The Greco-Roman mathematician Claudius Ptolemy is one of the most significant figures in the history of science. He is remembered today for his astronomy, but his philosophy is almost entirely lost to history. This groundbreaking book is the first to reconstruct Ptolemy’s general philosophical system—including his metaphysics, epistemology, and ethics—and to explore its relationship to astronomy, harmonics, element theory, astrology, cosmology, psychology, and theology. -/- In this stimulating intellectual history, Jacqueline Feke uncovers references to a complex and sophisticated (...) philosophical agenda scattered among Ptolemy’s technical studies in the physical and mathematical sciences. She shows how he developed a philosophy that was radical and even subversive, appropriating ideas and turning them against the very philosophers from whom he drew influence. Feke reveals how Ptolemy’s unique system is at once a critique of prevailing philosophical trends and a conception of the world in which mathematics reigns supreme. -/- A compelling work of scholarship, Ptolemy’s Philosophy demonstrates how Ptolemy situated mathematics at the very foundation of all philosophy—theoretical and practical—and advanced the mathematical way of life as the true path to human perfection. (shrink)

This book explores the changing perspective of astrology from the Middle Ages to the Early Modern Era. It introduces a framework for understanding both its former centrality and its later removal from legitimate knowledge and practice. The discussion reconstructs the changing roles of astrology in Western science, theology, and culture from 1250 to 1500. The author considers both the how and the why. He analyzes and integrates a broad range of sources. This analysis shows that the history of astrology—in particular, (...) the story of the protracted criticism and ultimate removal of astrology from the realm of legitimate knowledge and practice—is crucial for fully understanding the transition from premodern Aristotelian-Ptolemaic natural philosophy to modern Newtonian science. This removal, the author argues, was neither obvious nor unproblematic. Astrology was not some sort of magical nebulous hodge-podge of beliefs. Rather, astrology emerged in the 13th century as a richly mathematical system that served to integrate astronomy and natural philosophy, precisely the aim of the “New Science” of the 17th century. As such, it becomes a fundamentally important historical question to determine why this promising astrological synthesis was rejected in favor of a rather different mathematical natural philosophy—and one with a very different causal structure than Aristotle's. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Abraham, Planter of Mathematics":Histories of Mathematics and Astrology in Early Modern EuropeNicholas PopperFrancis Bacon's 1605 Advancement of Learning proposed to dedicatee James I a massive reorganization of the institutions, goals, and methods of generating and transmitting knowledge. The numerous defects crippling the contemporary educational regime, Bacon claimed, should be addressed by strengthening emphasis on philosophy and natural knowledge. To that end, university positions were to be created (...) devoted to "Artes and Sciences at large," rather than to the professions. High salaries would render lecturers "able and sufficient," undistracted from their task. Most famously, he argued that teaching of the "operatiue studie of many Scyences" should involve sophisticated technical education. The study of natural philosophy demanded not only books, but globes, astrolabes, and other "instrumentals." Most significantly, yielding reliable and meaningful knowledge from experiential gleanings required a rigorous system of deductive reasoning.The legacy of this colossal proposal has earned Bacon honored status as devisor of the scientific method.1 But Bacon's educational reform extended [End Page 87] beyond the methods of producing and transmitting knowledge. To facilitate more efficient "vse and administration" of the knowledge produced by his system, he also demanded a searching examination of the history of learning. This history would provide a mirror enabling his contemporaries to deploy the fruits of his method, by considering how learning in the past had been used successfully or ill-advisedly. Producing this history was the ambition of the Advancement, for he explained: "no man hath propounded to himselfe the generall state of learning to bee described and represented from age to age, as many have done the works of Nature, & the State civile and Ecclesiastical." He continued:And yet I am not ignorant that in divers particular sciences, as of the Iurisconsults, the Mathematicians, the Rhetoricians, the Philosophers, there are set down some smal memorials of the Schooles, Authors, and Bookes: and so likewise some barren relations touching the Invention of Arts, or usages. But a iust story of learning, containing the Antiquities and Originalls of Knowledges, & their Sects; their Inventions, their Traditions; their diverse Administrations and Managings; their Flourishings, their Oppositions, Decayes, Depressions, Oblivions, Removes, with the causes, and occasions of them, and all other events concerning learning, throughout the ages of the world; I may truly affirme to be wanting.2Bacon thus positioned himself not only as a Father of Modern Science, but also a Father of the History of Science.Following Bacon's suggestion, I will examine the "small memorials" of the history of mathematics—and particularly the mathematical art of astrology—in the sixteenth and seventeenth centuries. My conclusion, however, will not bear out Bacon's claims. Despite his frustration, Bacon was only one of many early modern scholars appraising the role of mathematics within history. And he devoted less energy than others to mapping its origins and tracing its transmissions between communities. In fact, Bacon's 1605 proposal for a history of mathematics was already out-of-date. Discussions [End Page 88] of the history of mathematics had been rife on the continent and in England throughout the previous century.3The evidence that Renaissance scholars inherited was sprawling and inconclusive. Several genealogies for mathematics could be found within classical Greek, Latin, and patristic references. One lineage claimed mathematics began in ancient Assyria, where the priestly caste, the Chaldeans, practiced a form of mathematics that seemed a corrupt admixture of philosophy, medicine, and religion, and relied heavily on observation of the heavens. Other scholars traced the origins to Egypt, claiming that the field developed to survey lands frequently flooded by the Nile. The real problem for ancient, late antique, and medieval scholars had not been the origins of mathematics, but what exactly mathematics were. For some, the term strictly referred to the quadrivium: geometry, arithmetic, astronomy, and music. But for others, mathematics' origins amongst the Egyptians or Chaldeans inextricably linked it to forms of astrological divination, augury, and necromancy that were unsavory to both Latin and Christian traditions. Mathematici were included alongside ghastly lists of Magi, Brahmins, Aruspices, Genethliaci, and other diabolic practitioners of idolatrous magic. These might or might not be distinguished from mathematici such as Pythagoras... (shrink)

