With the introduction of Greco-Islamic science and natural philosophy, medieval natural philosophers were confronted with three distinct astronomical systems: Aristotelian, Ptolemaic, and the system of al-Bitruji. A fundamental problem that each had to confront was how to explain simultaneous contrary motions in the heavens -for example, the sun's motion, which moves east to west with a daily motion while simultaneously moving west to east along the ecliptic- within an Aristotelian physical system that assumed that a simple body could (...) have only one proper motion. How medieval natural philosophers resolved this problem is the focus of the article. (shrink)

For Averroes, celestial circulation is evidence of a divinely mandated rational universe. This paper follows Averroes’ account on cosmic contact between the eternal and the temporal, in Tahafūt al-tahafūt contra al-Ghazālī. It argues that the polemical perspective of the Tahafūt al-tahafūt frames Averroes’ appeal to Aristotle’s account of cosmic motion. Consequently, Averroes’ exceptional account of the universe contrasts Aristotle’s exemplary account of the mutual participation of intellect and nature. Their accounts of celestial circulation implicate the status of (...) human nature conditioned by cosmic nature. As such, the possibility of human freedom rests on the nature of causality between divine intellect and cosmic manifestation. The convergence and divergence of Aristotle and Averroes regarding celestial circulation reveals Averroes’ politics that guide a rational argument for a strong cosmic causal connection between the unmoved mover and the universe, against al-Ghazālī’s rationally inaccessible divine will. (shrink)

In developing his theory of aether in De Caelo 1, Aristotle argues, in DC 1.4, that one circular motion cannot be contrary to another. In this paper, I discuss how Aristotle can maintain this position and accept the existence of celestial spheres that rotate in contrary directions, as he does in his revision of the Eudoxan theory in Metaphysics 12.8.

In Meta. Λ 8, Aristotle argues that the heaven –and, thus, the cosmos – is numerically unique on the grounds that its first unmoved mover is numerically unique. The latter is numerically unique because it is ‘essence’ and does not have matter. “But whatever is many in number has matter.” I refer to this inference as Aristotle’s metaphysical argument for the uniqueness of the cosmos. A problem arises: If the subsidiary unmoved movers of the planetary spheres are, like the prime (...) unmoved mover, immaterial substances and belong to the same species of unmoved mover, it seems that they could not be numerically distinct from that first unmoved mover – while Aristotle maintains that they are, in fact, numerically distinct. That is, as immaterial substance, it/they could not be individuated by matter. However, if they do, as souls or soul-like forms, inform matter, it seems that there is no reason why the first unmoved mover, which moves the sphere of fixed stars or outermost, celestial sphere, should not similarly inform the matter of that celestial sphere. In the latter case, Aristotle’s argument for the uniqueness of the heaven and cosmos would be vitiated. The first unmoved mover would be the form of the outermost celestial sphere; and there would evidently be no metaphysical reason why that form could not be materially instantiated by other outermost celestial spheres, each enclosing its own cosmos distinct from our own. I argue that neither of the two salient options for resolving this problem with Aristotle’s metaphysical argument for the uniqueness of the cosmos is satisfactory. The result, so I maintain, is Aristotle’s diremption of divinity into two essentially unrelated aspects: divinity as autonomous, ‘hermetic’ cognition and divinity as ultimate cause of cosmic motion and change. (shrink)

Plato's Tim. 90b1-c6 describes a pathway to the soul's salvation via the study of the heavens. This paper poses three questions about this theme in Platonism: 1. The epistemological question: How is the paradigmatic function of the visible heavenly bodies to be reconciled with various Platonic misgivings about the faculty of perception? 2. The metaphysical question: How can »assimilation« to the motions of bodies in the realm of Becoming provide for the salvation of souls when souls are »higher«- a mid-point (...) between Being and Becoming? 3. The psychological question: What can it mean for an incorporeal soul to utilise the motions of a body for an ethical and cognitive paradigm? And provides an account of how Proclus and some of his fellow Neoplatonists answered these questions. (shrink)

This richly detailed biography captures both the personal life and the scientific career of Isaac Newton, presenting a fully rounded picture of Newton the man, the scientist, the philosopher, the theologian, and the public figure. Professor Westall treats all aspects of Newton's career, but his account centers on a full description of Newton's achievements in science. Thus the core of the work describes the development of the calculus, the experimentation that altered the direction of the science of optics, and especially (...) the investigations in celestial dynamics that led to the law of universal gravitation. (shrink)

Here I reexamine Duhem's question of the continuity between medieval dynamics and early modern conservation theories. I concentrate on the heavens. For Aristotle, the motions of the heavens are eternally constant (and thus mathematizable) because an eternally constant divine Reason is their mover. Duhem thought that impetus and conservation theories, by extending sublunar mechanics to the heavens, made a divine renewer of motion redundant. By contrast, I show how Descartes derives his law of conservation by extending Aristotelian celestial (...) dynamics to the earth. Descartes argues that motion is intrinsically linear, not circular. But he agrees that motion is mathematically intelligible only where divine Reason moves bodies in a constant and eternal motion. Descartes strips bodies of active powers, leaving God as the only natural mover; thus both celestial and sublunar motions are constant, and uniformly mathematizable. The law of conservation of the total quantity of motion is an attempt to harmonize the constancy derived a priori with the phenomenal inconstancy of sublunar motions. (shrink)

