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The Realm of Reason

Stephen Gaukroger

in The Collapse of Mechanism and the Rise of Sensibility: Science and the Shaping of Modernity, 1680-1760

In the course of the eighteenth century, natural philosophy began to take on a new cultural standing, emerging as the paradigm bearer of, and the standard for, cognitive values. It was Fontenelle who ... More

In the course of the eighteenth century, natural philosophy began to take on a new cultural standing, emerging as the paradigm bearer of, and the standard for, cognitive values. It was Fontenelle who had established the standing of natural philosophy in France as a worthy and useful form of inquiry, but it was Voltaire who had elevated its standing further by making it into the model for cognitive grasp per se. In d'Alembert's preliminary Discours to the Encyclopédie, a more elaborate statement of the archetypal role of natural philosophy in cognitive enquiry was set out.Less

The Fortunes of a Mechanical Model for Natural Philosophy

Stephen Gaukroger

in The Collapse of Mechanism and the Rise of Sensibility: Science and the Shaping of Modernity, 1680-1760

The basic assumption of ‘rational mechanics’ was that all natural philosophy was mechanics, and that, as mechanics was pursued with greater and greater detail and sophistication, the rest of natural ... More

The basic assumption of ‘rational mechanics’ was that all natural philosophy was mechanics, and that, as mechanics was pursued with greater and greater detail and sophistication, the rest of natural philosophy would fall into place around it. The guiding idea, from Varignon and Hermann at the beginning of the eighteenth century, up to d'Alembert and Euler in mid‐century, was that mechanics could be pursued independently of other natural‐philosophical considerations, that it was the one absolutely secure physical discipline because of its mathematical (and effectively a priori) standing. The chapter explores the rational mechanics of d'Alembert and Euler, and questions whether what was proposed in fact had an a priori standing, and whether it was plausible to assume that recalcitrant phenomena such as the refraction of light, the behaviour of fluids, and gravitation could be accounted for by mechanics.Less

Historical Understanding and the Human Condition

Stephen Gaukroger

in The Collapse of Mechanism and the Rise of Sensibility: Science and the Shaping of Modernity, 1680-1760

In a context in which traditional religious and humanistic assumptions about universal moral, social, and other values have come loose, the eighteenth‐century employment of developmental stages in ... More

In a context in which traditional religious and humanistic assumptions about universal moral, social, and other values have come loose, the eighteenth‐century employment of developmental stages in understanding modern institutions takes on a new standing. In particular, d'Alembert's idea that the present is a culmination of and in many respects an inevitable outcome of the past depends on the idea that natural philosophy takes precedence over any other form of understanding. This idea is discussed in the contexts of discussions of the move from myth to reason, in that of the history of manners. Finally, Hume's very different, but equally historically based account of what understanding consists in is contrasted with that of d'Alembert, and the question of the balance between propositional and non‐propositional forms of understanding explored.Less

Anglomania, Anglicisme, and the ‘British Model’

Jonathan I. Israel

in Enlightenment Contested: Philosophy, Modernity, and the Emancipation of Man 1670-1752

This chapter discusses British Deism, the rejection of republican radicalism, and the French anglicisme in the mid-18th century. Voltaire, Montesquieu, and Maupertuis, the giants among the French ... More

This chapter discusses British Deism, the rejection of republican radicalism, and the French anglicisme in the mid-18th century. Voltaire, Montesquieu, and Maupertuis, the giants among the French philosophes in the mid 1740s, were, in various ways, all ardent protagonists of the ‘British Enlightenment’. Around 1745, the movement which d’Alembert dubbed anglicisme was indeed at its zenith, with d’Alembert himself frequently extolling Newton and Locke in these years while the young Diderot joined in with his part translation and part reworking of Shaftesbury’s Inquiry Concerning Virtue (1699), published in 1745.Less

Effictions

Peter Szendy

in Phantom Limbs: On Musical Bodies

A reading of some of Diderot’s texts (particularly Rameau’s Nephew) brings us to resume an old figure of rhetoric: effictio, in other words the description of a fictive body that still begins to ... More

A reading of some of Diderot’s texts (particularly Rameau’s Nephew) brings us to resume an old figure of rhetoric: effictio, in other words the description of a fictive body that still begins to exist, in effects.Less

