Historians have picked out many characteristics by which to define the profound alteration of natural philosophy from Galileo's adoption of Copernicanism in the late 1590s to the publication of Newton's Principia in 1687. Some historians note that many authors prominently put forward an ideal of mathematical demonstration, an ideal that in mechanics and astronomy was effectively realized in the period; others emphasize the insistence that theory be submitted to the test of observation and experiment; according to still others, the defining character of the new philosophy is that intervention and control came to supplant contemplation as the primary motive and goal in the study of nature. By now it is evident both that no one trait suffices, even with respect to what we now call the physical sciences, and that the historian must distinguish what was claimed for the new philosophy by its proponents from the more modest, piecemeal, and gradual changes that actually occurred.
Tenets of Mechanism
Ideologically if not always in practice, mechanism—the "mechanical philosophy," as physicist Robert Boyle (1627–1691) called it—became the character by which the new science in all its branches distinguished itself from its Aristotelian predecessor. The tenets of mechanism can be summarized as follows:
(1) The sensible world, or the system of objects of outward experience, consists of bodies possessing just a few, chiefly geometrical, properties. This was in opposition to the Aristotelian profusion of forms and qualities and to the sympathies, antipathies, and other "occult powers" attributed to things by alchemists and natural magicians. René Descartes (1596–1650), in the wake of Galileo's dictum that the book of nature is written in the language of mathematics, allowed to the body only those properties determinable from its essence as extension. What we call an individual body is nothing more than a region of space delimited from other such regions by its instantaneous motion.
Figure, size, and motion: Descartes's list proved rather quickly to be insufficient. Henry More argued, and many agreed, that impenetrability could not be demonstrated from extension and must be an original property of matter. Leibniz insisted that force could not be reduced to motion. Newton added universal gravitation (though he did not rule out an eventual mechanistic account). In the eighteenth century, electrical, magnetic, and chemical properties were added to the list, as were those vital powers of organisms that proved incapable of explanation on Cartesian terms.
(2) The preferred mode of explaining the sensible qualities of gross matter was reduction. From hypotheses concerning the underlying structure of a substance—the shape and size of the "corpuscles" of which it consisted—the phenomena of that substance were supposed to be derived using the laws of motion. The corpuscles being too small to affect the senses except en masse, hypotheses about their configuration could be verified only indirectly, typically by showing that they could explain a great many phenomena at once. Often, mechanical hypotheses were adaptations of hypotheses made earlier by Aristotelian philosophers: that transparency had something to do with pores through which particles of light could pass, for example.
The point was not novelty for its own sake but the elimination from natural philosophy of unwanted entities: Descartes's vortex theory of planetary motion, for example, eliminated the force of attraction that Kepler had found it necessary to propose; the planets stay in their orbits by virtue of being in dynamic equilibrium with the particles revolving around the Sun at their distance. In the science of life, sensation and action in animals were to be explained by reference not to the faculties of a mysterious soul but by invoking hypotheses about the shapes of the sense organs and the motions imposed by them on the "animal spirits" (a fluid consisting of very small, fast-moving particles) coursing through the nerves. Having no fluid dynamics worth the name, Descartes had no hope of actually deriving the phenomena from his hypotheses on the basis of the laws of motion. Instead, he tried to make them plausible by analogies with pulleys and pipe organs, whose manner of motion would be familiar to the educated reader.
That machines could perform even the functions of living things became more credible in view of the increasingly complex capacities of machines projected or built by late sixteenth-century and early seventeenth-century engineers, among them Salomon de Caus (d. 1626), Agostino Ramelli (1531–1608), and Vittorio Zonca. In the eighteenth century, the famous automata of Jacques de Vaucanson (1709–1782), which included a flute player and a duck with an apparently fully functioning digestive system, were adduced as evidence that the operations of living things could be simulated mechanically. Given that in the new physics, scale was irrelevant, nature in the large could be seen as a gigantic clock, and living things as (in Leibniz's words) machines whose parts were likewise machines—an infinite embedding of divinely engineered devices.