By defending the following views – that Aristotle identifies the generator and perhaps the obstacle remover as an essential cause of the natural sublunary elemental motion in Physics VIII 4; that this view is consistent with the view of Physics II 1 that the sublunary simple bodies have a principle of internal motion; and that the sublunary and the celestial elements have a nature in the very same way – I shall offer what has so far eluded (...) Aristotelian commentators: a consistent interpretation of Aristotle's theory of the natural motions of the sublunary and also the celestial elements. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:ST. THOMAS ON ANGELIC TIME AND MOTION J. J. MACINTOSH University ofCalgary Calgary, Alberta, Canada A. THOMAS'S STANDARD DOCTRINE: THE NEED FOR ASINGLE TIME. T HERE IS an under-discussed problem about time for St. Thomas. Most discussions of his views on time center around either the question of God's foreknowledge or around the notions of eternity and aeviternity. Even those discussions which deal directly with Thomas's views on (...) time ignore the issue I wish to discuss here.' The problem is this: St. Thomas held both that there is a single time, created by God, and that there are three distinct times: two for the angels, and one for the rest of creation. Moreover, he seems, fairly explicitly, to have been unwilling to adopt either of the obvious ways out of this apparent contradiction. Thomas believed, and often said, that time is unitary, and typically offered an Aristotelian reason for the claim: "the true reason why time is one, is to be found in the oneness of the first movement by which, since it is most simple, all other movements are measured. Therefore time is referred to that movement, not only as a measure is to the thing measured, but also as accident 1 See, for example, Piero Ariotti, "Celestial reductionism of time: on the scholastic conception of time from Albert the great and Thomas Aquinas to the end of the 16th century," Studia Internationale Filosofia 4 (1972): 91-120, and Antonio Moreno, "Time and Relativity: Some Philosophical Considerations," The Thomist 45 (1981): 62-79. I have referred to this problem earlier in "Time and St. Thomas" (in To Myselffrom Others, ed. David Miller [Warwick: University of Warwick, 1989)), and in "Aquinas, Ockham, and Prior (and the unexpected examination),'' Auckland Philosophy Papers, no. 1 (1990). 547 548 J. J. MACINTOSH is to subject; and thus receives unity from it."2 Moreover, such a doctrine is necessary if what he tells us about the foreknowledge of God, and God's inability to change the past,3 not to mention his views on the knowledge that angels and demons have of what is genuinely future, is to be correct. Briefly, those views commit him to a view of a single time that is linear past, and is nonbranching future as well.4 There is some exegetical question as to whether or not his views on time, contingency, and freedom led him to adopt a truth-gap account of genuinely future tense contingent propositions, but that the singleness of time is required has not been questioned.5 This is not the place to deal with the difficulties Aquinas faced concerning God's foreknowledge, but a brief introductory word is in order to show how central the singleness of time is for his thought in this area. Since all past- and present-tense truths have necessity per accidens (that is, they concern matters which are now irrevocable), the class of contingent truths is a proper subset of genuinely future-tense claims. A proper subset because 2 Summa Theologiae, I, q. 10, a. 6 c (hereafter cited as sn; English translation by the Fathers of the English Dominican Province, 5 vols., (1920; reprint, Westminster, Maryland: Christian Classics, 1981). This is the translation I have standardly used, sometimes with slight changes, but I have also made use of the translation by the Blackfriars (61 vols. [London: Blackfriars, in conjunction with Eyre and Spottiswood, 1964-81], hereafter cited as Blackfriars). 3 Thus, for example, "God can make the existence of an angel not future; but He cannot cause him not to be while he is, or not to have been, after he has been" (ST I, q. 10, a. 5, ad 3). 4 By contrast, Ockham, for example, adopted an implicit tense logic with branching future possibilities. As far as I know, no mediaeval thinker allowed branching pasts. For a discussion of that possibility, see John Mackie, Truth, Probability and Paradox: Studies in Philosophical Logic (Oxford: Clarendon Press, 1973). For a helpful general discussion of the issues involved, see R. Thomason, "Combinations of Tense and Modality," in D. Gabbay and D. Guenthner, eds., Handbook of Philosophical Logic, 3 vols. (Dordrecht: D. Reidel, 1984), 2... (shrink)

Astronomers have always considered the motion of the Moon as highly complicated, and this motion is decisive in determining the circumstances of such critical celestial phenomena as eclipses. Table-makers devoted much ingenuity in trying to find ways to present it in tabular form. In the late Middle Ages, double argument tables provided a smart and compact solution to address this problem satisfactorily, and many tables of this kind were compiled by both Christian and Jewish astronomers. This paper (...) presents multiple examples of the diversity of approaches adopted by compilers of tables who used this powerful tool, and brings to light intellectual interactions among them that are otherwise hidden from view. (shrink)

The Timaeus is the dialogue that was for many centuries the most influential of Plato’s works. Among its readers we find Descartes, Boyle, Kepler and Heisenberg. In the first division of Timaeus Plato deals with the theory of celestial motion, in the second he presents us with the first mathematical theory of the structure of matter. Here, in a gigantic step forward with respect to the preceding Democritean atomistic theory with its unalterable micro-entities, he introduces the intertransformability of (...) elementary corpuscles and with that the first “chemical” reactions in history. Plato’s geometrical interpretation of Empedocles’ elements and his geometrical atomism is described at the molecular, atomic and sub-atomic level. The “chemical” reactions reported in Timaeus are written in the enlightening chemical symbolism, analogies with modern chemistry are noticed throughout. (shrink)

I argue that scientific and poetic modes of objectivity are perspectival duals: 'views' from and onto basic natural forces, respectively. I ground this analysis in a general account of objectivity, not in terms of either 'universal' or 'inter-subjective' validity, but as receptivity to basic features of reality. Contra traditionalists, bare truth, factual knowledge, and universally valid representation are not inherently valuable. But modern critics who focus primarily on the self-expressive aspect of science are also wrong to claim that our knowledge (...) is or should be ultimately mediated by ourselves. In objective science, we represent nature as a field of phenomena determined by and within explanatorily-basic physical structures that encode the causal impact of elemental physical forces. These causally-basic forces hence ground the possibility of objective scientific theory, even though (I argue) they are systematically excluded from its representational contents. I show how my notions of force and field emerge partly through my effort to naturalize concepts of 'God' and 'Laws' in 17th-century natural philosophy. In science, we use the structure of basic forces' impact to see corresponding objects. We do not see these forces themselves—and this relates to the 'transcendence' of 'God'. I supplement this historical analysis by critiquing standard accounts of objectivity, and by synthesizing elements from neo-Kantian epistemology and current 'structural' realism into a view that I call 'dynamic structuralism'. Finally, I argue that physics systematically relies on passive characterizations of phenomena like inertia and impressed force. Dynamic alternatives that are just as empirically adequate are possible, but they are non-scientific. Poetic objectivity involves a direct presentation of nature as an order of interacting forces. I elaborate first by developing a novel theory of the relation between beauty and sublimity, mediated by a basic category of 'sensory force' (e.g. a 'singing' tone in a beautiful melody). I then describe the interaction between sensory and affective dimensions of aesthetic experience, in relation to an original historical analysis of passion and 'disinterestedness' in Kant, Schiller and Nietzsche. I synthesize these lines of analysis into a critique of the role of 'expression' in art. I also resist 'spectator'-centric aesthetics, in this connection, by developing an account of artistic objectivity in dialogue with Ruskin's critique of the 'pathetic fallacy'. I contrast artistic objectivity with Romantic ideals of self-expression, while elaborating its positive relation to certain currents within Victorian and Modernist aesthetics, including Imagists' stress on 'exteriority'. My project creatively extends Nietzsche's view that philosophical and scientific theories are 'perspectival' expressions of theorists' drives. It is a virtue of Nietzsche's account that he takes the outlet of strong human drives in creative acts of theorizing to be just one among many higher modes of 'will to power' in nature—many of which are totally impersonal. But Nietzsche is still too focused on self-expression or willing one's own power. Objective science involves external forces' 'expression' in and through us, not just 'expressing' our own powers. And Nietzsche's vitalistic 'will to power' must be replaced by a basic ontology that better accommodates inorganic phenomena, like the 'lawful' order of celestial motions. Thus I aim to de-anthropomorphize and 'de-organicize' post-Kantian notions of willful striving and organic development, while preserving for force the primary ontological and evaluative status that theorists from Schiller and Goethe to Schelling and Schlegel to Emerson and Nietzsche attributed to will or to life. (shrink)

