The present volume represents a development of themes that the authors had articulated in an earlier essay entitled ‘How Physics Flew the Philosopher’s Nest’ (Brading and Stan [2021]). In the present work, they encapsulate their central thesis as follows:
The 18th century was a golden age for philosophical mechanics. As the century begun, physics was a subdiscipline of philosophy and its primary task was Body. By 1800, this was no longer the case. Physics had become an independent discipline and Body was not its driving concern anymore […] This is an entirely new way of thinking about philosophy, physics and mechanics, differing sharply from prior accounts. (p. 25)
Here the term ‘Body’ codifies the task of ‘determining the nature of bodies and their essential properties, causal powers and generic behaviors’, leading to doctrines that they label as providing a ‘philosophically grounded mechanics for Body’. Over the course of this lengthy volume they review the contributions of an impressive number of scientifically minded authors writing in the eighteenth century, such as Malebranche, the Bernoullis, Wolfe, d’Alembert, Euler, Kant, and the ever-perceptive Emilie du Chatelet. Later chapters extend the book’s coverage to Lagrange and the early-nineteenth-century contributions of Navier and Cauchy. Their discussion is well informed and detailed throughout, although I was sometimes puzzled by their attempts to envelope all these developments within the common cloth of an escape from philosophical speculation.
But these mild disagreements do not affect the manifest utility of this book. A welcome turn within recent scholarship of the early modern era has recognized that earlier philosophical commentaries upon the period were often impaired by the inaccurate presumption that ‘surely Newton had gotten all of this science stuff right’, leading to a profound underappreciation of the descriptive dilemmas with which notable authors struggled for a significant stretch of time. The present volume attempts to remedy these lacunae by concentrating largely upon the entangled scientific and philosophical developments characteristic of the 1700s.
It may assist the reader if I return to beginnings a bit more than Brading and Stan themselves do. Their discussion initiates with the notoriously awful ‘laws of collision’ that Descartes offered in his 1644 Principles of Philosophy. Their philosophical ‘problem of Body’ then becomes the task of articulating a more plausible approach to body-upon-body collision based upon conservation principles (linear momentum or vis viva) or doctrines centred upon apriorist tenets such as the principle of sufficient reason. They claim that a significant adjustment in focus emerges later in the century as the challenges of mathematically treating localized systems bound by rigid constraints (for example, a bead sliding along a wire) becomes central within the scientific literature developed by d’Alembert and Lagrange. However, as I understand his motivating objectives (Wilson [2022]), Descartes had originally hoped to develop a general physics of mechanism that exemplifies the explanatory advantages that Robert Boyle ([1991], p. 138) underscored:
The […] thing which recommends the corpuscular principles is their extensiveness. The genuine and necessary effect of the strong motion of one part of matter against another is either to drive it on, in its entire bulk, or to break and divide it into particles of a determinate motion, figure, size, posture, rest, order or texture.
However, mechanisms in the usual sense (such as clocks) are normally constituted of four or more rigid parts linked together in a manner that, in the absence of friction, allows the unit to store an internal capacity for performing work over time. As such, mechanisms obey a special ‘science of machinery’ privileged unto themselves. Descartes, however, made the natural mistake of presuming that this specialized science could be reconstituted upon a simpler basis by providing rules that specify how one rigid part within a mechanism can ‘drive on’ its attached neighbours, thereby leading to the dedicated focus upon body-upon-body collisions and their associated conservation laws that we find in the Principles. Mathematically, this innocuous-looking transmutation converts a descriptive project centred upon the mathematically smooth motions of a mechanism such as a clock into a goal focused upon the impactive singularities between colliding masses. Even to this day, circumventing the latter successfully remains a challenging task, involving a large number of delicate supportive considerations. Eventually, rigid bodies (in the guise of ‘constraints’) re-enter the book’s narrative at the end of the seventeenth century, but this adjustment in ambition doesn’t strike me as revolutionary as the authors appear to suggest.