Boundary Layers

S. G. Rajeev

in Fluid Mechanics: A Geometrical Point of View

It is found experimentally that all the components of fluid velocity (not just thenormal component) vanish at a wall. No matter how small the viscosity, the large velocity gradients near a wall ... More

It is found experimentally that all the components of fluid velocity (not just thenormal component) vanish at a wall. No matter how small the viscosity, the large velocity gradients near a wall invalidate Euler’s equations. Prandtl proposed that viscosity has negligible effect except near a thin region near a wall. Prandtl’s equations simplify the Navier-Stokes equation in this boundary layer, by ignoring one dimension. They have an unusual scale invariance in which the distances along the boundary and perpendicular to it have different dimensions. Using this symmetry, Blasius reduced Prandtl’s equations to one dimension. They can then be solved numerically. A convergent analytic approximation was also found by H. Weyl. The drag on a flat plate can now be derived, resolving d’Alembert’s paradox. When the boundary is too long, Prandtl’s theory breaks down: the boundary layer becomes turbulent or separates from the wall.Less

Drama and Life

Angelica Goodden

in Rousseau's Hand: The Crafting of a Writer

This chapter details Rousseau's writing of and on drama, and dwells on the Lettre à d’Alembert's contrasting the effects of playgoing with the moral benefits of daily life in theatre-free, ... More

This chapter details Rousseau's writing of and on drama, and dwells on the Lettre à d’Alembert's contrasting the effects of playgoing with the moral benefits of daily life in theatre-free, craft-loving communities such as Geneva's. His ambivalence towards other forms of leisure is explored, and again linked with his utilitarian theory of art. The writing and hand-copying of La Nouvelle Héloïse is described along with his defence of the book's moral ambiguities.Less

Coda: Newton and Mathematical Physics in France in the Twilight of the Sun King

J.B. Shank

in Before Voltaire: The French Origins of "Newtonian" Mechanics, 1680-1715

This Coda closes the book by reflecting on the initial reception of Newton's Principia in France as it relates to the eruption after 1715 of the "Newton Wars," and the very different understanding of ... More

This Coda closes the book by reflecting on the initial reception of Newton's Principia in France as it relates to the eruption after 1715 of the "Newton Wars," and the very different understanding of the Principia that sustained them. Stressing the contingent nature of this history, the chapter explores how French science was shaped overall by the peculiar dynamics of Newton's influence. Noting how eighteenth-century mathematicians in the United Kingdom tended to follow the Old Style mathematicians in France in their rejection of mathematical analysis, the irony of the French origin of what we now call "Newtonian mechanics" through a failure to follow Newton as literally as his English and Scottish colleagues is noted. The emergence of Newton's new identity as a mathematical natural philosopher and defender of the theory of universal gravitation after 1715 is also explored, along with the changing French understanding of the Principia and its place in French science. Pointing to The Newton Wars and the Beginning of the French Enlightenment, which picks up the story from here, the book concludes by pointing to some of the ways that Enlightenment French Newtonianism as practiced after 1730 reveal the historical traces of this earlier history.Less

2

Philippe Lacoue-Labarthe

in Poetics of History: Rousseau and the Theater of Originary Mimesis

This chapter continues the argument from the previous chapter, developing it through a more detailed reading of the Letter to d’Alembert on the Theater, in which Rousseau’s well known condemnation of ... More

This chapter continues the argument from the previous chapter, developing it through a more detailed reading of the Letter to d’Alembert on the Theater, in which Rousseau’s well known condemnation of the theater occurs. Lacoue-Labarthe argues that Rousseau in fact does not condemn imitation as such, his target being rather imitation that seeks to produce effects of pleasure and complacency by way of flattering identifications. It is in this light that Rousseau critiques catharsis as a harmful illusion of relief from evil that leaves the evil in place. But when one turns to what Rousseau says about tragedy, and Greek tragedy in particular, another perspective emerges: catharsis and Aufhebung as a speculative sublation of historically embedded conflicts. Greek tragedy was not merely theater, but the staging of a originary agon between two kinds of “Greece,” one of which is absolutely anterior to theater as such and so is purely archaic. In this sense, Greek tragedy for Rousseau is a philosophical scene par excellence, the scene of a historical dialectic.Less

‘Changing the Common Mode of Thinking’: d’Alembert and Diderot on the Encyclopedia

Genevieve Lloyd

in Enlightenment Shadows

The chapter opens with a discussion of metaphors of light and of motion in Bacon’s essay On Truth, leading into an examination of the tensions between timelessness and change in the Enlightenment ... More