Philip Melanchthon, humanist and colleague of Martin Luther, is best known for his educational reforms, for which he earned the title Praeceptor Germaniae. His most influential form of philosophical writing was the academic oration, and this volume, first published in 1999, presents a large and wide-ranging selection of his orations and textbook prefaces translated into English. They set out his views on the distinction between faith and reason, the role of philosophy in education, moral philosophy, natural (...) class='Hi'>philosophy, astronomy and astrology, and the importance of philosophy to a true Christian, as well as his views on Classical philosophical authorities such as Plato and Aristotle and on contemporaries such as Erasmus and Luther. Powerfully influential in their time, inspiring many Protestant students to study philosophy, mathematics and natural philosophy, they illuminate the relationship between Renaissance and Reformation thought. (shrink)

What were the reasons of the Copernican Revolution ? How did modern science (created by a bunch of ambitious intellectuals) manage to force out the old one created by Aristotle and Ptolemy, rooted in millennial traditions and strongly supported by the Church? What deep internal causes and strong social movements took part in the genesis, development and victory of modern science? The author comes to a new picture of Copernican Revolution on the basis of the elaborated model of scientific revolutions (...) that takes into account some recent advances in philosophy, sociology and history of science. The model was initially invented to describe Einstein’s Revolution of the XX century beginning. The model considers the growth of knowledge as interaction, interpenetration and unification of the research programmes, springing out of different cultural traditions. Thus, Copernican Revolution appears as a result of revealation and (partial) resolution of the dualism , of the gap between Ptolemy’s mathematical astronomy and Aristotelian qualitative physics. The works of Copernicus, Galileo, Kepler and Newton were all the stages of mathematics descendance from skies to earth and reciprocal extrapolation of earth physics on skies. The model elaborated enables to reassess the role of some social factors crucial for the scientific revolution. It is argued that initially modern science was a result of the development of Christian Weltanschaugung . Later the main support came from the absolute monarchies. In the long run the creators of modern science appeared to be the “apparatchics” of the “regime of truth” built-in state machine. Natural science became a part of ideological state apparatus providing not only scientific education but the internalization of values crucial for the functioning of state. -/- . (shrink)

Review of Liba Taub, Ptolemy's universe; The natural philosophical and ethical foundations of Ptolemy's astronomy. Chicago: Open Court 1993. xiv, 188 p.

In a somewhat polemical article on ‘Solstices, Equinoxes, and the Presocratics’ D. R. Dicks has recently challenged the usual view that the Presocratics in general, and the Milesians in particular, made significant contributions to the development of scientific astronomy in Greece. According to Dicks, mathematical astronomy begins with the work of Meton and Euctemon about 430 B.C. What passes for astronomy in the earlier period ‘was still in the pre-scientific stage’ of ‘rough-and-ready observations, unsystematically recorded and imperfectly understood, of (...) practical men’ whose chief concern was to fix the seasons for ploughing, seed-time, sailing voyages and religious festivals. Ionian speculation, says Dicks, took very little note of such observation: ‘some of its wilder flights of fancy might have been avoided, if it had taken more’. In this account of the rise of Greek astronomy, the natural philosophers have no part to play. Their theories represent a speculative enterprise without a scientific future, a philosophic sideline with no impact on the development of observational science from Hesiod to Meton or the development of mathematical astronomy from Meton to Ptolemy.I believe that such a dichotomy between early philosophy and early science in Greece is misguided in principle, and that it seriously distorts our picture of the initial phases of each discipline. It also imposes a considerable strain upon our credulity. Take the case of Anaxagoras who, according to Plato and Theophrastus, had given a causal explanation of eclipses of the moon a generation before Meton. (shrink)

