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)

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)

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)

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)

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)

ABSTRACT As well as the mathematically-supported celestial mechanics that Newton developed in his Principia, Newton also proposed a more speculative natural philosophy of interparticulate forces of attraction and repulsion. Although this speculative philosophy was not made public before the ‘Queries’ which Newton appended to the Opticks, it originated far earlier in Newton’s career. This article makes the case that Newton’s short, unfinished manuscript, entitled ‘De Aere et Aethere’, should be seen as an important landmark in Newton’s intellectual development, being (...) the first work in which Newton assumed there are repulsive forces operating at a distance between the particles of bodies. The article offers an account of how Newton came to write ‘De Aere et Aethere’ and why. It also outlines its relationship to the ‘Conclusio’, with which Newton briefly intended to finish the Principia, and to the ‘Queries’ in the Opticks. The date of the manuscript is disputed, and the article also aims to settle this dispute. Claims that the ‘De Aere et Aethere’ must have been written before the ‘Hypothesis... of Light’ of 1675 are dismissed, and it is suggested, following R. S. Westfall, that it was written after a well-known letter Newton wrote to Boyle early in 1679. (shrink)

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)

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)

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

The elliptical orbits resulting from Newtonian gravitation are generated with a multifaceted symmetry, mainly resulting from their conservation of both angular momentum and a vector fixing their orientation in space—the Laplace or Runge-Lenz vector. From the ancient formalisms of celestial mechanics, I show a rather counterintuitive behavior of the classical hydrogen atom, whose orbits respond in a direction perpendicular to a weak externally-applied electric field. I then show how the same results can be obtained more easily and directly from (...) the intrinsic symmetry of the Kepler problem. If the atom is subjected to an oscillating electric field, it enjoys symmetry in the time domain as well, which is manifest by quasi-energy states defined only modulo ħω. Using the Runge-Lenz vector in place of the radius vector leads to an exactly-solvable model Hamiltonian for an atom in an oscillating electric field—embodying one of the few meaningful exact solutions in quantum mechanics, and a member of an even more exclusive set of exact solutions having a time-dependent Hamiltonian. I further show that, as long as the atom suffers no change in principal quantum number, incident radiation will produce harmonic radiation with polarization perpendicular to the incident radiation. This unusual polarization results from the perpendicular response of the wavefunction, and is distinguished from most usual harmonic radiation resulting from a scalar nonlinear susceptibility. Finally, I speculate on how this radiation might be observed. (shrink)

September 2008 Abstract: We consider the precursors to the discovery of sensitive dependence on initial conditions by Edward Lorenz (1963) in his model of climatic fluid dynamics. This will focus on work in various disciplines that imply either such sensitivity, irregular endogenous dynamic patterns, or fractal nature of an attractor, as is also found in the attractor underlying the model Lorenz studied. Going from ancient hints in Anaxagoras through nineteenth century mathematics and physics, the main areas of such development will (...) be argued to have been in celestial mechanics, oscillators, and economics. (shrink)

The Bohr formulation—the original one—is now largely a matter of history. The usual career of a theory was its fate. It explained much, but it failed at the first signs of complication, even for the simplest molecules as hydrogen and helium. Some results were either only approximate in a loose or incomplete fashion, e.g. in the application of the correspondence principle to intensities, the only reliable predictions being only for an absence of certain lines, or they quite disagreed with experiment, (...) e.g. in the case of the hydrogen molecule and the hydrogen molecule ion, the normal and excited states of helium, the anomalous Zeeman effect, the Ramsauer effect, and in the treatment of problems where more than one electron was involved. In the last mentioned cases the perturbation method, so successful in solving “many-body” problems in celestial mechanics, failed completely because systems of several electrons, possessing frequencies of the order of light waves, cannot interact classically. A bit of much forced pragmatism was practiced in treating the many electron atom as a variation of the hydrogen atom. Besides, there were technical oddities, like ½ quantum numbers, and impenetrated anologies between visible and X-ray spectra. (shrink)