This is the first volume compiling English translations of Leibniz's journal articles on natural philosophy, presenting a selection of 26 articles, only three of which have appeared before in English translation. It also includes in full Leibniz's public controversies with De Catelan, Papin, and Hartsoeker. The articles include work in optics, on the fracture strength of materials, and on motion in a resisting medium, and Leibniz's pioneering applications of his calculus to these issues by construing them as mini-max and (...) inverse tangent problems. Other topics covered by the articles include: criticisms of the Cartesian estimate of motive force and Leibniz's proposal of a different way of estimating force to replace it; a proposed theory of celestial motions and gravitation, and derivation of the inverse square law; challenge problems concerning the isochronous curve and the catenary; a sample of work on gaming theory; and Leibniz's critique of atomism. (shrink)

Pierre Gassendi is widely known as a reviver of Epicurean atomism. But he was also regarded as an accomplished astronomer by his contemporaries. Along with the life-long observational pursuits, Gassendi developed his theories of the causes underlying celestial motions. In elaborating them, he absorbed seveal ideas coming from the astronomy of Johannes Kepler. Moreover, Gassendi went further to incorporate some theological principles from the Keplerian cosmology, especially the idea that God is a Geometer. The present paper thus explores Kepler's (...) influence on the philosophy of Gassendi in both astronomical and theological spheres. (shrink)

: In earlier work, Bernard R. Goldstein and the present author have introduced a procedural rule for historical inquiry, which requires that one take pains to establish the credibility of any citation of ancient thought by later writers in antiquity through a process of verification. In this paper, I shall apply what I call the Rule of Ancient Citations to Simplicius' interpretation of Aristotle's remarks in Meta L. 8, which is the primary point of departure for the modern understanding of (...) Greek planetary theory. I first sketch several lines of argument that lead me to conclude that Simplicius' interpretation should not be accepted because it assumes a concern with planetary phenomena unknown to the Greeks before the late 2nd and early 1st centuries BC. Then, after showing that there is a fairly well defined range of readings of Aristotle's remarks more in keeping with what we actually know of astronomy in the 5th and 4th centuries BC, I conclude that neither Aristotle's report about the Eudoxan and Callippan accounts of the celestial motions nor Simplicius' interpretation of this report is a good starting point for our understanding of early Greek planetary theory. (shrink)

Clock time involves two motions, one of which can be easily counted, such as the movement of one of the hands around the face of a watch or the movement of sand from one part of a timer to another. The repetition and regularity of such motions make them easy to number. They can be made to keep on repeating themselves, each can easily be taken as the same as any other, and we can easily tell that there have been (...) "three" or "eight" of them. At one time the primary instance of clocking motions were the movements of the sun, moon, and stars, but the precision of our clocks has made these celestial motions recede into the background in our handling of time. Six A.M. or seven P.M., 600 hours or 1900 hours, are more prominent for us than sunrise and sunset; we say that the sun rises at 600 hours and sets at 1900, as though the rising and setting were placed against a process more fundamental than these solar events. But of course our clocks still run against the pattern of the sun, moon, and stars, and many of the standard sums we reckon with in clock time are defined by the less accurate but larger wholes, the days, months, and years, that the movements of the heavens provide. (shrink)

This paper argues for a different interpretation of Roberval’s scepticism in his Aristarchi Samii de mundi systemate. Roberval’s mild sceptical attitude, along with his fake attribution of hiscosmological treatise to the ancient Aristarchus of Samos, are explained by prudential reasons related to censure. I will instead provide a more internalist reading. There are deeper metaphysical and epistemological reasons for Roberval’s pessimism about the prospect of a perfect science of celestial motions, as well as for his (non-realistic) acceptance of heliocentrism (...) as just a more plausible system than Ptolemy’s or Tycho’s. I start by spelling out two distinct sceptical worries conflated in the Aristarchi. The first is a general agnosticism regarding certainty about the causes of the motions of the heavens—it is more of a worry that the true system of the world can never be known. The second is a particular pessimism regarding the prospects of improving astronomy. The same effect (the apparent motions of the heavenly bodies) can be produced by diverse causes. Judging by what seemed to be the most probable physical causes of the heavenly motions, Roberval saw no reason for the existence of a precisely predictable regularity in heavenly motions. Both sceptical attitudes have to do, aside from the cosmology of the Aristarchi, with the theory of science he expounds in his private Principes du debvoir et des cognoissances humaine, and in a fragment he wrote for Mersenne’s Curiouse perspective de Niceron. (shrink)

In Ennead II.1 (40) Plotinus is primarily concerned to argue for the everlastingness of the universe, the heavens, and the heavenly bodies as individual substances. Here he must grapple both with the philosophical issue of personal identity through time and with the rich tradition of cosmology which pitted the Platonists against the Aristotelians and Stoics. What results is a historically informed cosmological sketch explaining the constitution of the heavens as well as sublunar and celestial motion. This book contains (...) an extensive introduction aimed at providing the necessary background in Platonic, Aristotelian, and Stoic cosmology, the text itself, and a line-by-line commentary designed to elucidate its philosophical, philological and historical details. (shrink)