The Epistles of the Brethren of Purity' is an encyclopedic compendium, probably composed in tenth-century Iraq by a society of adepts with Platonic, Pythagorean, and Shi'i tendencies. Its 52 sections ('epistles') are divided into four parts (Mathematics, Natural Philosophy, Sciences of the Soul and Intellect, and Theology). The current volume provides an edition, translation, and notes to Epistle 3 ('On Astronomia'), which forms one of the 14 sections on Mathematics. The content is a mixture of elementary astronomy and (...) astrology, but it is not a beginner's textbook. Rather, the purpose is to use examples from those disciplines to provide spiritual, moral, and soteriological guidance. Thus the Epistle uses the argument from design to show the necessity for a Creator who made the harmonious universe; this wondrous design is then employed by the authors as a model, providing humans with a paradigm for proper ethical, political, and even economic conduct; and the study of Astronomia helps the soul achieve ultimate happiness as it seeks to throw off the shackles of this mundane world and oppressive body in favour of the purity of the celestial realm.0Although by no means typical of Islamic astronomical literature, Epistle 3 of the Brethren of Purity gives a window into a fascinating and intriguing group operating during the early period of Islam who sought to continue and adopt one of the esoteric strands of Hellenistic philosophy within an Islamic context, meshing astronomy, astrology, Platonic-Pythagorean philosophy, Quranic and Biblical quotations, and anecdotes from the lives of the Abrahamic prophets. (shrink)

In the first part of chapter 2 of book II of the Physics Aristotle addresses the issue of the difference between mathematics and physics. In the course of his discussion he says some things about astronomy and the ‘ ‘ more physical branches of mathematics”. In this paper I discuss historical issues concerning the text, translation, and interpretation of the passage, focusing on two cruxes, the first reference to astronomy at 193b25–26 and the reference to the more physical branches at 194a7–8. In (...) section I, I criticize Ross’s interpretation of the passage and point out that his alteration of has no warrant in the Greek manuscripts. In the next three sections I treat three other interpretations, all of which depart from Ross's: in section II that of Simplicius, which I commend; in section III that of Thomas Aquinas, which is importantly influenced by a mistranslation of, and in section IV that of Ibn Rushd, which is based on an Arabic text corresponding to that printed by Ross. In the concluding section of the paper I describe the modern history of the Greek text of our passage and translations of it from the early twelfth century until the appearance of Ross's text in 1936. (shrink)

The paper explores the historical reasons why Ptolemy’s Almagest was cultivated in Antiquity as a legitimate part of ancient culture. It tries to elucidate first the precise nature of Ptolemy’s project in the Almagest, its relation to ethics as well as to the particular conception that Ptolemy had of mathematics. It then proposes an explanation for the fact that this treatise, both in Ptolemy's period and afterwards, was studied within the milieu of ancient astrologers.

T. Kuhn’s theory of scientific revolutions has repeatedly been the subject of criticism. It is important to note that Kuhn pays very limited attention to the phenomenon of the scientific revolution itself, comparing the revolution either with a religious conversion or with a gestalt switch. Such comparisons, however, are very superficial. This paper outlines a new understanding of the scientific revolution as a result of the resonance of the intellectual trends of the early modern period. It was the quasi-simultaneous action (...) of various factors that led to revolutionary changes in natural philosophy, which, in turn, gave rise to the actual scientific revolution. In addition, the article shows that the Copernican Revolution cannot be described within the model of scientific revolution developed by T. Kuhn. Ptolemy’s theory was mathematically constructed so that it could not make inaccurate predictions of planetary motion, because – as we are now clear – the function characterizing the trajectory of planetary motion was actually represented as a Fourier series. The Copernican revolution was not a Kuhn-type scientific revolution, nor was it caused by the empirical failures of Ptolemaic astronomy. Events unfolded according to a different scheme. Copernicus set out to carry out the principle of the uniform circular motion of the planets more consistently than had been done in Ptolemy’s theory, at the same time presenting to this theory those requirements of an aesthetic and methodological order, which the cognitively fragmented system of Ptolemy, for all its flexibility, could not satisfy and, by the conditions of its creation, could not satisfy. In addition, the article shows that Copernicus, in constructing his heliocentric theory, was essentially seeking answers to the challenges that Alberti’s artificial perspective and Nicholas of Cusa’s theological speculation posed to the visual experience in the sixteenth century. (shrink)