The persisting conception of Hegel's criticism of Newton's physics as an irrational or at least hopelessly exaggerated one partly has its roots mainly in Hegel's terminology and in his style. This does not mean that a mere translation of Hegel's arguments into any contemporary philosophical language be sufficient to immediately convince every Newtonian scientist. However, a non-Hegelian way of rephrasing the core of Hegel's anti-Newtonian philosophy of nature can help to understand to which extent the latter does satisfy any scientist's (...) criteria for a rational and self-consistent theory. To demonstrate this is the central aim of my talk, which is structured as follows: In the first part, I'm trying to highlight basic features of Hegel's criticism of Newton's optics and celestial mechanics, eventually focussing on his concept of a "sense of nature". This part has the character of a review. Second -­ and that is supposed to be the "reconsideration" part of my paper -­ I'll try to highlight the fundamental difference between Newton's and Hegel's ideas of natural laws and of the relation between mathematics and physics. Third, the metaphysical background of this difference will be analyzed. It is by the analysis of this metaphysical background that I hope to render Hegel's criticism of Newton's scientific revolution more understandable. (shrink)

The idea of a canonical transformation emerged in 1837 in the course of Carl Jacobi's researches in analytical dynamics. To understand Jacobi's moment of discovery it is necessary to examine some background, especially the work of Joseph Lagrange and Siméon Poisson on the variation of arbitrary constants as well as some of the dynamical discoveries of William Rowan Hamilton. Significant figures following Jacobi in the middle of the century were Adolphe Desboves and William Donkin, while the delayed posthumous publication in (...) 1866 of Jacobi's full dynamical corpus was a critical event. François Tisserand's doctoral dissertation of 1868 was devoted primarily to lunar and planetary theory but placed Hamilton–Jacobi mathematical methods at the forefront of the investigation. Henri Poincaré's writings on celestial mechanics in the period 1890–1910 succeeded in making canonical transformations a fundamental part of the dynamical theory. Poincaré offered a mathematical vision of the subject that differed from Jacobi's and would become influential in subsequent research. Two prominent researchers around 1900 were Carl Charlier and Edmund Whittaker, and their books included chapters devoted explicitly to transformation theory. In the first three decades of the twentieth century Hamilton–Jacobi theory in general and canonical transformations in particular would be embraced by a range of researchers in astronomy, physics and mathematics. (shrink)

An investigation of what might be called the logical formalization of the process of theory change due to anomalies is presented. By anomaly, we mean an observed fact falling into the explanatory scope of a theory that does not agree with the theory prevision. A classical approach to restore the explicative power of a theory faced with an anomaly is to propose new, tentative auxiliary hypotheses which, along with part of the old set of auxiliary hypotheses, are able to solve (...) the anomaly. After laying down some conclusions about the structure of such process, we propose a multi-modal and non-monotonic logical framework able to represent some key aspects of this important facet of the dynamics of scientific theories. Due to the necessity of accommodating incompatible tentative hypotheses, this framework incorporates a weak form of paraconsistency. As a case study, we analyze the anomalous behaviour of the planet Uranus that threatened the Newtonian celestial mechanics for more than half a century and gave rise to the discovery of Neptune. (shrink)

‘Poor Borelli!’ exclaimed Alexandre Koyre at the end of his wonderful and by now classic study of Borelli's ‘celestial mechanics’. Koyre frankly admitted that Borelli lacked Newton's genius and intellectual audacity. However, in his story Borelli deserved a place between Kepler and Newton for his ‘imperfect but decisive’ unification of terrestrial and celestial physics. This framework finds a powerful justification in Borelli's extensive usage of Keplerian astronomy and in Newton's references to Borelli's work on the Medicean planets, Theoricae (...) mediceorum planetarum , both in his correspondence with Edmond Halley, with regard to a controversy with Robert Hooke, and in Philosophiae naturalis principia mathematica . Newton's own copy of Borelli's work with signs of his reading – the famous dog-earings – is preserved in the library of Trinity College, Cambridge. The magnitude of Newton's achievement has haunted Borelli's work ever since Principia mathematica appeared in print. For example, although Christiaan Huygens was sent a copy of Borelli's book by Prince Leopold in 1666, his marginal annotations in his own copy of the book were written after he had read Newton's masterpiece, as if Huygens had felt the need to read the book again after 1687. From then onwards Borelli's work has almost inevitably appeared in a new light that has coloured its subsequent readings.My ambition in this paper is to provide a fresh reading of Borelli's work by reconstructing its circumstances of composition, establishing a comparison with a relevant strictly contemporary source, and attending to the immediate reception of Theoricae. Borelli's work was written with an eye to a composite audience including Roman Jesuits, Sicilian intellectual circles and Leopold de' Medici's correspondents across the Alps, such as the Copernican astronomer Ismael Boulliau in Paris. Borelli was aware that his Sicilian readers were likely to have different concerns from those of Roman Jesuits or the Medici. Thus the task of charting the reception of his work is a formidable one. For a variety of reasons, including availability of sources, limitations of space, taste and competence, my analysis of Borelli's work on the Medicean planets is limited to a few themes and is not only no less partial than Koyre's, but in many respects it relies on it. If readers feel stimulated to re-read Koyre's text, one of the aims of this paper will have been fulfilled. (shrink)