Leibniz's dispute with Newton over the physico-mathematical theories expounded in the Principia Mathematica have long been identified as a crucial episode in the history of science. Dr. Bertoloni Meli examines several hitherto unpublished manuscripts in Leibniz's own hand illustrating his first reading of and reaction to Newton's Principia. Six of the most important manuscripts are here edited for the first time. Contrary to Leibniz's own claims, this new evidence shows that he had studied Newton's masterpiece before publishing An Essay on (...) the Causes of Celestial Motions. This article, representing his response to Newton, is included here in English translation. Dr. Bertoloni Meli analyses the important implications of this episode on a variety of themes ranging from priority claims to the mathematization of nature in the seventeenth century. Besides providing a careful study of Leibniz's style and strategy, the author examines how our perception of Newton's achievement is affected and the reception of the rival theories by the mathematical community around 1700. "Bertoloni's book provides a very detailed and deep analysis of Leibniz's calculus and dynamics by focusing on a consistent and important set of previously unknown manuscripts..." Niccolo Guicciardini, Universita de Bologna "...Equivalence and Priority is a major contribution to our understanding of the development of mathematical physics in the late seventeenth and early eighteenth century." Daniel Garber, University of Chigago. (shrink)

Chaos, once considered antithetical to scientific law and order, is presently the subject of a vigorous and progressive scientific research program. "Chaos" as it is used in current scientific literature is a technical term: it refers to stochastic behavior generated by deterministic systems. This behavior has appeared in models of a wide range of phenomena including atmospheric patterns, population dynamics, celestial motion, heartbeat rhythms, turbulent fluids, chemical reactions and social structures. In general, chaos arises in the nonlinear dynamics (...) of complex systems. Grebogi, Ott and Yorke reflect the sentiment of the scientific community when they state that chaotic nonlinear dynamics has "fundamental implications." This dissertation explores these results in a philosophic context. ;The research is organized as follows: The Context of Science. Scientific results are achieved in and make sense in the practical context of research which includes both experiment and theory. Drawing on the work of Dyke, Galison, Garfinkel and Hacking, a philosophic context is described which more accurately reflects the significance of scientific results than do the contexts of discovery and justification. Models. Chaos theory is constituted by a family of numerical models. In this chapter, Giere's account of modeling is extended to both bio-medical and numerical models. Chaos in Scientific Models. This is a rather lengthy primer of chaos theory that is, although technically accurate, accessible to nonspecialists. It constitutes a road map for the primary literature on chaos. Chaos and Prediction. Chaos theory shows a limit of our science, namely, chaotic systems are deterministic yet unpredictable in the long run. The chapter includes a discussion of scientific determinism following Popper and, it concludes by providing evidence against the laplacian claim that deterministic systems are predictable. Chaos and Complexity. This shows what contribution chaos theory makes toward answering the challenge of organized complexity articulated by Weaver. It discusses attempts to characterize complexity and shows how the results of chaos theory can help. I draw on the work of Abraham, Arecchi, Atlan, Chaitin, Eckmann, Peacocke, Rosen, Ruelle, and others. Chaos theory provides a thoroughly nonvitalistic framework for understanding dynamical complexity in organic, as well as inorganic, systems. (shrink)

Summary The Almagest of Ptolemy (mid-second century ad) contains eleven dated reports of observations of the positions of planets made during the third century bc in Babylon and Hellenistic Egypt. The present paper investigates the character, purpose, and conventions of the observational programmes from which these reports derive, the channels of their transmission to Ptolemy's time, and the fidelity of Ptolemy's presentation of them. Like the Babylonian observational programme, about which we have considerable knowledge through cuneiform documents, the Greco-Egyptian ones (...) were not directed towards the deduction of mathematical models of celestial motion but appear to have investigated patterns, correlations, and periodicities of phenomena. Ptolemy's immediate sources most likely were not the original series of observational records, but treatises by various astronomers of the intervening four centuries, including Hipparchus. While Ptolemy does not appear to have tampered with the wording of the reports, he faced difficulties and uncertainties in interpreting them; critically, he lacked sufficiently detailed information about the ancient calendars to be able to convert the reported dates accurately into his own chronological framework based on the Egyptian calendar. (shrink)

Aristotelian cosmology implies the plurality of celestial motion for the process of generation and corruption in the sublunar world. In order to investigate the structure of the cosmos and the degree of dependence of the sublunar on the supralunar region, medieval Latin commentators on Aristotle explored the consequences of the cessation of celestial motion. This paper analyses the position of some philosophers of the fourteenth-century Parisian school, namely Nicole Oresme, John Buridan and Albert of Saxony.

Suárez's discussion of time in the Metaphysical Disputations is one of the earliest long treatises on time (extending over sixty pages), and includes detailed arguments supporting the view that physical actions take place within an absolute temporal reference frame. Whereas some previous thinkers, such as John Duns Scotus and Peter Aureole, had made tantalising suggestions that time exists independently of physical changes, their ideas were primarily negative theses in response to perceived problems with the dominant view that time was caused (...) by the celestial motion. Suárez, in contrast, provides a positive thesis based on his revision of traditional, Scholastic metaphysics. He argues that the ordering of earlier and later events can only be understood by conceiving events as existing within the embrace of a ?flowing and successive space? which he refers to as ?entirely necessary and immutable in its own flux? (omnino necessarium et immutabile in suo fluxu) - something at least very like an absolute temporal reference frame. Yet it would be simplistic to describe Suárez's work on time only in terms of its nascent absolutism, since for him there is a second kind of time, a more properly ?real? time, which is an accident of material being. This kind of time is ontologically tied to the most intimate existence of objects, creating a plurality of individual continua of time - one for each distinct being. He calls this kind of time ?intrinsic time? (tempus intrinsecum). Suárez's dualistic account of time, in which he proposes an ?intrinsic time?, linked to being, which exists within a second order absolute temporal reference frame, or ?imaginary succession?, forms a bridge between scholasticism and early modern philosophy providing a foundation for the work of later absolutists like Gassendi and Newton. (shrink)