It was quickly realized that none of the macroscopic ‘bodies here among us’ (Newton’s phraseology) can possibly illustrate tidy collision laws of the character that Descartes sought, for experiments by Mersenne and others clearly indicated that the close-to-perfect ‘elasticity’ of a properly manufactured billiard ball partially depends upon the complex capacities that material scientists today label as ‘shape memory’: the ball’s capacity for compressing when repelling an intruder yet afterwards regaining its original configuration quickly. So the prospects for defending the advantages of the ‘mechanical philosophy’ now looked as if they reduced to the task of providing structural underpinnings for these two restorative capacities. In the early proposals to this end (which the authors characterize as ‘philosophical mechanics’), macroscopic bodies were presumed to consist of a relatively permanent exoskeleton built from interlaced atomic ingredients whose preferred ‘natural rest state’ configuration could be temporally expanded or compressed by external influences (thus the ‘shape memory’ of a billiard ball reflects an underlying network of connected ingredients that can ‘remember’ the ball’s original spheroidal shape once the outside disturbances have passed). These persisting frameworks were presumed to contain a large number of exogenous ‘pores’ through which the external factors responsible for the ball’s evanescent compressions and expansions could act upon the body. In the accounts endorsed by Descartes, Leibniz, and (possibly) Newton himself in his Optics, these restorative ‘forces’ were attributed to the pressure effects of an ambient fluid comprised of tiny submundane particles that re-enter the channels within a compressed billiard ball and pump it back up to original size.
Although such speculative proposals strike us as naïve today, they nonetheless reflect a significant measure of genuine insight into the microscopic geometrical arrangements that underlie the elastic capacities of a billiard ball, whose component crystals (in the absence of material damage) manage to stay bonded together in networks that retain their topographical connectivity throughout intermediate episodes of severe shearing.
Newton offered a variety of rather gnomic remarks on the elasticity problem (his friend Henry Pemberton reported that his purpose in doing so was merely one of encouraging further research). So it is not clear that Newton himself conceptualized the restorative ‘forces’ that he believed were implicated in shape memory as comprising action-at-a-distance processes akin to gravitation (although such a proposal was clearly endorsed by many of his later disciples such as R. J. Boscovich whose views Brading and Stan discuss at considerable length).
However, Newton ([1687], p. 795) did feel confident that material bodies must contain component atoms that are both impenetrable and perfectly hard:
That abundance of bodies are hard, we learn by experience; and because the hardness of the whole arises from the hardness of the parts, we therefore justly infer the hardness of the undivided particles not only of the bodies we feel but of all others. That all bodies are impenetrable, we gather not from reason, but from sensation. The bodies which we handle we find impenetrable, and thence conclude impenetrability to be a universal property of all bodies whatsoever.
Insofar as I can determine, Newton here presumes that any adequate explanation of ‘shape memory’ will require some appeal to the fixed geometries of ‘hard atom’ components. He further concluded on an a priori basis that when two particles of this type directly collide, their motions must abruptly halt, for by remaining perfectly ‘hard’, they lack any of the internal mechanisms for shape restoration that we empirically witness within ‘the bodies here about us’. (Notoriously, this presumption also led Newton to posit the assistance of angels who could reanimate the universe after an excessive number of motion-cancelling collisions; Scott [1970].)
Allied views on impenetrability and hard body molecular composition continued to be endorsed by later writers such as Euler ([1835], p. 42), who trenchantly dismissed the Leibniz-inspired views of Christian Wolfe in his Letters to a German Princess:
Finally, let those philosophers turn themselves which way soever they will in support of their monads, or those ultimate and minute particles divested of all magnitude, of which, according to them, all bodies are composed, they still plunge into difficulties, out of which they cannot extricate themselves. They are right in saying that it is proof of dullness to be incapable of relishing their sublime doctrines; it may however be remarked that here the greatest stupidity is the most successful.