Late ancient Platonists discuss two theories in which geometric entities xplain natural phenomena : the regular polyhedra of geometric atomism and the ccentrics and epicycles of astronomy. Simplicius explicitly compares the status of the first to the hypotheses of the astronomers. The point of omparison is the fallibility of both theories, not the reality of the entities postulated. Simplicius has strong realist commitments as far as astronomy is concerned. Syrianus and Proclus, too, do not consider the polyhedra as devoid (...) of physical reality. Proclus rejects epicycles and eccentrics, but accepts the reality of material homocentric spheres, moved by their own souls. The spheres move the astral objects contained in them, which, however, add motions caused by their own souls. The epicyclical and eccentric hypotheses are useful, as they help us to understand the complex motions resulting from the interplay of spherical motions and volitional motions of the planets. Yet astral souls do not think in accordance with human theoretical constructs, but rather grasp the complex patterns of their motions directly. Our understanding of astronomy depends upon our own cognition of intelligible patterns and their mathematical images. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Role of the Heavens in the Thought of Philip MelanchthonCharlotte MethuenPhilip Melanchthon has long been recognized as one of the central figures in the German Lutheran Reformation. His theological contribution to the Reformation may be found in his codifying of Lutheran theology in the Confessio Augustana and in the Loci Communes, the first major Lutheran theological textbook, which long remained a central text for the teaching of theology (...) in Lutheran schools and universities. A teacher at the University of Wittenberg from 1518 until his death, Melanchthon was also involved in the reform of universities and the establishment of school systems throughout Lutheran Germany. These reforms facilitated the spread of the Reformation by encouraging the development of Lutheran educational principles and the establishing of Humanist education as the basis for the schools and universities of Lutheran Germany, and Melanchthon’s role in this process has led to his being accorded the title Praeceptor Germaniae. 1 More recently, Melanchthon has also been hailed as the initiator of a new “Lutheran” approach to natural philosophy. 2 It is my contention in this article that Melanchthon’s interest in natural philosophy is integrally connected to his educational interest and that these hang upon a particular theological and cosmological [End Page 385] understanding of the universe, particularly the heavens, as becomes clear from his defense of astronomy.I. Despite his theological interests and his commitment to the dissemination of Lutheran theology, Melanchthon was reluctant to teach theology and remained primarily concerned with the teaching of the subjects which made up the curriculum of the arts faculty in a sixteenth-century university. It was as Professor of Greek that he was originally appointed to the University of Wittenberg, and he had a deep interest in the teaching of ancient languages, especially Greek, and in the study of ancient texts in their original form rather than through later commentators. His promotion of the trivium (grammar, logic, and rhetoric) led him to write a textbook in each of these areas; and these works continued to be used as prescribed works in many German universities into the seventeenth century. 3 As an educator Melanchthon was thus firmly in the humanist mold. However, Melanchthon’s interests did not only take in the teaching of languages; he also promoted the teaching of both moral and natural philosophy. 4 Moreover, he was a strong advocate of the teaching of the mathematical sciences, particularly arithmetic, geometry, and astronomy. These, together with music, made up the quadrivium, which complemented the linguistic arts.In Melanchthon’s day the mathematical sciences had long been accepted as part of the arts curriculum, 5 even if in practice minimal attention had been paid them at many universities. 6 Their ambiguous status is reflected by the attitude taken by many humanist reformers, who did not regard arithmetic, geometry, astronomy, and music as an essential part of the curriculum. Thus Erasmus believed that music, arithmetic, and geography should be taught only to pupils who had a particular interest in these subjects 7 and that knowledge of nature, astrology, architecture, and other related subjects would come from reading the ancient authors. 8 In a similar vein Juan Luis [End Page 386] Vives argued that mathematics tended to divorce the mind from the practical concerns of life and that its study was not, therefore, to be recommended. 9 In contrast Melanchthon seems to have recognized the value of the study of the mathematical sciences from the beginning of his scholarly career. Perhaps he was inspired by his professor of mathematics at Tübingen, Johannes Stöffler, a gifted mathematician who wrote his own Arithmetic and was also fluent in the praise of his subject. 10 In an early oration, De artibus liberalis, delivered in Tübingen in 1517, Melanchthon praises arithmetic as a principal part of philosophy; geometry for its role in producing the wonderful machines of war and the beautiful ornaments of cities; music for its elegance and harmony; and astronomy (very briefly) for its applications in medicine. 11This oration should almost certainly be read as part of the tradition of orations and odes which extolled each of the liberal arts for its practical (and often also... (shrink)