This book continues the classical Newtonian theory in both its initial spirit and the spirit of general relativity. It throws a bridge between classical Newtonian theory of forces and some contemporary concepts of the atomic, nuclear and particle theories. This book takes the Skyrme theory of nuclear matter mainly from the point of view that it allows the initial analogy between the atomic edifice and the solar system in all details. Especially important is the detail that the atomic nucleus works (...) exactly like the Sun, and they can be described in the same way. Based on this unitary description, the authors go further on, in showing that the Skyrme theory is the only theory naturally suited for the explanation of structure of nuclear matter. Thus it should be actually a classical theory, inasmuch as it simply carries over into microcosmos the very Newtonian theory of forces extracted from the planetary Keplerian synthesis of celestial motions. By this the problem of structure of the nucleus becomes actually a problem of classical physics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.1 (2003) 128-129 [Access article in PDF] Robert Crocker, editor. Religion, Reason and Nature in Early Modern Europe. Dordrecht: Kluwer, 2001. Pp. xix + 228. Cloth, $77.00. By describing the early modern period as such, we thereby avow a continuity with it that ill squares with the following, insufficiently appreciated fact. The early modern counterparts of the largely atheistic American Philosophical Association, let's (...) say, were to an even greater degree theistic, and, moreover, theism affected their description and explanation of the world in a profound way—certainly more so than it does their few theistic descendents. This is true even of authors, like Hobbes and Spinoza, who might be read as leading to later atheism. The fact of early modern theism and its centrality in early modern philosophy and science are amply demonstrated in one after another of the eleven essays of this book.An emblematic figure is Robert Boyle, who figures as a main player in three of the essays, and is at least mentioned in five of the others. Lotte Mulligan, for example, investigates the role of "right reason" in Boyle's argument that religion is illuminated and made [End Page 128] plausible by metaphorically expressed analogies with natural philosophy, and conversely. The upshot is that only the "Christian Virtuoso," endowed with right reason whereby he is inspired to notice and express these analogies, was in a position to interpret the codes expressed both in the book of revelation and in the book of nature, one being incomplete without the other.Luisa Simonutti treats Boyle's engagement with the theological and scientific work of Spinoza through Spinoza's correspondence with Oldenburg. And G. A. J. Rogers deploys the work of Boyle, as well as of Locke, Newton, and the Cambridge Platonists, against the once-standard view (vide Butterfield) that "a major feature of the seventeenth-century was a secularization of knowledge." (Given just the other papers in this volume, this may seem like shooting fish in a barrel. Even so, perhaps one or two of the shots appear to miss. Newton seems proleptically to answer Hume's skepticism about induction by invoking, not divine simplicity, but an argument to the best explanation.)These papers overlap with two others, forming the core of the book. Sarah Hutton and Robert Crocker take on Cambridge Platonism. The former deals with Ralph Cudworth's rejection of Cartesian voluntarism in favor of an intellectualism of goodness and wisdom that grounds both the providential governance of the world and its intelligibility to human inquiry. The latter deals with Henry More's doctrine of the soul's pre-existence, a prima facie unlikely doctrine, but one that is less problematic, according to More, than the orthodox alternatives (creationism and traducianism).Three other papers fall outside this core, but their topics are no less relevant. Perhaps the most undeniable connection between the natural and the supernatural is to be found in Grotius, here studied by Jacqueline Lagree. Likely the most unexpected player will be the eccentric esprit fort, Cyrano de Bergerac. His work of nearly pure fantasy, in the Rabelaisian tradition, might well have made later, more serious heterodoxies possible. James E. Force provides a nice case study in Newton's reliance on what he took to be providentially guided comets as sources for the replenishment of otherwise declining celestial motion and matter (a line which, ironically, was picked up by Hume as a premise of an argument designed to undo the argument from design). Richard H. Popkin outlines three views of Judaism in the period. There is little connection with nature, but an important one with reason via a problem that exercised Cudworth and Newton: most peoples are polytheistic despite the clear monotheism of revelation. One theory had it that Judaism was the original, pure religion, which degenerated into various forms of paganism. But this degeneracy was soon read by the English deists such that originally there was a natural religion, of which Judaism and all others were a degeneration. Transmitted to the Enlightenment by Spinoza... (shrink)

This little book contains lectures given by Vlastos in the summer of 1972 in the Danz Lectures series of the University of Washington. His theme relates to that often rather paternalistic exercise of plotting out the extent to which Science was Revealed to the Greeks. In his view, "it was not given to them... to grasp the essential genius of the scientific method." However, they did discover "the conception of the cosmos that is presupposed by the idea of natural science (...) and by its practice". This discovery, an intellectual "revolution," was of the view, upheld by the Presocratic physiologoi, that the world is characterized by "unbreachable regularities" which make the world a "cosmos," which "constitute the order of nature and, if known, would yield the ultimate explanation of every natural phenomenon". This was revolutionary since it rejected the traditional belief in an unlimited area of possible divine supernatural intervention in the world, a belief which made perception of the universe a perception of an "irrational universe". Thus, "for the first time in history", man achieved, with Presocratic physiologia, "a perception of a rational universe". In the remaining two chapters of the book, Vlastos examines Plato, represented as a "fierce opponent" of the revolution who appropriated the newly discovered cosmos, refashioning it "on the pattern of his own idealistic and theistic metaphysics". This interpretation of Plato is developed mainly through a study of the Timaeus and especially of the "Theory of Celestial Motions" and of the "Theory of the Structure of Matter". Plato appears as opposed to the "impiety" of the physiologoi, proposing himself in the Timaeus a transcendent god as his primary cosmological principle. At the same time, the Timaeus reflects, as Vlastos shows in a brief survey of earlier and contemporary Greek astronomy, an awareness of the "empirical facts" established by the astronomers and Plato’s desire to reconcile these facts with his metaphysical, theological, a priori convictions. This reconciliation involved postulating a system of celestial circular motions, a theory whose "scientific value" Vlastos does not doubt, despite its dependence on a "metaphysical scheme". Vlastos concludes that although Plato fully acknowledged a supernatural power in the universe, he guaranteed the regularities of nature against divine intervention. There is an unfailing natural law. However, its ground for Plato is not natural but supernatural. In examining the "Theory of the Structure of Matter", Vlastos again finds that Plato’s world-order resembles very much that of the physiologoi and, like theirs, is "safe from supernatural interference". The "elementarism" of the Timaeus is shown to be indebted to the Atomists, but also to innovate by opening the way to the intertransformability of elementary corpuscules. What "scientific value" does this theory of the transformation of elements have? It is neither entailed nor contradicted by observation. Vlastos suggests rather that its grounds are "aesthetic". At any rate, Vlastos concludes that although Plato opposed the physiologoi in reintroducing supernatural agency, he annexed their conception of cosmos. In his "perversely original way," he thus "sustained the faith that our world is cosmos. He gave rational men a pious faith to live by in two millennia all through which science was more prophecy than reality". Some of Vlastos’ more extensive footnotes are collected in an Appendix, which is followed by a Bibliography and Indices. (shrink)

