The purpose of this note is to examine a recent axiomatization of classical particle mechanics, and its relation to an alternative axiomatization I had earlier proposed. A comparison of the two proposals casts some interesting light on the problems of operationalism in classical celestial mechanics.1. Comparison of the Two Axiomatizations. The basic differences between the two proposals arise from the nature of the undefined terms. Both systems take the set of particles, time, and position as primitive notions. (...) Both systems assume that there exists a set of particles having continuous, twice-differentiable paths over some time interval. In addition, CPM takes mass and force as primitive notions, and assumes that with each particle there is associated a mass and a set of forces such that Newton's Second Law is satisfied. A system with these properties is called in CPM “a system of particle mechanics.” If, in addition, the set of forces in the system satisfies Newton's Third Law, the system is called in CPM “Newtonian.”. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Mechanisms of Violent Retribution in Chinese Hell Narratives Charles D. Orzech University ofNorth Carolina Greensboro Ai! The criminals in this hell have all had their eyes dug out and the fresh blood flows [from them], and each of them cries out, their two hands pressing their bloody eye-sockets—truly pitiful! To the left a middle-aged person is just having an eye pulled out by one of the shades; he struggles (...) unceasingly, screaming; his left eye has already been extracted... (56b) Ai-yah!... Each of the criminals is bound to a an iron pillar and the ox-headed demons are in the process of administering punishment—using iron or copper blades they peel the skin of the person's face, just as a butcher kills a pig and then flays it. Each of the criminal ghosts screams in pain... (59b) The criminal ghost's hands are bound about an iron pillar which is entirely red [with heat] and the criminal ghost's two hands are entirely cooked and it is unbearable... (126a) Record ofA Journey to Hell These passages are found, not in some medieval description of hell, nor in a work for sadists, but in a modern and quite popular Chinese "good book" (shan-shu) titled Record ofA Journey to Hell (Ti-yu yu-chi). Record ofA Journey to Hell is the most recent work of a genre which emerged in tenthcentury China and which may be found throughout Asia from Vietnam to Japan. This persistent fascination with gruesome scenes of torture stands in striking contrast to Michel Foucault's observations that by the first quarter of the nineteenth century "punishment had gradually ceased to be a spectacle" in Europe (9). In Record ofA Journey to Hell we are not faced with a seachange in the discourse and practice of a society. Rather, we must come to 112Charles D. Orzech grips with and seek to understand the persistence of images oftorture as well as actual torture and public execution in some modern Chinese societies. The Chinese hells—more properly purgatories, as punishment there is not eternal—are a product of cultural adaptation and interaction. Before the first century of our era we have evidence of only the most attenuated notions of the underworld, a "yellow springs" (huang-yiian) where "all, good and bad, huddled together in darkness being guarded jealously by the god of the Soil who ended by devouring them" (Thompson 29). The ruling elite avoided this fate through elaborate ancestral ritual indexed by the possession of a surname. Social status was, from the earliest times, "inscribed" on tablets which gave visible form to both social and cosmological hierarchies (Li 247-54). However, the rise of the Taoist Celestial Masters movement (T'ien-shih tao, second century) with its heavenly and infernal bureaucracies soon coupled with newly imported Indian Buddhist descriptions of the workings of karma and the hells. The result of this amalgam is the popular Chinese vision of the underworld as a vast bureaucracy centered on ten "courts," and headed by Yama, the South Asian lord of the dead (Seidel). At death the soul is summoned before the lords of hell who administer punishments appropriate to the misdeeds of the soul. After almost interminable periods of suffering, often in all of the hells in succession, the soul is reborn as a human, an animal, or even an insect, to start the whole process again. By the tenth century this distinctly Chinese version ofthe underworld had found wide dissemination and was the framework for worship and ritual directed to the recently dead.18 Unlike the South Asian prototypes, Chinese hells appear to be modeled on the imperial bureaucracy and administered by a hellish staff. The "court" layout often major and numerous subsidiary hells mimics Chinese palace and temple architecture and is quite distinct from the mandala-like layout found in "orthodox" Buddhist prototypes. Taoist priests, Buddhist monks and nuns, and a variety of folk practitioners and mediums act as intermediaries between this world and the other. They grease the wheels of the bureaucracy with their ritual knowledge and with community offerings to obtain release for imprisoned souls. Knowledge of the workings of the underworld is, according... (shrink)