Thomas Hobbes adheres to a conception of philosophy as causal knowledge that bears the mark of the Aristotelian tradition, as Cees Leijenhorst has elaborated in another issue of The Monist. Referring to Aristotle, Hobbes states explicitly in two mathematical studies of the 1660’s: “To know is to know by causes.” But according to Hobbes, we encounter obstacles when we search for causes in the field of natural philosophy. Consequently, his well-known definition of philosophy consists of (...) two parts. The earliest version, elaborated in the so-called A 10 manuscript, reads: “Philosophy is the knowledge, acquired by correct ratiocination, of properties of bodies from their conceived manners of generation, and again, of such manners of generation, as may be, from known properties.” This definition reappears almost literally in several of Hobbes’s other essays, for example in De Cive and in the Leviathan, and in a modified version in De Corpore. In the latter, he replaces “properties of bodies” by “effects or appearances” and “manners of generation” by “causes or manners of generation.” But one essential point remains unchanged: the second part of the definition is not a simple reversal of the first part, since Hobbes does not speak of “manners of generation” or of “causes,” but only of possible manners of generation or of possible causes. It is this second part of Hobbes’s theory that refers to natural philosophy. Hobbes stresses repeatedly that in the case of natural philosophy, causes can be concluded only from known effects. In contrast, in First Philosophy or geometry, conclusions can be drawn from known and true principles to their effects. According to Hobbes, this is the essential distinction of natural philosophy, which does not exist by accident. This essay explicates Hobbes’s argumentation for claiming this distinction for natural philosophy but not for geometry. In addition, the consequences of Hobbes’s methodological argument for natural philosophy are examined, especially the consequences for optics and astronomy. Finally, the question of whether there is a development in this theory will be explored. (shrink)

The essays which comprise this collection made their first appearance in 1948 to celebrate the one hundred and fiftieth anniversary of the founding of the British science journal, The Philosophical Magazine, which initially published many monographs in which distinguished scientific discoveries were announced. The present edition is a reprint of the supplement to the regular issue of 1948 and is now put out in book form to be more available for students of the history of science. The "natural (...) class='Hi'>philosophy" in the title reflects the way in which the meaning of the term "philosophy" has changed over the past two centuries, for all the essays are devoted to science as we now know it, even as The Philosophical Magazine has itself become a journal now devoted mainly to solid-state physics. Thus a succession of chapters details the history of astronomy, physics, chemistry, mathematics, and engineering through the eighteenth century; other topics include the history of The Philosophical Magazine and histories of scientific periodicals generally, of scientific instruments, and of scientific societies throughout the same era. The concluding essay, by F. Sherwood Taylor, is entitled "The Teaching of the Physical Sciences at the End of the Eighteenth Century"; this is a well documented study of syllabi for courses taught in the universities, as well as an account of the educations received by men who figured prominently in eighteenth-century science. The essays, whose authors include such notables as Sir H. Spencer-Jones, Herbert Dingle, J. R. Partington, J. F. Scott, and Douglas McKie, are uniformly good. They will interest mainly historians of science for their detailed coverage of both internalist and externalist aspects of eighteenth-century thought. They will also appeal to philosophers, however, if only to remind them how their own discipline gave birth to the "new science," and indeed gave it a unity in its early stages that it would do well to recover in the present day.—W.A.W. (shrink)