(3) With the advance of mechanism, two new skills became requisite for a natural philosopher. The first was that of deriving conclusions mathematically from laws (treated as axioms) and initial conditions concerning the locations, shapes, and motions of bodies. The development of calculus by Leibniz and Newton in the late seventeenth century greatly increased the reach of mathematical physics. Newton and Christiaan Huygens (1629–1695) were among the seventeenth-century virtuosi of mathematical physics. In the eighteenth century, noted names included the Bernoulli family (Johann [also known as Jean], Jakob [also known as Jacques], and Daniel), Jean Le Rond d'Alembert, Leonhard Euler, Joseph-Louis Lagrange, and Pierre Simon Laplace, whose Mécanique céleste (Celestial mechanics, 1798–1825) was the capstone of the edifice begun by Newton.
The other requisite skill was the ability to generate experimental setups (or observational situations) capable of putting to the test conclusions drawn from theory. The now familiar dynamic by which the theorist is required to derive new testable claims, hence providing motive for new experiments, some of which generate new phenomena to be explained, was largely absent from Scholastic natural philosophy. One of the weaknesses of Cartesianism was likewise its inability, in the hands of its foremost proponents, to incorporate this dynamic. The more modest style of Marin Mersenne (1588–1648), Descartes's colleague and correspondent, was to prove the more enduring. The examples of Cartesianism and Gassendism (the atomist philosophy of Pierre Gassendi and his followers, including Walter Charlton and François Bernier) show that mechanism and the "experimental dynamic" were not inseparable. Nevertheless, the association of the two is not mere coincidence: mechanism emerged as the setting of natural philosophy was shifting from the schools to the competitive world of gentlemanly amateurs like Boyle and freelance teachers like the Cartesians Jacques Rohault and Pierre Sylvain Régis.
Success and Limitations of Mechanism
Mechanism as an ideology for the pursuit of knowledge was enormously successful. It claimed for itself a clarity and explanatory prowess that Aristotelianism, despite the efforts of Honoré Fabri (1607–1688), who accepted the experimental method but not the ontology of mechanism, could not match. The examples of Nicolas Malebranche (1638–1715), Pierre Varignon (1659–1722), and Louis Carré—all described by Bernard le Bouvier de Fontenelle (1657–1757), the "perpetual secretary" of the Académie Royale des Sciences in Paris, as finding a new light, even a new universe, in the philosophy of Descartes—show how persuasive the new philosophy could be to those educated in the old.
Nevertheless, there was no universal agreement that mechanism of the strict Cartesian sort was adequate to explaining the whole of nature. There were unreformed Aristotelians like Fabri who, while advancing hypotheses not unlike those of the mechanists (for example, concerning elasticity), nevertheless retained the Aristotelian distinction of form and matter and the system of four elements (earth, water, air, fire) defined by the very sorts of qualities Descartes had thought to banish. Other seventeenth-century dissenters, like Henry More, Ralph Cudworth, and Anne Conway, insisted on the necessity of attributing active powers to bodies—contrary to the Cartesian definition of matter as extension, which precluded any active powers. Leibniz argued that the "mutual rest" Descartes held to be the glue holding bodies together was quite inept to explain cohesion; this required instead an internal principle of unity. Newtonian gravity was a serious blow, as was Newton's demolition of the vortex theory. By the end of the seventeenth century, moreover, the promise of Cartesian mechanism in explaining the phenomena of life had diminished to the point that Georg Ernst Stahl and other physiologists were ready to revive the animal and plant souls Descartes had extinguished. In particular, Stahl believed that the filtering of fluids in the digestive system could not be explained as the passage of particles through successive sieves; some selective power of attraction was instead required. In the first decades of the eighteenth century, the practice of hypothesizing configurations of subvisible particles had become "old hat." Such hypotheses could be, if urged on the basis of analogy alone, no less question-begging than hypotheses about forms or occult qualities (Gabbey).
Mechanism could not quite deliver on its promises in the seventeenth century. Its ontology proved too sparse. In particular the science of life resisted "mechanization." Nevertheless, the reduction of all of nature to the interaction of a few basic entities and forces, whose phenomena were to be derived mathematically from first principles, has not only been enormously successful in fundamental physics but has also provided a model to all the natural sciences.
Bibliography
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—DENNIS DES CHENE
where F = degree of freedom of mechanism, l = number of links of mechanism, j = number of joints of mechanism, fi = degree of freedom of relative motion at ith joint, σ = 