The ArgumentOne of the earliest arguments for Copernicanism was a widely accepted fact: that on a horizontal plane a body subject to no external resistance can be set in motion by the smallest of all possible forces. This fact was contrary to Aristotelian physics; but it was a physical argument (by abduction) for the possibility of the Copernican world system. For it would be explained if that system was true or at least possible.Galileo argued: only nonviolent motions can be caused (...) by the smallest of all possible forces; hence resistance-free horizontal motions are nonviolent; this confirms Copernicanism insofar as it designates the rotations of celestial spheres (being resistance-free horizontal motions) as nonviolent.Galileo's argument was compatible with (and supportive of) the specific Copernican version of impetus mechanics; but it was also compatible with a (somewhat qualified) principle of inertia. Thus it promoted decisively the transition from impetus mechanics to classical inertial mechanics. (shrink)

Catherine Keller's Cloud of the Impossible knits together process theology and relational ontology with quantum mechanics. In quantum physics, she finds a new resource for undoing the architecture of classical metaphysics and its location of autonomous human subjects as the primary gears of ethical agency. Keller swarms theology with the quantum perspective, focusing in particular on the phenomenon of quantum entanglement, by which quantum particles are found to remain influential over each other long after they have been physically separated—what (...) Albert Einstein and his collaborators recklessly dismissed as “spooky action at a distance.” This spooky action, Keller suggests, reroutes process thought—classically concerned with flux—to a new concern with intransigence—particularly the intransigence of the ethical relationship. Attending to the ethical urgency of the Other, she leaves process theology in a position of susceptibility to the moral imperative posed by the marginalized, the victimized, and the oppressed. This essay argues that although the ontological work of Keller's book productively integrates quantum physics into process theology, the ethical dimension of relationality is left cold in the quantum field. This is because, contra the ethical framework of contemporary deconstruction, which, following Emmanuel Levinas, sees ethical relationships as emerging out of a dynamic of infinite distance, moral connection has nothing to do with the remote reaches of the quantum scale or the macro-scale limits of space—nothing to do with “infinity” at all. Ethics emerges out of a much messier landscape—the evolved dynamic of fleshy, finite, material bodies. Rather than seeing ethical labor as a matter of physics, my contention is that interdisciplinary undertakings like Cloud of the Impossible are ethical disciplinary practices, re-acquainting us with the non-sovereignty of the self in order to open up new habits of relating rather than spotlighting ethical imperatives. (shrink)

The first edition of Newton’s Principia opens with a “Praefatio ad Lectorem.” The first lines of this Preface have received scant attention from historians, even though they contain the very first words addressed to the reader of one of the greatest classics of science. Instead, it is the second half of the Preface that historians have often referred to in connection with their treatments of Newton’s scientific methodology. Roughly in the middle of the Preface, Newton defines the purpose of philosophy (...) as a twofold task: to investigate the forces of the phenomena of nature and, once having established the forces, to demonstrate the remaining phenomena. Newton then introduces a distinction between the first two books, which deal with general propositions, and the third, where the propositions are applied to particular instances of celestial phenomena. From these phenomena, Newton claims, the force of gravity, thanks to which bodies tend toward the Sun, is derived. By assuming this force in mathematical propositions, other motions are deduced: the motions of the planets, the comets, the moon, and the sea. Newton then declares his hope that phenomena relative to small particles will also be explained, as per the celestial ones, thanks to the understanding of attractive forces hitherto unknown to philosophers. The Preface ends with a well-deserved laudatio of Edmond Halley and an apologetic passage concerning certain imperfections in the presentation of advanced subjects, such as the motions of the moon. It is these lines to which historians have given most attention in their various studies. (shrink)