Like a number of other authors from this era, Euler himself regarded the impenetrability of small-scale matter as exhibiting a supplementary form of inertia that provides bodies with an inherent resistance to alteration of shape comparable to the usual inertial truculence with respect to adjustments in linear and angular velocity. Doctrines of this simplistic character cannot render adequate justice to the complexities of shape memory, but the authors do a good job in illuminating Euler’s supportive reasoning.
As I understand him, in his later Metaphysical Foundations of Science, Kant eventually rejected allied attempts (which he labelled as ‘mechanical’) to deduce the microscopic qualities of material bodies upon an a priori basis and instead favoured a contrary ‘dynamical’ methodology that resembles the top-down approach that Cauchy successfully implemented in his celebrated 1823 essay upon the elasticity of a continuous material. Kant complains that Euler-like arguments are excessively speculative in their ‘metaphysical’ modes of reasoning:
Everything that relieves us of the need to resort to empty spaces is a real gain for natural science, for they give the imagination far too much freedom to make up by fabrication for the lack of any inner knowledge of nature. In the doctrine of nature, the absolutely empty and the absolutely dense are approximately what blind accident and blind fate are in metaphysical science, namely, an obstacle to the governance of reason, whereby it is either supplanted by fabrication or lulled to rest on the pillow of occult qualities. ([1991], p. 71)
On this basis, his book concludes with the bleak conclusion:
And so ends the metaphysical doctrine of body with the empty, and therefore the inconceivable, wherein it shares the same fate as all other attempts of reason, when… nothing is left to it [except] turn away from the objects to itself, so as to explore and determine, not the ultimate limits of things, but rather the ultimate limits of its own unaided powers. ([1991], p. 104)
Kant had previously articulated an account of material composition in his Physical Monadology that more closely resembles the speculations of Boscovich. It is worth noting that his revised musings upon the proper approach to the physics of flexible bodies directly encapsulate the ‘Copernican revolution’ whereby Kant sought to redirect metaphysical endeavour across a wider canvas.
I believe that such remarks illustrate why a warmer appreciation of the grand philosophical themes of the era can greatly benefit from a closer study of the surrounding scientific literature such as Brading and Stan here provide.
In an allied vein, even before Kant, a fair number of critical thinkers had extracted a variety of crucial philosophical lessons from the failure of ‘mechanical philosophy’ to redeem its promissory notes with respect to Body in a satisfactory manner. Besides collision, many of these complaints were motivated by the daunting problems of cohesion and fracture. In the quotation cited above, Boyle assumes that the guiding principles underlying these twin processes can be readily provided. But this optimistic presumption is plausible only insofar as we comprehend the qualities of the glue that binds these composites together. Critics of atomist atheism such as George Berkeley and Joseph Glanvill were accordingly fond of pointing out that the mysteries of material tenacity appear to lie as far beyond the limits of human comprehension as any of the puzzlements found within the Holy Word:
I think the emergent difficulties, which are its attendants, unanswerable: proof enough of the weakness of our now reasons, which are driven to such straights and puzzles even in things which are most obvious, and which have so much the advantage of our faculties. (Glanvill [1661], p. 46)
In an allied vein, Hume’s blunt empiricism with respect to ‘law’ and ‘cause’ appears to have been directly inspired by the inability of physics to develop adequately detailed accounts of both cohesion and billiard ball collision:
Elasticity, gravity, cohesion of parts, communication of motion by impulse: These are probably the ultimate causes and principles which we shall ever discover in nature, and we may esteem ourselves sufficiently happy, if, by accurate enquiry and reasoning, we can trace up the particular phenomena to, or near to, these general principles […] Thus the observation of human blindness and weakness is the result of all philosophy, and meets us at every turn, in spite of our endeavors to elude or avoid it. ([2007], p. 112)
In point of fact, a factor that contributes significantly to a billiard ball’s capacities for rebounding in a nearly elastic manner traces to the concave shape of its rear wall, which refocuses the incoming distortion waves arriving from the initial collision into caustic surfaces that can effectively repel the incoming ball a bit later (a pleasing behaviour that explains why we play pool with balls rather than rectangular slugs). However, the technical resources for tracing out these wave processes lay far beyond the capabilities of Hume’s era (indeed, I am not aware of any contemporaneous appeals to caustic focusing in the context of billiard ball behaviour despite the fact that allied processes were familiar from the optics of raindrops and curved mirrors). I have sometimes wondered whether Hume might have waxed so briskly dismissive with respect to the underpinnings of ‘causal processes’ had he been familiar with a modern step-by-step simulation of the internal wave processes inside a real life billiard ball.