The formal study of both astronomy and astrology in later medieval Europe was firmly based in the universities. Instruction in astrology is attested by the presence of an educational board game, known as the ludus astronomorum, in several university-related miscellanies of fifteenth-century English provenance. William Fulke also published an edition of the game a century later , which is attested in a number of Elizabethan libraries. The game serves to rehearse for its players the celestial motions and astrological principles (...) described by Ptolemy. It also employs principles of stellar rays described by al-Kindi in his De radiis stellarum. (shrink)

Distortion of Scientific Terms by Supposed Modernizing Translations: The Example ‘orbis’ (sphere)/‘orbita’ (orbit). The use of modern terminology and thinking hinders to understand historic astronomical and physical texts and often misleads the reader, because between celestial physics from Aristotle and Ptolemy to Copernic on the one side and since Kepler and Newton on the other side a fundamental change of paradigm had taken place. The former started from the assumption that planets are indirectly moved by large equally rotating etherical (...) spheres combined with each other to form every kind of unequally apparent planetary motion as a resultant, whereas the later started from Kepler's idea that every motion of a planet is directly caused by two forces moulding his (naturally unequal) ‘orbit’. ‘orbita’ was Kepler's new specific term for the way of the planet coined in late 1604; in contrast, the Latin term of the elder paradigm has been ‘orbis’ (‘sphere’), on the one hand as concentric ‘orbis totalis’ of a planet (or the fixed stars), on the other hand as non‐concentric ‘orbes particulares’ (of the eccenters and epicycles) within the space of an ‘orbis totalis’. These terms were interpreted and translated in accordance with modern dynamic (as the supposed ‘true’) thinking as if they were ‘orbits’ (German: ‘Bahn’). But you cannot bring the two paradigms into line. As a result, the texts of seemingly ‘modern’ translations become incomprehensible, absurd and wrong. The study shows this on thinking (1st) about Aristotelian physics of former times using terms and ideas of modern dynamics, and on thinking (2nd) about the former explanation of apparent motions of heavenly bodies using these dynamics and ignoring the different special Aristotelian and Ptolemaic physics of ‘orbes’ (spheres). (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)

Aristotle’s theory of human happiness in the Nicomachean Ethics explicitly depends on the claim that contemplation (theôria) is peculiar to human beings, whether it is our function or only part of it. But there is a notorious problem: Aristotle says that divine beings also contemplate. Various solutions have been proposed, but each has difficulties. Drawing on an analysis of what divine contemplation involves according to Aristotle, I identify an assumption common to all of these proposals and argue for rejecting it. (...) This allows a straightforward solution to the problem and there is evidence that Aristotle would have adopted it. (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)

A conservation principles tell us that some quantity, quality, or aspect remains constant through change. Such principles appear already in ancient and medieval natural philosophy. In one important strand of Greek cosmology, the rotatory motion of the celestial orbs is eternal and immutable. In optics, from at least the time of Euclid, the angle of reflection is equal to the angle of incidence when a ray of light is reflected. According to some versions of the medieval impetus theory (...) of motion, impetus remains in a projected body (and the associated motion persists) permanently unless the body is subject to outside interference. These examples could be multiplied. But it was in the seventeenth century that conservation principles began to play an absolutely central role in scientific theories. Each of Galileo Galilei, René Descartes, Christiaan Huygens, Gottfried Leibniz, and Isaac Newton founded his approach to physics upon the principle of inertia—that unless interfered with a body will undergo uniform rectilinear motion. A multitude of other conservation principles gained currency during the seventeenth century—some still with us, some long ago left behind. Descartes provides an interesting example of an author who attempted to derive all of his physical principles from conservation laws (Principles of Philosophy, see especially articles 36 to 42 of Part II). Descartes believed that the principles of his physics could be derived from the immutability of God, supplemented only by very weak assumptions about the existence of change in the world. He claims, in fact, that we ought to postulate the strongest conservation laws consistent with such change. These include. (shrink)

In 1454 Georg Peurbach taught astronomy at the Collegium Civium in Vienna by reading a work of his own: the Theoricae novae planetarum. In 1483 Albert of Brudzewo, teaching astronomy at Cracow University, adopted Peurbach’s text together with a commentariolum of his own. Among the numerous commentaries preserved both in manuscript and in printed form, Brudzewo’s stands out because it submits Peurbach’s work to a subtle analysis that, while recognising the merits for which it was widely accepted, also focuses on (...) the limitations of the celestial spheres described in it. Budzewo’s commentary is of interest, in itself both for its criticism of Peurbach’s descriptions of solar, lunar and planetary theory and also for its importance to Copernicus’s own planetary theory. For Copernicus makes clear in the Commentariolus that his concern was the very same issue, violation of uniform circular motion by the rotation of spheres, that Brudzewo criticises in detail. In this way, Brudzewo’s commentary stands as the original motivation for the investigation of the motion of the planets that was eventually to lead Copernicus to a planetary theory based strictly upon uniform rotation of spheres, and through that investigation to the motion of the Earth and the heliocentric theory. (shrink)

This paper analyses a kinematic model for the solar motion by Quṭb al-Dīn al-Shīrāzī, a thirteenth-century Iranian astronomer at the Marāgha observatory in northwestern Iran. The purpose of this model is to account for the continuous decrease of the obliquity of the ecliptic and the solar eccentricity since the time of Ptolemy. Shīrāzī puts forward different versions of the model in his three major cosmographical works. In the final version, in his Tuḥfa, the mean ecliptic is defined by an (...) eccentric of fixed mean eccentricity and a mean obliquity fixed with respect to the celestial equator, and the center of the epicycle, which is inclined to the eccentric, moves on the eccentric with an annual period. By an additional slow motion of the sun on the epicycle, the true eccentricity of the solar deferent, defined by the annual motion of the sun, and the sun’s extreme declination from the equator change, accounting for the reduction of the eccentricity and the obliquity of the ecliptic since the time of Ptolemy. (shrink)

