁴ As for the German philosopher Christian Wolff, whose system was an important reference point for Kant at all stages of his career, he writes in the third volume of his 1716 Anfangs-Gründe aller mathematischen Wissenschaften (Fundamentals of All Mathematical Sciences), dedicated to mechanics, that the lever is simply “a straight line AB, which lies in a point C, upon whose one point A the force and on another B the weight can be applied.”⁵ For all their differences, in each of these cases, the emphasis is on the lever as a discrete object (a line, a stick, a bar), whether physical or not. The entry “lever” from Gehler’s Physikalisches Wörterbuch (Physical Dictionary) of 1798 takes a somewhat different approach. Drawing verbatim from the work of two influential German mathematicians, Abraham Kästner and Johann Erxleben,⁶ Gehler does not identify the lever with a material object. Instead, he writes:

If one can think of three points on a firm, inflexible connection [Verbindung] of bodies, around one of which, the fulcrum, the entire connection can turn, in that two forces on both of the other points act in opposition to each other, this connection is called a lever.⁷

Gehler’s definition serves as a reminder that, for all that the lever pivots back and forth between physical and mathematical applications—between material and immaterial regimes—it is at heart a figure of pure connection, a Verbindung. Not all connections are levers, but in many kinds of connections, the minimal requirements for a lever are met. The following pages and subsequent chapters will show how this general understanding of what a lever is and can be allows for more flexibility in identifying levers and the mechanical thinking that informs them.

In addition to being a figure of connection, the lever also functions as one of ratio or proportion when its law of equilibrium is taken into consideration. Like a simple mechanical scale, a lever is in equilibrium when the product of the weight and the weight’s distance from the fulcrum on one side is equivalent to the product of a second weight applied to the lever and its distance from the fulcrum on the other side.⁸ Apart from being a fundamental law in the field of statics, this aspect of the lever is also central to the cases I analyze because it entails bringing two things that are not the same into a relationship of equivalence. As we saw above, in the example taken from Hegel’s philosophy, the lever is a simple mechanical device that also allows us to think of one thing in terms of something else. To that end, it is also a figure of translation. Translation, in this context, invokes both the materiality of the lever or scale, as something that balances forces applied to one side and another, and its ability to mediate differences more generally. The same quality Hegel identifies when he recognizes the lever’s suitability for mediating between the real and the ideal makes an argument for why the lever, when its mechanics are taken into consideration, can be “more” than metaphor. It is an instrument that preserves differences: it maintains the equivalence of effect (or mechanical “product”) without claiming a relationship of identity. As the basic unit of translation, the lever can therefore do the work of a metaphor while maintaining its integrity—the lever is the instrument that makes this process of translating differences into equivalences visible. This is also the key to the lever’s discursive mobility, to its usefulness as a figure of thought when taken from mechanics and applied to a number of other discourses. For the lever to function as a kind of organizing principle, then, there needs to be a basic willingness to quantify the abstract, so it can bring diverse things (whether objects, concepts, or something else) into a relationship. As a consequence, within many of the examples I address in this study one finds a historical interest in techniques of quantification, whereby things that were traditionally not thought of in such terms (such as processes of thinking, or emotions) find themselves subjected to quantitative, analytical descriptions. There is a unique phenomenon to be observed here. Even though it is easy enough to understand the lever as something that lends itself to application, the opposite also holds true. There are certain contexts where a particular set of concerns will cluster together, conjoin for the purpose of an experiment in thinking, and concretize in the lever. One of the objectives of my project is therefore to observe the conditions under which this phenomenon occurs.

The history of the lever that is the focus of this chapter centers around Kant’s precritical essay, “Versuch, den Begriff der negativen Grössen in die Weltweisheit einzuführen,” (“Attempt to Introduce the Concept of Negative Magnitudes to Philosophy”) (1763). For readers whose knowledge of Kant is based primarily on his three critiques, the essay on negative magnitudes might seem like an unusual place to start. After all, mechanical theory is usually not the first association one might have with Kant’s philosophy at any stage of his career, and it is therefore reasonable to ask what he knew about statics in general and levers in particular. Fortunately, Kant’s understanding of classical mechanics and other branches of scientific knowledge has been well-documented in recent years by Michael Friedman, Eric Watson, and Martin Schönfeld, among others.⁹ We know, for example, that Kant possessed a thorough knowledge of mechanical theory as articulated by Newton, Galileo, Descartes, Leibniz, and Wolff. Kant’s very first published essay, “Thoughts on the True Estimation of Living Forces” (1747), also makes frequent mention of the lever.¹⁰ Almost forty years later comes the publication of the Metaphysical Foundations of Natural Science (1786), which contains an entire chapter on mechanics, and Michael Friedman has shown how Kant’s universit...

Table of contents

• Cover
• Half-Title
• Dedication
• Title
• Contents
• Acknowledgments
• Introduction. An Object and Its Positions: The Lever, the Fulcrum, and the Archimedean Point
• 1 The Balance of Life / Quantifying Kant
• 2 The Levers of German Romanticism
• 3 The Contested God of Naturphilosophie
• 4 From Naturphilosophie to a Mechanically Minded Psychology
• Concluding Thoughts
• Bibliography
• Index
• Copyright