The present authors have given a mathematical model of Mach's principle and of the Mach–Einstein doctrine about the complete induction of the inertial masses by the gravitation of the universe. The analytical formulation of the Mach–Einstein doctrine is based on Riemann's generalization of the Lagrangian analytical mechanics (with a generalization of the Galilean transformation) on Mach's definition of the inertial mass and on Einstein's principle of equivalence. All local and cosmological effects—which are postulated as consequences of Mach's principle by (...) C. Neumann, Mach, Friedländer and Einstein—result from the Riemannian dynamics with the Mach–Einstein doctrine. In celestial mechanics it follows, in addition, Einstein's formula for the perihelion motion. In cosmology, the Riemannian mechanics yields two models of an evolutionary universe with the expansion lows R ~ t or R ~ t2. In this paper, secular consequences of the Mach–Einstein doctrine are examined concerning palaeogeophysics and celestial mechanics. The research predicted secular decrease of the Earth's flattening and secular acceleration of the motion of the Moon and of the planets. The numerical values of this secular effect agree very well with the empirical facts. In all cases, the secular variation $\dot{\alpha}$ of the parameter α is the order of magnitude $\dot{\alpha}=-H_0 \alpha$ , where H0 is the instantaneous value of the Hubble constant: $H_0 =\left({\dot{R}/R} \right)_0 \approx \left( {0.5-1.0} \right) \times 10^{-10}a^{-1}$ . The relation of the secular consequences of the Mach–Einstein doctrine to those of Dirac's hypothesis on the expanding Earth, and to Darwin's theory of tidal friction are also discussed. (shrink)

Despite growing consumerism and skepticism about authority in the culture as a whole, most patients continue to be pliant. If there is a serious threat to physician autonomy, it is more likely to come from third‐party payers and new forms of medical practice, particularly the rise of for‐profit hospital chains, than from patients. Though physicians are restless, they will learn to adapt to the new conditions of practice.

The Kolmogorov-Sinai entropy is a fairly exotic mathematical concept which has recently aroused some interest on the philosophers’ part. The most salient trait of this concept is its working as a junction between such diverse ambits as statistical mechanics, information theory and algorithm theory. In this paper I argue that, in order to understand this very special feature of the Kolmogorov-Sinai entropy, is essential to reconstruct its genealogy. Somewhat surprisingly, this story takes us as far back as the beginning (...) of celestial mechanics and through some of the most exciting developments of mathematical physics of the 19th century. (shrink)

These original essays explore the philosophical implications of Newton's work.

A “frame of reference” is a standard relative to which motion and rest may be measured; any set of points or objects that are at rest relative to one another enables us, in principle, to describe the relative motions of bodies. A frame of reference is therefore a purely kinematical device, for the geometrical description of motion without regard to the masses or forces involved. A dynamical account of motion leads to the idea of an “inertial frame,” or a reference (...) frame relative to which motions have distinguished dynamical properties. For that reason an inertial frame has to be understood as a spatial reference frame together with some means of measuring time, so that uniform motions can be distinguished from accelerated motions. The laws of Newtonian dynamics provide a simple definition: an inertial frame is a reference-frame with a time-scale, relative to which the motion of a body not subject to forces is always rectilinear and uniform, accelerations are always proportional to and in the direction of applied forces, and applied forces are always met with equal and opposite reactions. It follows that, in an inertial frame, the center of mass of a system of bodies is always at rest or in uniform motion. It also follows that any other frame of reference moving uniformly relative to an inertial frame is also an inertial frame. For example, in Newtonian celestial mechanics, taking the “fixed stars” as a frame of reference, we can determine an inertial frame whose center is the center of mass of the solar system; relative to this frame, every acceleration of every planet can be accounted for as a gravitational interaction with some other planet in accord with Newton 's laws of motion. (shrink)