Between the appearance of Copernicus’ De Revolutionibus in 1543 and the works of Kepler and Galileo that appeared in 1609–10, there were probably no more than a dozen converts to physical heliocentrism. Following Westman we take this list to include Rheticus, Maestlin, Rothmann, Kepler, Bruno, Galileo, Digges, Harriot, de Zúńiga, and Stevin, but we include Gemma Frisius and William Gilbert, and omit Thomas Harriot. In this paper we discuss the reasons this tiny group of true Copernicans give for believing that (...) Copernicus, not Ptolemy or Tycho Brahe, was correct. We conclude that the early followers of Copernicus can be divided into two main groups, designated mathematicians and physicists. Two main arguments appear in the works of the former: first, the relationship between the velocity of a planet and its distance from the center of the world; second, the explanation of retrogradations. Early Copernicans differed on the reality of celestial spheres, and several attempted to reconcile heliocentrism with scripture. The mathematicians continued to accept a traditional definition of the scope of astronomy and the methods of science, both issues challenged by Kepler and Galileo. Hence the work of Copernicus set in motion a train of events that led to a decisive epistemological shift, but did not itself represent such a shift. The real revolution is the replacement of the methods and goals of Ptolemaic astronomy and Aristotelian physics with Copernicanism in its modern form, which incorporates the conceptual structure of Kepler and the astronomical evidence of Galileo. (shrink)

Newton's Philosophiae Naturalis Principia Mathematica provides a coherent and deductive presentation of his discovery of the universal law of gravitation. It is very much more than a demonstration that 'to us it is enough that gravity really does exist and act according to the laws which we have explained and abundantly serves to account for all the motions of the celestial bodies and the sea'. It is important to us as a model of all mathematical physics.Representing a decade's work (...) from a distinguished physicist, this is the first comprehensive analysis of Newton's Principia without recourse to secondary sources. Professor Chandrasekhar analyses some 150 propositions which form a direct chain leading to Newton's formulation of his universal law of gravitation. In each case, Newton's proofs are arranged in a linear sequence of equations and arguments, avoiding the need to unravel the necessarily convoluted style of Newton's connected prose. In almost every case, a modern version of the proofs is given to bring into sharp focus the beauty, clarity, and breath-taking economy of Newton's methods.Subrahmanyan Chandrasekhar is one of the most reknowned scientists of the twentieth century, whose career spanned over 60 years. Born in India, educated at the University of Cambridge in England, he served as Emeritus Morton D. Hull Distinguished Service Professor of Theoretical Astrophysics at the University of Chicago, where he has was based from 1937 until his death in 1996. His early research into the evolution of stars is now a cornerstone of modern astrophysics, and earned him the Nobel Prize for Physics in 1983. Later work into gravitational interactions between stars, the properties of fluids, magnetic fields, equilibrium ellipsoids, and black holes has earned him awards throughout the world, including the Gold Medal from the Royal Astronomical Society in London, the National Medal of Science in the United States, and the Copley Medal from the Royal Society. His many publications include Radiative transfer, Hydrodynamic and hydromagnetic stability, and The mathematical theory of black holes, each being praised for its breadth and clarity. Newton's Principia for the common reader is the result of Professor Chandrasekhar's profound admiration for a scientist whose work he believed is unsurpassed, and unsurpassable. (shrink)

We invite systematic consideration of the metaphors of cycles and circulation as a long-term theme in the history of the life and environmental sciences and medicine. Ubiquitous in ancient religious and philosophical traditions, especially in representing the seasons and the motions of celestial bodies, circles once symbolized perfection. Over the centuries cyclic images in western medicine, natural philosophy, natural history and eventually biology gained independence from cosmology and theology and came to depend less on strictly circular forms. As potent (...) ‘canonical icons’, cycles also interacted with representations of linear and irreversible change, including arrows, arcs, scales, series and trees, as in theories of the Earth and of evolution. In modern times life cycles and reproductive cycles have often been held to characterize life, in some cases especially female life, while human efforts selectively to foster and disrupt these cycles have harnessed their productivity in medicine and agriculture. But strong cyclic metaphors have continued to link physiology and climatology, medicine and economics, and biology and manufacturing, notably through the relations between land, food and population. From the grand nineteenth-century transformations of matter to systems ecology, the circulation of molecules through organic and inorganic compartments has posed the problem of maintaining identity in the face of flux and highlights the seductive ability of cyclic schemes to imply closure where no original state was in fact restored. More concerted attention to cycles and circulation will enrich analyses of the power of metaphors to naturalize understandings of life and their shaping by practical interests and political imaginations. (shrink)

In the field of astronomy, Thomas Hobbes's mechanistic philosophy was influenced by Johannes Kepler. Whereas Galilei still sticks to the circular motion of the planets, Hobbes takes over the Keplerian ellipses. According to Kepler, he defines astronomy as ' celestial physics'. As a consequence, he tries to determine the cause for the planetary motion and the reason why the orbit of the earth is eccentric. Hobbes modifies Kepler's explanation given in the Epitome astronomiae Copernicanae that the earth (...) consists of two parts: one well-disposed, the other hostile towards the sun. Referring to this doctrine, Hobbes developed various astronomical theories throughout a time span of about 35 years in works like "De motu" , De corpore , and the "Decameron physiologicum". (shrink)

I argue that Copernicus accepted the reality of celestial spheres on the grounds that the equant problem is unintelligible except as a problem about real spheres. The same considerations point to a number of generally unnoticed liabilities of Copernican astronomy, especially gaps between the spheres, and the failure of some spheres to obey the principle that their natural motion is to rotate. These difficulties may be additional reasons for Copernicus's reluctance to publish, and also stand in the way (...) of strict realism as applied to De Revolutionibus, although a realistic astronomy may be envisioned as a goal for Copernicus's research program. (shrink)