ArgumentThe subject of the paper is the shift from an astrology-oriented astronomy towards an allegedly more objective, mathematically grounded approach to astronomy. This shift is illustrated through a close reading of Tycho Brahe's scientific development and the contemporaneous changes in his communicational strategies. Basing the argument on a substantial array of original sources it is claimed that the Danish astronomer developed a new astronomical discourse in pursuit of credibility, giving priority to observational astronomy and natural philosophical questions. The abandonment (...) of astrology in public discourse is primarily explained by Tycho's social position and greater sensibility to controversial issues. Tycho's example suggests that the changes in rhetorical strategies regarding astrology (which happened earlier than changes in astrological belief) should be given more recognition in the history of astronomy. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Before Science: The Invention of the Friars’ Natural Philosophy by Roger French, Andrew CunninghamIrven M. ResnickRoger French and Andrew Cunningham. Before Science: The Invention of the Friars’ Natural Philosophy. Hants, UK: Scolar Press, 1996. Pp. x + 298. Cloth, $68.95.This is a peculiar book that depicts thirteenth-century natural philosophy as wholly dependent on the theological interests of the mendicant orders. For the (...) Friars, “Natural philosophy was a study in which the central concerns were the detection, admiration and appreciation of God’s existence, goodness, providence, munificence, forethought and provision for His creation” (4). Although conceived as “a positive contribution to the discipline of the history of science” (3), the work begins and ends with the claim that medieval natural philosophers were not engaged in science.One difficulty is that the authors never make clear what they mean by science, although they evidently understand that it entails a repudiation of metaphysics and a doctrine of nature’s radical autonomy. Consequently, for French and Cunningham medieval “science” is a mythic construct of modern historians, since “[t]here was no scientific tradition (in the modern sense of the term ‘scientific’) of looking at nature in the thirteenth century, only a religio-political way of doing so” (273).Thus, when summarizing the accomplishments of Roger Bacon, they note that “[Bacon] has been credited, along with Grosseteste, with creating early ‘experimental science’. Bacon could not of course have been a ‘scientist’ because he lived in the wrong [End Page 623] age for this” (238). This seemingly casual conclusion is rather stunning not only in its own right, but also as a revelation of the authors’ own effort to disenfranchise medieval ‘scientists’ for having had the misfortune of living too soon.French and Cunningham propose that polemical or apologetical interests urged the Friars to study nature as a response to various heretics and especially the Cathars who, seemingly like moderns, sought to disengage the natural world from the Christian God, while using the vocabulary of Aristotle’s libri naturales. However this central argument demands better support. Since the authors can cite only one surviving Cathar text—De duobus principiis (ca. 1230)—almost everything known of this group is derived from anti-Cathar polemics. Based on this single text the authors can say no more than that it used “what looks very much like a commentary on Aristotle’s Physics or Metaphysics,” (134) but fail to identify more precisely its sources. It is clear that thirteenth-century orthodox polemics increasingly relied on Aristotelian materials, but the conclusion that natural philosophers did so only in response to heretics who beat them to the Aristotelian punch seems tendentious. The historian will likely remain unconvinced that the unparalleled translating activity of the late eleventh and twelfth centuries—the rendering into Latin of Arabic scientific knowledge (as in Constantine the African’s Pantegni or Adelard of Bath’s Quaestiones naturales), Greek medical literature (e.g. Galen’s Methodus medendi translated by Gerard of Cremona and Burgundio of Pisa) and mathematics (e.g. Euclid’s Optics, Theodosius’s Spherics, Archimedes’ On the Quadrature of the Circle, and Ptolemy’s Tetrabiblos and Almagest) culminating with thirteenth-century translations of Aristotle’s biological works—should all have stemmed from a preoccupation with heresy.A further shortcoming of this book is the limited attention given to works on natural philosophy by the Friars themselves. The book’s first seven of eleven chapters explore the educational establishments in which natural philosophy arose: first monastic and cathedral schools, and then the universities. The works of individual Friars receive only the briefest summary. Among the Dominican natural philosophers Albertus Magnus—the patron saint of scientists and one of a very few scholastics to have commented on all of Aristotle’s biological works—is awarded only five pages. For his mastery of Aristotle’s libri naturales Albertus has been called “the dominant figure in Latin learning and natural science of the thirteenth century.” (Cf. Lynn Thorndike, History of Magic and Experimental Science [New York: Macmillan, 1929], 2:521) Albertus described not only the natural world but also explored the philosophical foundations for scientific knowledge. Yet curiously French and Cunningham give much more attention... (shrink)

The purpose of this paper is to highlight an aspect of Elisabeth’s intellectual life that has received little scholarly attention so far, namely Elisabeth’s involvement with the sciences of her day. Firstly, this paper provides a survey of Elisabeth’s interest in and engagement with various scientific disciplines, such as mathematics, medicine, natural philosophy, and microscopy, drawing on her letter exchange with Descartes and several other intellectuals as well as additional documents, such as dedications of scientific works to Elisabeth. (...) Secondly, this paper investigates Elisabeth’s involvement with one particular scientific discipline, namely astronomy. Analyzing Elisabeth’s letter exchange with Andreas Colvius and Constantijn Huygens and additional letters and testimonies, I show that Elisabeth played an active part in at least three current debates in astronomy, namely concerning the discoveries of the satellites of Jupiter, the emerging maps of the moon, and the invention of the new telescopes. Based on the evidence provided in this paper, it is argued that Elisabeth’s intellectual biography should be broadened. It is not sufficient to perceive her only as a critic of Descartes’ philosophy, as this characterization does not accommodate her scientific commitments, but rather as a multitalented intellectual. (shrink)