The chapter opens with a discussion of metaphors of light and of motion in Bacon’s essay On Truth, leading into an examination of the tensions between timelessness and change in the Enlightenment understanding of knowledge. Those tensions surface in reflections which d’Alembert and Diderot offered on conceptual aspects of their Encyclopedia project—concerned both with displaying the timeless structure of the human mind and, on the other hand, emphasizing what is new in the understanding of knowledge in their own time. Central to the discussion is Diderot’s approach to judgement, which he sees as involved both in the understanding of genius in the arts, and in the selection and ordering of subject entries in the Encyclopedia. The chapter concludes with a comparison of Diderot’s concept of genius with the account of judgement offered by Kant in his third Critique. Less

Coda: Instituting the French Enlightenment: Diderot and d'Alembert Encyclopédie

in The Newton Wars and the Beginning of the French Enlightenment

Too many historians have recognized Denis Diderot and Jean le Rond d'Alembert's Encyclopédie as the defining text of the French Enlightenment. Just as many have argued that the project's initial ... More

Too many historians have recognized Denis Diderot and Jean le Rond d'Alembert's Encyclopédie as the defining text of the French Enlightenment. Just as many have argued that the project's initial publication, scandalous reception, and eventual prohibition were the key catalysts in the formation of the Enlightenment as a French social movement. What has not often been stressed, however, is that these undeniably transformative events also completed a half-century process of intellectual and social change in France. This coda proposes, not a reinterpretation of the history of the Encyclopédie, but a retelling of this familiar story in ways that highlight how it served both as the climax of Isaac Newton's reception in eighteenth-century France and, seamlessly, as the final stitch between this reception and the beginning of the French Enlightenment.Less

Rationalism in the History of Mechanics

Olivier Darrigol

in Physics and Necessity: Rationalist Pursuits from the Cartesian Past to the Quantum Present

This chapter is a history of necessity arguments in classical mechanics, including the seventeenth-century opposition between Descartes’s rationalism and Newton’s empiricism, the rationalism of ... More

This chapter is a history of necessity arguments in classical mechanics, including the seventeenth-century opposition between Descartes’s rationalism and Newton’s empiricism, the rationalism of earlier statics since Archimedes, the varieties of rationalism defended by Leibniz, Euler, and d’Alembert in the eighteenth century, and the nineteenth-century persistence of a few deductive arguments against the empiricist tide. Some of the rational derivations of the laws of mechanics relied on theological arguments; others were of a more conceptual nature. They often were very ingenious. Despite evident flaws, they all contributed to a restructuration of mechanics and to a better understanding of its foundations.Less

The Necessity of Classical Mechanics

Olivier Darrigol

in Physics and Necessity: Rationalist Pursuits from the Cartesian Past to the Quantum Present

This chapter combines some assumptions of the rationalist founders of mechanics (the impossibility of perpetual motion, the causal relation between force and motion, the relativity principle, and ... More

This chapter combines some assumptions of the rationalist founders of mechanics (the impossibility of perpetual motion, the causal relation between force and motion, the relativity principle, and what I call the secularity principle) with the definitions of four classes of ideal mechanical systems (connected systems, particles acting at a distance, continuous media, colliding particles) in order to derive the laws of equilibrium and motion of these systems. The usual laws of mechanics are retrieved in each case. The conclusion is that classical mechanics is the only theory of motion complying with a few natural requirements on the comprehensibility of motion at the macroscopic scale.Less

Two Non-senses of “Probability”

Wayne C. Myrvold

in Beyond Chance and Credence: A Theory of Hybrid Probabilities

This chapter engages in some ground-clearing. Two concepts have been proposed to play the role of objective probability. One is associated with the idea that probability involves mere counting of ... More

This chapter engages in some ground-clearing. Two concepts have been proposed to play the role of objective probability. One is associated with the idea that probability involves mere counting of possibilities (often wrongly attributed to Laplace). The other is frequentism, the idea that probability can be defined as long-run relative frequency in some actual or hypothetical sequence of events. Associated with the idea that probability is merely a matter of counting of possibilities is a temptation to believe that there is a principle, called the Principle of Indifference, which can generate probabilities out of ignorance. In this chapter the reasons that neither of these approaches can achieve its goal are rehearsed, with reference to historical discussions in the eighteenth and nineteenth centuries. It includes some of the prehistory of discussions of what has come to be known, misleadingly, as Bertrand’s paradox.Less