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 Galilei invariance of classical dynamics does not automatically imply the third Newtonian axiom and the center of mass theorem. For the deduction of these theorems from Galilei invariance we must have, generally, a “kinematical potential” (Helmholtz) and a “potential function” (Clausius), respectively. In celestial mechanics it is possible to have conservation of the motion of the center of gravity but not of the mass center. In this case, the active and the passive masses are different quantities.

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)

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)

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)

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)

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)

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.

One of the distinctive features of George Smith’s work on celestial mechanics is his emphasis on the role of what he calls “second-order phenomena” in the production of high-quality evidence. On Smith’s view, these gaps between theoretical predictions and observations can, under certain circumstances, be a source of evidence far stronger than that achievable through the hypothetico-deductive method. The practice of examining gaps between predictions and observations for the purposes of discovery and testing is commonplace in certain sciences such (...) as seismology, and has played an important role in their development. I use the term reasoning from residuals as a general term for this practice. I think it is worth investigating examples of this set of practices from the history of science, in order to understand the different ways in which reasoning from residuals is done, under what situations it is done, and how it contributes to the growth of knowledge in certain sciences. (shrink)

Like a number of other authors, Miller uses the term “emergent” interchangeably with “unpredictable” and employs it as a property term, i.e., in contexts of the form “Event E is emergent.” As we showed in our article, however, predictability and unpredictability as well as emergence are relations; they can be predicated of an event only relatively to some body of information. Thus, a lunar eclipse is predictable by means of information including data on the locations and speeds, at some particular (...) time, of the celestial bodies involved, and the laws of celestial mechanics plus certain principles of optics; it is unpredictable on the basis of, say, alone. Consequently, the phrase “Event E is unpredictable” is incomplete, and hence meaningless, in much the same sense as the expression “Straight line l is parallel.” Similar observations apply to the term “emergent,” which is frequently used to characterize events which, in a sense examined in detail in our article, are not explainable by a micro-structure theory. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:LAW AND THOMISTIC EXEMPLARISM JOHN PETERSON University of Rhode Island Kingston, Rhode Island CIVIL LAW differs from empirical law in that the former prescribes regularities in human action while the latter describes and predicts regularities in the world apart from human action. By an empirical or descriptive law scientists mean a law that is knowable on the basis of observed regularities. An example is Boyle's law. That at a (...) constant temperature the volumes occupied by a constant mass of gas are in inverse ratio to the pressures they support is an observed regularity. This law also describes and predicts a regular occurrence in the world apart from human action. The same is true of Galileo's law that the acceleration of free fall on Earth is thirty-two feet per second per second. But the law that citizens ought to pay taxes in proportion to their incomes prescribes a type of action human beings are obliged to take at regular intervals. A notable difference is that predictability is much lower in the case of civil law than it is in the case of empirical law. You can infallibly predict that the inverse ratio of volumes to pressures in a gas will hold in the next case or that the next free fall will accelerate at thirtytwo feet per second per second. But that your neighbors will pay their fair share of taxes next year is a risky guess. This is part of what it means to say that empirical natural laws are in the world in a way that the laws of society and the state are not. Events, activities, or relationships in the world do not fail to conform to laws whereas actions of citizens often fail to conform to the laws of the state. From empirical laws scientists distinguish theoretical laws. These more general laws are usually called theories or hypotheses. Unlike empirical laws, theories are never generalizations drawn from observations of phenomena. Moreover, theories are often the explanation of empirical laws. So the latter both enter 81 82 JOHN PETERSON into the explanation of a phenomenon and are for their own part explained by theories. Empirical laws are thus both explanans and explanandum as regards phenomena and theories respectively. Thus, Galileo's law of acceleration both enters into the explanation of the particular event of the free fall of this stone at thirty-two feet per second per second and is itself partly explain~d by Newton's laws of motion and his law of gravity.1 But whether or not causal-deductive explanation includes empirical laws that are themselves explained by theoretical laws, all such explanation includes both explanandum and explanans. The former is always some empirical phenomenon. And the latter, as Carl Hempel and Paul Oppenheim point out, is generally made up of two parts, a law or laws and statements of fact or antecedent conditions.2 In the following schema the first two lines comprise the explanans and the last line the explanandum. Thus: C1, C2,..., Cn (statements of conditions) L1, L2,... Ln (laws) E (description of phenomenon to be explained)3 While much causal-deductive explanation in science follows this pattern, not all of it does. For while the explanans must include a law, it need not include a statement that is not a law. For example, Hempel and Oppenheim cite the case in which the regularities that govern the motion of the double stars are explained solely in terms of the laws of celestial mechanics.4 In any case, whether it is the explanandum of a theory or the explanans of a particular observed phenomenon, an empirical law has these three characteristics: first, it is originally based on observations; second, no term in the statement of it fails to occur in the observation statements from which (in the order of knowl1 Carl G. Hempel and Paul Oppenheim, "Studies in the Logic of Explanation," in Janet A. Kourany, ed., Scientific Knowledge: Basic Issues in the Philosophy ofScience (Belmont, Cal.: Wadsworth, 1987), 31. 2 Ibid., 31.·1 Ibid., 32. 4 Ibid., 31. LAW AND THOMISTIC EXEMPLARISM 83 edge) it is based; and third, no values of its variable terms are determined in relation... (shrink)