My title, of course, is an exaggeration. The world no more became mathematical in the seventeenth century than it became ironic in the nineteenth. Either it was mathematical all along, and seventeenth-century philosophers discovered it was, or, if it wasn’t, it could not have been made so by a few books. What became mathematical was physics, and whether that has any bearing on the furniture of the universe is one topic of this paper. Garber says, and I (...) agree, that for Descartes bodies are the things of geometry made real ( Ref). That is a claim about the world: what God created, and what we know in physics, is nothing other than res extensa and its modes. Others, including Marion, hold that in modern science, here represented at its origins by Descartes, representation displaces beings: the knower no longer confronts Being or beings but rather a system of signs, a “code” as Marion calls it, to which the knower stands in the relation of subject to object. The Meditations, or perhaps even the Regulæ, are the first step toward the transcendental idealism of Kant. Most of this paper will be devoted to a more concrete question. Physics in the seventeenth century increasingly became a matter of applying mathematical knowledge to the solution of physical problems. The “mixed sciences” of astronomy, optics, and music, sciences then distinct from physics, became models of understanding for all of natural philosophy. My interest here is in one aspect of that development: how particular physical situations are transformed into mathematical. I will look at the work of Descartes and Isaac Beeckman, contrasting their visions of “physico-mathematics”. (shrink)

Mathematical Astronomy as the most developed branch of ancient exact sciences has been widely discussed - especially epistemological issues e.g. concerning astronomy as a prime example of the distinction between instrumentalist and realist understanding of theories. In contrast to these the very methodology of ancient astronomy has received little attention. Following the work of Jaakko Hintikka and Unto Remes Aristarchus' method of determining the distance of the Sun is sketched and Ptolemy's solar model is discussed in detail.

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.3 (2003) 426-427 [Access article in PDF] Timothy Smiley, editor. Mathematics and Necessity: Essays in the History of Philosophy. New York: Oxford University Press, 2000. Pp. ix + 166. Cloth, $35.00.Mathematics and Necessity contains essays by M. F. Burnyeat, Ian Hacking, and Jonathan Bennett based on lectures given to the British Academy in 1998. All concern the history of the philosophical (...) treatment of mathematics, necessity, or both, although there is no single thread running through all three essays.Burnyeat focuses on Plato's understanding of mathematics in the Republic, making use of the Timeaus in particular to defend his interpretation. Plato claimed that in the ideal society mathematics should be studied for a full ten years, which many have thought excessive. To explain it, Burnyeat argues that the role of mathematics is pervasive: ethics and politics are mathematical, because in Plato's view mathematics is a constitutive part of ethical understanding. On Burnyeat's interpretation, goodness is part of the objective world, and mathematics is a science of values. The link between mathematics and goodness in the objective world is forged by the concord, harmony, and unity of proportions, which express the goodness of the Divine Craftsman's beneficent design. Proportions are both intrinsically good and the proper study of mathematics.Burnyeat explains why Plato thinks abstract kinematics (the pure non-sensible counterpart to astronomy) and abstract harmonics lead to knowledge of the good. Abstract kinematics concerns the "harmony of the spheres" described in the Republic. Drawing heavily on the Timeaus, Burnyeat argues that the circular motions of the spheres are motions in the intelligence of the world soul and that there are similar motions in human souls. The world soul and human souls are spatial and have circular motions (invisibility and intangibility make them incorporeal). Souls are the most important subject matter of abstract harmonics—the study of good proportions. A soul that understands the various mathematical disciplines and their relations takes on the harmony and hence goodness of the world soul. Such a soul serves as a model for organizing the social world, a model which properly trained rulers can use to shape a community. Burnyeat's well-argued essay is compelling and exciting. [End Page 427]Ian Hacking's views provide a great contrast to Burnyeat's Plato. Hacking conducts a phenomenological inquiry into why some philosophers have become obsessed by mathematics as a source of philosophical inspiration. He holds that mathematics concerns a relatively minor part of human culture and that the influence of mathematics on philosophy is pernicious; he even describes it as an infection.Hacking examines the views of six philosophers: Plato, Leibniz, Mill, Descartes, Lakatos, and Wittgenstein. Hacking's assessment of the six philosophers is at times disputable, but it is also interesting and stimulating, and serves his phenomenological inquiry.Hacking traces philosophy's infection by mathematics to two factors. A mathematical proof can be perspicuous; that is, a proof can be "grasped," which requires seeing directly why something must be true and being able to recapitulate it. A mathematical proof can also anticipate facts about the world. He thinks that these two factors affect us in two ways: they give us the idea of a priori knowledge, and they dazzle us into unreasoned conviction in proofs. One might respond that, setting aside the feeling proofs give us, we are still justified in being impressed by them. Hacking argues that much of what impresses is based on a misunderstanding of their nature, which he attempts to correct.According to Hacking, a mathematical demonstration involves shifts of meaning that analytically bind the proof and the theorem it establishes. They thereby mutually support each other and provide what he calls self-authentication. The correctness of the proof is supported by the "analytified" truth of the theorem and the theorem is considered true because proven.This bootstrapping feature of mathematical proofs supports Hacking's deflationary account of necessity. Hacking suggests that the "must" of logical necessity rests upon our unwillingness to accept empirical counter-examples to the... (shrink)