Some of my chief difficulties in following the developmental arc that Brading and Stan hope to establish stems from considerations that mainly lie on the mathematical side of the ledger, for modellers working the beginning of the eighteenth century were forced to find clever stratagems for capturing inherently three-dimensional phenomena within the reach of a limited mathematical calculus that requires some central choice of a single independent variable (for example, the one-dimensional curve of a loaded strut at equilibrium). Reliance upon these modelling expedients often renders the philosophical perspectives of their employers rather opaque. To be sure, vital improvements in expressive capability were eventually achieved by the middle of the century through d’Alembert’s and Euler’s pioneering developments within the field of partial differential equations. Notoriously, however, such equations divulge their secrets only reluctantly and, in the particular case of billiard ball collisions, it wasn’t until far into the twentieth century that suitably adapted numerical methods and fast enough computers became available that could adequately track the complicated stress wave patterns that arise within the interiors of two colliding billiard balls. So no comparable retort to Hume was available to any of the authors in his era.
Similar remarks apply to the geometrical constraints (for example, the rigid wire along which a bead slides) that d’Alembert and Lagrange managed to integrate successfully with descriptions posed at the point mass level. Such mixed treatments assume that the wire or machine part will retain its shape throughout the physical interactions. But this presumption is not invariably true: a heavy bead will send some kind of pressure wave advancing though the wire. Once again, these descriptive shortfalls were successfully addressed only within the continuum mechanics of wave motion that appeared in the mid-nineteenth century. After this transition took hold, the fundamental challenges involved in modelling matter mathematically began to look quite different in the vein that Lord Kelvin highlighted in 1884:
With respect to the somewhat cloud-land molecular beginnings of the theory of elasticity, we have long passed away from the stage in which Father Boscovich is accepted as being the originator of a correct representation of the ultimate nature of matter and force. (Thompson [1884], p. 125)
But this is not to say that the Victorians didn’t continue to puzzle mightily over how matter, and the aether, can possible behave as they do. Indeed, the central methodological contrast that Brading and Stan draw (pp. 265–68), following Einstein, between a ‘constructive approach’ (based upon compositional hypotheses) and a ‘principle approach’ (based upon theoretical laws) to the justificatory underpinning of classical physics remained highly controversial throughout the remainder of the nineteenth century. Indeed, the real life complexities of ‘shape memory’ still strike me as indicative of the modelling tensions that illustrate why firm methodological morals on this score remain elusive to the present day. A material’s capacities for shape reclamation are highly variable and subject to hysteresis and temperature effects in complex ways that frequently prove more amenable to modelling tactics pitched at the molecular level than to a principled ‘top-down’ continuum physics methodology.
As the authors correctly remark, our present day appreciation of our ‘classical mechanics’ heritage has become substantially marred by a long history of reductive claims to the effect that ‘everything can already be found in Newton’ (a historical injustice to which Lord Kelvin and P. G. Tait significantly contributed in their Treatise on Natural Philosophy). Much of this dubious heritage hinges upon excessively generous parsings of Newton’s second law of motion that the authors effectively critique in their valuable overview of Euler’s acknowledged advances in these respects. Nonetheless, a large number of philosophers today remain unjustifiably confident that they fully understand the contours of what ‘classical mechanics’ involves. The present book performs a valuable service in attempting to lift these misty fogs over our philosophical heritage.
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The BJPS2025-03-18 07:00:442025-03-25 15:49:13Katherine Brading and Marius Stan, Philosophical Mechanics in the Age of Reason // Reviewed by Mark Wilson