In this paper I discuss the kinds of idealisations invoked in normative theories—logic, epistemology, and decision theory. I argue that very often the so-called norms of rationality are in fact mere idealisations invoked to make life easier. As such, these idealisations are not too different from various idealisations employed in scientific modelling. Examples of the latter include: fluids are incompressible (in fluid mechanics), growth rates are constant (in population ecology), and the gravitational influence of distant bodies can be ignored (...) (in celestial mechanics). Thinking of logic, epistemology, and decision theory as normative models employing various idealisations of these kinds, changes the way we approach the justification of the models in question. (shrink)

The scientific realism debate has now reached an entirely new level of sophistication. Faced with increasingly focused challenges, epistemic scientific realists have appropriately revised their basic meta-hypothesis that successful scientific theories are approximately true: they have emphasized criteria that render realism far more selective and, so, plausible. As a framework for discussion, I use what I take to be the most influential current variant of selective epistemic realism, deployment realism. Toward the identification of new case studies that challenge this form (...) of realism, I break away from the standard list and look to the history of celestial mechanics, with an emphasis on twentieth century advances. I then articulate two purely deductive arguments that, I argue, properly capture the historical threat to realism. I contend that both the content and form of these novel challenges seriously threaten selective epistemic realism. I conclude on a positive note, however, arguing for selective realism at a higher level. Even in the face of threats to its epistemic tenet, scientific realism need not be rejected outright: concern with belief can be bracketed while nonetheless advocating core realist tenets. I show that, in contrast with epistemic deployment realism, a purely axiological scientific realism can account for key scientific practices made salient in my twentieth century case studies. And embracing the realists favored account of inference, inference to the best explanation, while pointing to a set of the most promising alternative selective realist meta-hypothesis, I show how testing the latter can be immensely valuable to our understanding of science. (shrink)

Newton’s impact on Enlightenment natural philosophy has been studied at great length, in its experimental, methodological and ideological ramifications. One aspect that has received fairly little attention is the role Newtonian “analogies” played in the formulation of new conceptual schemes in physiology, medicine, and life science as a whole. So-called ‘medical Newtonians’ like Pitcairne and Keill have been studied; but they were engaged in a more literal project of directly transposing, or seeking to transpose, Newtonian laws into quantitative models of (...) the body. I am interested here in something different: neither the metaphysical reading of Newton, nor direct empirical transpositions, but rather, a more heuristic, empiricist construction of Newtonian analogies. Figures such as Haller, Barthez, and Blumenbach constructed analogies between the method of celestial mechanics and the method of physiology. In celestial mechanics, they held, an unknown entity such as gravity is posited and used to mathematically link sets of determinate physical phenomena (e.g., the phases of the moon and tides). This process allows one to remain agnostic about the ontological status of the unknown entity, as long as the two linked sets of phenomena are represented adequately. Haller et. al. held that the Newtonian physician and physiologist can similarly posit an unknown called ‘life’ and use it to link various other phenomena, from digestion to sensation and the functioning of the glands. These phenomena consequently appear as interconnected, goal-oriented processes which do not exist either in an inanimate mechanism or in a corpse. In keeping with the empiricist roots of the analogy, however, no ontological claims are made about the nature of this vital principle, and no attempts are made to directly causally connect such a principle and observable phenomena. The role of the “Newtonian analogy” thus brings together diverse schools of thought, and cuts across a surprising variety of programs, models and practices in natural philosophy. (shrink)

In this paper I challenge and adjudicate between the two positions that have come to prominence in the scientific realism debate: deployment realism and structural realism. I discuss a set of cases from the history of celestial mechanics, including some of the most important successes in the history of science. To the surprise of the deployment realist, these are novel predictive successes toward which theoretical constituents that are now seen to be patently false were genuinely deployed. Exploring the (...) implications for structural realism, I show that the need to accommodate these cases forces our notion of “structure” toward a dramatic depletion of logical content, threatening to render it explanatorily vacuous: the better structuralism fares against these historical examples, in terms of retention, the worse it fares in content and explanatory strength. I conclude by considering recent restrictions that serve to make “structure” more specific. I show however that these refinements will not suffice: the better structuralism fares in specificity and explanatory strength, the worse it fares against history. In light of these case studies, both deployment realism and structural realism are significantly threatened by the very historical challenge they were introduced to answer. (shrink)