Introduction

Jennifer Coopersmith

in The Lazy Universe: An Introduction to the Principle of Least Action

The chapter explains how the Principle of Least Action yields a unique answer to a physical problem irrespective of the frame of reference. The motivation arises from d’Alembert’s rousing words: “To ... More

The chapter explains how the Principle of Least Action yields a unique answer to a physical problem irrespective of the frame of reference. The motivation arises from d’Alembert’s rousing words: “To someone who could grasp the Universe from a unified standpoint the entire creation would appear as a unique truth and necessity.” The requirement is that one “algorithm” can cope with all the specificity, variety, and complexity across the whole of physics. That one algorithm could ever be up to the task is made plausible by use of an allegory involving a King, the princess, and some suitors. Finally, the link with Least Action is made. Note that the terms extremal, objectivity, observer, and viewpoint are explained.Less

D’Alembert’s Principle

Jennifer Coopersmith

in The Lazy Universe: An Introduction to the Principle of Least Action

It is explained how the mysterious Principle of Virtual Work in statics is extended to the even more mysterious Principle of d’Alembert’s in dynamics. This is achieved by d’Alembert’s far-sighted ... More

It is explained how the mysterious Principle of Virtual Work in statics is extended to the even more mysterious Principle of d’Alembert’s in dynamics. This is achieved by d’Alembert’s far-sighted stratagem: considering a reversed massy acceleration as an inertial force. A worked example is given (the half-Atwood machine or “black box”). Some counter-intuitive aspects are made intuitive by more examples: the Pluto-Charon system of orbiting planets; Newton’s and then Mach’s explanation of Newton’s bucket. Also, it is demonstrated that the law of the conservation of energy actually follows from d’Alembert’s Principle. The reader is alerted to the astoundingly fundamental nature of d’Alembert’s Principle. It is the cornerstone of classical, relativistic, and quantum mechanics. As Lanczos writes: “All the different principles of mechanics are merely mathematically different formulations of d’Alembert’s Principle”.Less

A Hundred and One Years of Mechanics: Newton to Lagrange via Daniel Bernoulli

Jennifer Coopersmith

in Energy, the Subtle Concept: The discovery of Feynman's blocks from Leibniz to Einstein

Vis viva (kinetic energy) was discovered by Leibniz, and ‘s Gravesande’s experiments showed that both momentum and kinetic energy were important measures. The concept of ‘potential energy’ slowly ... More

Vis viva (kinetic energy) was discovered by Leibniz, and ‘s Gravesande’s experiments showed that both momentum and kinetic energy were important measures. The concept of ‘potential energy’ slowly emerged (from the works of Parent, the Bernoullis, Clairaut, and Laplace). Daniel Bernoulli was the first to understand ‘energy’ in a modern way—as kinetic and potential energy, but also as a source of fuel for engines. He managed to calculate the amount of ‘live force’ in air, introducing the formula ‘integral over PdV’. Maupertuis, Euler, and Lagrange brought in a new idea—the Principle of Least Action, and Lagrange developed a new generalized mechanics using this principle. The Newtonian ‘force approach’ and the Lagrangian ‘energy approach’ are compared and contrasted; and the reason why ‘T – V’ is as important as ‘T + V’ is explained. It is shown that Newton missed discovering energy.Less

Music as Science: The Contribution of d’Alembert

Cynthia Verba

in Music and the French Enlightenment: Rameau and the Philosophes in Dialogue

There was considerable agreement among the philosophes that Rameau had achieved a breakthrough in music theory precisely because of his application of scientific principles. Despite this consensus, ... More

There was considerable agreement among the philosophes that Rameau had achieved a breakthrough in music theory precisely because of his application of scientific principles. Despite this consensus, however, the realm of music as science underwent a series of conflicts or debates that were closely analogous to those in the aesthetic realm. Whether the subject was art or science, the Cartesian concept of truth or knowledge—still widely accepted in France until well into the eighteenth century—was increasingly exposed to serious scrutiny or challenge. A principal concern of this chapter is the gradual breakdown of Cartesian rationalism within the scientific realm of music and with d’Alembert’s promotion of Newtonian empirical science. It will be shown that Rameau himself contributed to that breakdown—that despite his Cartesian claims and rhetoric, it was musical practice that ultimately determined his rules and laws of harmony.Less