The ArgumentThis paper, an attempt at an institutional history of ideas, compares patterns of reproduction of scientific knowledge in Catholic and Protestant educational institutions. Franciscus Eschinardus'Cursus Physico-Mathematicusand Jean-Robert Chouet'sSyntagma Physicumare examined for the strategies which allow for accommodation of new contents and new practices within traditional institutional frameworks. The texts manifest two different styles of inquiry about nature, each adapted to the peculiar constraints implied by its environment. The interpretative drive of Eschinardus and a whole group of “modern astronomers” is (...) here seen as pushing beyond the traditional task of “saving the phenomena,” towards celestial hermeneutics which is thoroughly experimental and mathematical. In spite of the insistence on physical interpretation of celestial phenomena, Eschinardus' astronomical discourse is yet constrained by a complex game of intellectual-political considerations. Commitment to the Thomistic organization of knowledge, which sets a boundary between a science of motion and the “geometry of heavens”, suppresses any impulse to ask about the mechanical causes of celestial appearances. The Copernican cosmology is thus rejected qua an attempt to cross this guarded boundary. Chouet in Geneva, by contrast, frees himself from these constraints on the organization of natural knowledge. By strictly separating philosophy from theology, he can combine physics and astronomy, favor a Copernican cosmology and adopt a Cartesian mechanistic worldview. Moreover, unlike the Jesuit Eschinardus, Chouet seeks toexplainnatural phenomena in terms of causes, rather than justinterpretthem. Yet he does so within a philosophical discourse largely scholastic in nature, which best suits the conservative institutional framework in which he teaches. Whereas the Jesuit Eschinardus employs a new type of discourse without severing his links with the traditional Thomistic worldview, the Calvinist Chouet adopts a new Cartesian worldview and adapts it to a largely traditional type of discourse. (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)

'The interpretours of Plato,' wrote Sir Thomas Elyot in The Governour, 'do think that the wonderful and incomprehensible order of the celestial bodies, I mean sterres and planettes, and their motions harmonicall, gave to them that intensifly and by the deepe serche of raison beholde their coursis, in the sondrye diversities of number and tyme, a forme of imitation of a semblable motion, which they called daunsigne or sltation.' The image of the planets and stars engaged in an (...) ordered and measured dance is an ancient one. Plato articulated it in a passage in the Timaeus, where he likened the apparent motions of the planets and stars to 'choreiai'. Through the centuries the analogy has challenged Plator's interpreters to define and elaborate the image. Miller has examined a range of poetic and philosophical texts influenced by Plato cosmology, and has discovered frequent comparisons of the cosmic order to 'daunsigne.' He suggests that the vision of the cosmic dance did not develop at random in Western intellectual history but originated in a specific philosophical context and passed through stages of evolution that reflect Gnostic, Christian, Stoic, and Neoplatonic responses to Plato. He argues that the historical variations of the image were often closely related to adaption or criticisms of Plato's theories of visual perception and intellectual vision. The dance, in conjunction with images such as the Great chain of Being and the Lyre of the Heavens, became the dominant image of a peculiarly Late Antique world-view which Miller has called the 'poetic universe'; a world where metaphors, metonymies, and personifications could exist in fact as well as in word. The result of Miller's analysis is vast in scope. The nine chapters of the book each present a thesis on a particular author, but all function together like links in a chain. Miller has been described as 'an historian of visions'; the book has been likened to Auerbach's Mimesis. It is a remarkable contribution to an understanding of the complex interaction of ideas and images in time. (shrink)

How did it become possible to philosophize about history? Man has generally sought to locate himself in natural space rather than in historical time. The various oriental philosophies give no place to history. “Humanistic” Greece herself, in other respects so eager to explore human conduct in all its characteristic dimensions and in all its aspects, prudently recoiled from anything which might give value to time or cause history to appear as the specifically human mode of existence. No other culture, perhaps, (...) carried so far the concern for harmonizing human relationships, and yet the idea of progress was completely lacking in it. The organization of the terrestrial city always remained the central point of the reflection of Greek poets and philosophers, who were almost all teachers and law-givers—but they never thought to situate the true destiny of man in the historical world, much less to grant man a place in the universe which would make him forget the precariousness of his condition and his subordination to that which surpasses him. And, if we listen to Aristotle: “The life of moral virtue,” he says, “is happy only in a secondary degree. For the moral activities are purely human, ανθρωπικαι.” Naturally, “it is true that, being a man and living in the society of others, he chooses to engage in virtuous action, and so will need external goods to carry on his life as a human being, πρos τo ανθρωπɛνɛσθαι.” But we must take care not to assert “that man is superior to the other animals … since there are other things far more divine in their nature than man, for instance, to mention the most visible (ϕανɛρωτατα), the things of which the things of which the celestial system is composed.” Aristotle was referring to the stars—and, indeed, it was in the circular motions of the luminaries, much more than in the human domain, that the classic Greeks saw that which is manifested in being with the greatest splendor. If we limit ourselves to the specifically human—as do those whom Plotinus designates under the frankly disdainful term oι ανθρωπικωτɛρoι—we risk losing contact with the Good that revolves in the cosmos and is our sole guaranty against the senseless non-being which threatens us from every side. Under these conditions the question of knowing whether or not history has meaning, and whether or not it is provided with an appropriate logic which expresses the profound structure of our being, appears meaningless. (shrink)

Within twenty years of one another, Bacon and Descartes proposed cosmologies which relied heavily on matter theory. In both, the distribution of matter in the cosmos determined what centers of rotation there were, and rotating bodies were carried around by the motion of an all-encompassing celestial fluid in which they were embedded. But the role of matter theory in the two accounts is very different, both in motivation and in the level at which it is active in guiding (...) physical theory. Matter theory in Baconian cosmology stands as a foundational discipline, being virtually constitutive of physical theory, as it had been for natural philosophers from Thales onwards, whereas in Descartes it is subservient to the needs of his optics and his mechanics. Comparison of the two cases shows how the role of matter theory came to be radically modified in seventeenth-century cosmology. (shrink)

When we examine the history of astronomy up to the end of the seventeenth century by considering the relation between mathematical astronomy and natural philosophy, it has been argued that there were two groups of philosophers and astronomers: instrumentalists and realists. However, this classification is deficient when we consider attitudes toward the explanatory power of mathematics in determining astronomical theories. I offer the solution of dividing realists into two subcategories—mathematical realists and physical realists. Mathematical realists include those who thought mathematics (...) could provide the real motions of celestial bodies. The physical realists, who include Ibn Rushd (Averroës), believed mathematics could not provide us with the real structure of the heavens. To avoid contradictions between the physical and mathematical models, the physical realists held that a mathematical model of the heavens should be designed by considering physics. I argue, in this article, that Francis Bacon can be considered a physical realist. (shrink)