Henri Poincaré was not just one of the most inventive, versatile, and productive mathematicians of all time--he was also a leading physicist who almost won a Nobel Prize for physics and a prominent philosopher of science whose fresh and surprising essays are still in print a century later. The first in-depth and comprehensive look at his many accomplishments, Henri Poincaré explores all the fields that Poincaré touched, the debates sparked by his original investigations, and how his discoveries still contribute to (...) society today. Math historian Jeremy Gray shows that Poincaré's influence was wide-ranging and permanent. His novel interpretation of non-Euclidean geometry challenged contemporary ideas about space, stirred heated discussion, and led to flourishing research. His work in topology began the modern study of the subject, recently highlighted by the successful resolution of the famous Poincaré conjecture. And Poincaré's reformulation of celestial mechanics and discovery of chaotic motion started the modern theory of dynamical systems. In physics, his insights on the Lorentz group preceded Einstein's, and he was the first to indicate that space and time might be fundamentally atomic. Poincaré the public intellectual did not shy away from scientific controversy, and he defended mathematics against the attacks of logicians such as Bertrand Russell, opposed the views of Catholic apologists, and served as an expert witness in probability for the notorious Dreyfus case that polarized France. Richly informed by letters and documents, Henri Poincaré demonstrates how one man's work revolutionized math, science, and the greater world. (shrink)

The standard mathematical models in population ecology assume that a population's growth rate is a function of its environment. In this paper we investigate an alternative proposal according to which the rate of change of the growth rate is a function of the environment and of environmental change. We focus on the philosophical issues involved in such a fundamental shift in theoretical assumptions, as well as on the explanations the two theories offer for some of the key data such as (...) cyclic populations. We also discuss the relationship between this move in population ecology and a similar move from first-order to second-order differential equations championed by Galileo and Newton in celestial mechanics. (shrink)

We treat the classical dynamics of the hydrogen atom in perpendicular electric and magnetic fields as a celestial mechanics problem. By expressing the Hamiltonian in appropriate action–angle variables, we separate the different time scales of the motion. The method of averaging then allows us to reduce the system to two degrees of freedom, and to classify the most important periodic orbits.

During the late nineteenth century, scientists around the world disagreed as to the types of instruments and methods that should be used for determining the most important constant of celestial mechanics: the solar parallax. Venus’s 1874 transit across the sun was seen as the best opportunity for ending decades of debate. However, a mysterious “black drop” that appeared between Venus and the sun and individual differences in observations of the phenomenon brought traditional methods into disrepute. To combat these (...) difficulties, the astronomer Jules Janssen devised a controversial new instrument, the “photographic revolver,” that photographed Venus at regular intervals. Another solution came from physicists, who rivaled the astronomers’ dominance in precision measurements by deducing the solar parallax from physical measurements of the speed of light. Yet other astronomers relied on drawings and well‐trained observers. The new space emerging from this debate was characterized by a decline in faith in photography and in geometry and by the growing realization of the importance of alternative elements needed for establishing scientific truths: power and authority, skill and discipline, standardization, mechanical reproducibility, and theatricality. By examining the “cinematographic turn” in science and its alternatives, this essay brings to light unexplored multidisciplinary connections that contribute to the histories of psychology, philosophy, physics, and film studies. (shrink)

The following paper, together with its sequel ("The use and non-use of mathematics"), is a study in the mathematization of nature. It looks into the history of one of the most emblematic achievements of this fundamental aspect of the making of modem science - the Inverse Square Law of universal gravitation - before its celebrated application by Newton to celestial mechanics. What did it take, we ask, to tum a particular mathematical ratio into a candidate for a law (...) of nature? (shrink)