Neste trabalho, é apresentada uma investigação do que poderia ser chamado de formalização lógica do processo de mudança de teorias devido a anomalias. Por anomalia entende-se um fato observado que faz parte do escopo explanatório de uma teoria, mas que vai de encontro à previsão da mesma. Uma abordagem clássica para restaurar o poder explicativo de uma teoria ameaçada por uma anomalia é a postulação de hipóteses novas e provisórias que, em conjunto com as demais hipóteses auxiliares originais, sejam capazes (...) de resolver a anomalia. Após chegar à algumas conclusões sobre a estrutura de tal processo, propomos um framework lógico multimodal e não-monotônico capaz de representar alguns aspectos-chave dessa faceta importante da dinâmica de teorias científicas. Devido à necessidade de acomodar hipóteses provisórias incompatíveis, esse framework incorpora uma forma fraca de paraconsistência. Como um estudo de caso, analisamos o comportamento anômalo do planeta Urano que ameaçou a mecânica celeste Newtoniana por mais de meio século e ensejou a descoberta do planeta Netuno. -/- In this work, an investigation of what could be called the logical formalization of the theory change process due to anomalies is presented. An anomaly is understood as an observed fact that is part of the explanatory scope of a theory, but that goes against its prediction. A classic approach to restoring the explanatory power of a theory threatened by an anomaly is to postulate new and provisional hypotheses that, together with the other original auxiliary hypotheses, are capable of resolving the anomaly. After reaching some conclusions about the structure of such a process, we propose a multimodal and non-monotonic logical framework capable of representing some key aspects of this important facet of the dynamics of scientific theories. Due to the need to accommodate incompatible provisional hypotheses, this framework incorporates a weak form of paraconsistency. As a case study, we analyze the anomalous behavior of the planet Uranus that threatened Newtonian celestial mechanics for more than half a century and prompted the discovery of the planet Neptune. (shrink)

Ecology shows that living beings, with all their diversity, make up a homogenous system on the earth's surface, with rules that are no less exacting than those applicable to gravitational astronomy (celestial mechanics). The physical energy coming from the sun in the form of radiation is attracted by green plant-life, be it vegetation growing on the land or microscopic algae floating on the surface of the ocean; this energy is then transformed into chemical energy, with, incidentally, a modest yield, (...) due to the process of chlorophyllian synthesis. This stage is the only one to include a productive process—an anabolism. Other sorts of living beings derive their energy and the elements necessary for their sustenance and multiplication from organic matter devised in this way. Some vegetarian animals feed on them and are in their turn prey to predators which are themselves devoured by other predators. Food chains, grouped in bunches or network systems, are thus established on the principle of a complex pyramid. Each consumer occupies a place at a trophic level, which is clearly defined, where he guarantees the conveyance of matter and energy which are degraded in accordance with the laws of thermodynamics. These biological mechanisms entail numerous species, ranging from the most elementary forms of life to birds and mammals. Decomposition agents then recycle the mineral elements and make them available to plants. In any given area, the inert chemical elements and the community of living beings (embracing all species) together constitute a biological entity or ecosystem, this is a kind of supraspecific organism which functions with a certain flexibility, and yet is ordered down to the last detail. Just as a man consists of a heart, lungs, a liver, so a natural community consists of “organs” which are each made up of one of the various constituent species. These ecosystems are the fundamental units of the living world and they are relatively independent of one another, although exchanges do occur between them. They all come together to form a balanced system which encompasses the whole complex of living beings. This is the biosphere, a gigantic mechanism with innumerable cogs and gears which have evolved in harmony with each other throughout the whole of history, going as far back as the first trace of life on earth. (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)

The artistic work of photographer Gudio Baselgia focuses on landscapes formed by nature s forces and, more recently, on the sky with the stellar and solar movements and phenomena as we see them from earth. Celestial mechanics have fascinated mankind in all known cultures, the Babylonians and ancient Egyptians as well as the Greek and Celts, the Maya, or the ancient Indians and Chinese. Until the present day we look at the sky and keep being amazed, and try to (...) read what it tells us. Many artists throughout history have been captivated by the spectacle we observe above us day and night. The modern term astrodynamics describes all movements of celestial bodies, in particular the solar system including the moon and other satellites, asteroids and comets, but also movements of stars within a stellar system or galaxy, or of galaxies towards each other. They are well understood today and depicted in coordinate systems and elaborate visualizations. Guido Baselgia s artistic project on astrodynamics and celestial phenomena has no scientific or didactic ambition. His analogue camera is used as a recorder inscribing the movement of stars on the light-sensitive surface of photographic paper. Thus Baselgia s images make traceable the trajectory of celestial bodies invisible to the human eye and show us astounding occurrences of light and shadow. Baselgia has been captivated in particular also by the phenomenon of the umbra, planet earth s shadow thrown into space. It becomes visible occasionally on a clear evening at sunset when a slight mist lies at the horizon: looking in opposite direction to the sun, a dark and sharply marked band of shadow can be seen rising while sun sets behind the observer. But also by recording sunrise and sunset at the polar circle or the tropic, Baselgia visualizes the geometry of celestial mechanics and the concurrence of forces, as well as the miracle of light as such that leaves us awestruck today as much as it did our ancestors. The new book "Guido Baselgia Light Fall" presents 80 outstanding black-and-white images from the artist s Light Fall project taken in Norway, the Tierra del Fuego archipelago in Argentina, in Ecuador, and the Swiss Alps. The brilliant tritone plates are complemented with essays by the German scholar Andrea Gnam and Swiss photography critic Nadine Olonetzky. ". (shrink)

Although Aristotle’s Metaphysics received much attention in the nineteenth and the twentieth centuries, scholars and historians of science were not particularly interested in clarifying the aim of Aristotle’s appeal to astronomy in Λ 8. Read with monotheistic prejudices, this chapter was quickly abandoned by Aristotelian scholars as a gratuitous insertion, which downgrades Aristotle’s God for the sake of some supplementary principles, whose existence was dictated by celestial mechanics. On the other hand, historians of astronomy read the astronomical excursus as (...) providing a picture of Aristotle as an able astronomer, who made an important contribution to the theory of concentric celestial spheres of Eudoxus and Callippus by adding the counteracting spheres. The present article argues (a) that Aristotle purposefully turned to astronomy as the only mathematical science whose objects were correlative to the immaterial first substances or gods, the number of which had to be precisely determined by his own project of first philosophy; and (b) that he had no aspiration of improving the astronomical theory of his peers, contrary to an interpretation that first emerged with the Peripatetic exegete Sosigenes in the second century A.D. (shrink)

ABSTRACT Greek historical accounts of ancient eclipses were an important, if peculiar, focus of scientific attention in the nineteenth century. Victorian-era astronomers tried to correct the classical histories using scientific methods, then used those histories as data with which to calibrate their lunar theories, then rejected the histories as having any relevance at all. The specific dating of these eclipses—apparently a simple exercise in celestial mechanics—became bound up with tensions between scientific and humanistic approaches to the past as well (...) as with wider social debates over the power and authority of science in general. The major figures discussed here, including G. B. Airy, Simon Newcomb, and T. H. Huxley, argued that the critical question was whether science could speak authoritatively about the past. To them, the ability of science to talk about the past indicated its power to talk about the future; it was also the fulcrum of fierce boundary disputes among science, history, and religion. (shrink)