EVEN in Aristotle’s day, there were some problems about the status of the "mixed sciences," mechanics, optics, astronomy, harmonics. They were mathematical in form, and depended on generalizations drawn from repeated and careful observation. In both respects they differed from "physics," as Aristotle saw it; he made them "the most physical part of mathematics," and thus inaugurated a long two-thousand year history of separation between two ways of approach to nature, the philosophical, and the mathematical. Galileo’s central achievement, (...) perhaps, was to end this split; he showed that a single account was possible. Though he claimed the titles both of "Philosopher" and of "Mathematician" to the Grand Duke of Tuscany, the "new science" he proposed in 1638 would not need two separate talents. Mechanics for a while to come would still be classified as "natural philosophy," but it would rapidly become evident that philosophers could no longer claim the competence to intervene in it on their own account. True, some of the first great exponents of the new physics, Descartes, Newton, Leibniz, were also philosophers. But it was abundantly clear that the new science of nature was mathematical-experimental in form, not "philosophical" as that narrowed term had come to be understood. (shrink)

Johannes Kepler belonged to a long tradition of inquiring into nature with reference to God. This applies to Ptolemy, N. Copernicus, Chr. Clavius. Kepler's „new kind of poem” is analyzed in five sections which are based on Keplerian key words: Innovation, Hypothesis, Cause, Soul, Picture. Kepler consciously adhered to new questions, new answers, new methods. He relied on a new notion of hypothesis. His celestial dynamics included a celestial psychology whereby he used a visual conception of astronomy.

The eighth-century Latin manuscript Milan, Veneranda Biblioteca Ambrosiana, L 99 Sup. contains fifteen palimpsest leaves previously used for three Greek scientific texts: a text of unknown authorship on mathematical mechanics and catoptrics, known as the Fragmentum Mathematicum Bobiense (three leaves), Ptolemy's Analemma (six leaves), and an astronomical text that has hitherto remained unidentified and almost entirely unread (six leaves). We report here on the current state of our research on this last text, based on multispectral images. The text, incompletely (...) preserved, is a treatise on the construction and uses of a nine-ringed armillary instrument, identifiable as the “meteoroscope” invented by Ptolemy and known to us from passages in Ptolemy's Geography and in writings of Pappus and Proclus. We further argue that the author of our text was Ptolemy himself. (shrink)

The assumption that Ptolemy adopted star coordinates from a star catalog by Hipparchus is investigated based on Hipparchus’ equatorial star coordinates in his Commentary on the phenomena of Aratus and Eudoxus. Since Hipparchus’ catalog was presumably based on an equatorial coordinate system, his star positions must have been converted into the ecliptical system of Ptolemy’s catalog in his Almagest. By means of a statistical analysis method, data groups consistent with this conversion of coordinates are identified. The found groups show a (...) high degree of agreement between Hipparchus’ and Ptolemy’s data. The value of the obliquity of the ecliptic underlying the conversion is estimated by adjustment and statistically agrees with Ptolemy’s value of this parameter. The results allow the assumption that Ptolemy’s coordinates were determined from Hipparchus’ coordinates by an accurate star globe or even by calculation. For a calculative derivation of ecliptical coordinates from equatorial ones, possible calculation methods are discussed considering the mathematics of the Almagest. (shrink)

In this article, I analyze the coincidence of the prediction of the Earth–Sun distance carried out by Ptolemy in his Almagest and the one he carried out, with another method, in the Planetary Hypotheses. In both cases, the values obtained for the Earth–Sun distance are very similar, so that the great majority of historians have suspected that Ptolemy altered or at least selected the data in order to obtain this agreement. In this article, I will provide a reconstruction of some (...) way in which Ptolemy could have altered or selected the data and subsequently will try to argue in favor of its historical plausibility. (shrink)

Reconstructs Reid's career as a mathematician and natural philosopher for the first time.

This volume considers contingency as a historical category resulting from the combination of various intellectual elements – epistemological, philosophical, material, as well as theological and, broadly speaking, intellectual. With contributions ranging from fields as diverse as the histories of physics, astronomy, astrology, medicine, mechanics, physiology, and natural philosophy, it explores the transformation of the notion of contingency across the late-medieval, Renaissance, and the early modern period. Underpinned by a necessitated vision of nature, seventeenth century mechanism widely identified apparent (...) natural irregularities with the epistemological limits of a certain explanatory framework. However, this picture was preceded by, and in fact emerged from, a widespread characterization of contingency as an ontological trait of nature, typical of late-Scholastic and Renaissance science. On these bases, this volume shows how epistemological categories, which are preconditions of knowledge as “historically-situated a priori” and, seemingly, self-evident, are ultimately rooted in time. Contingency is intrinsic to scientific practice. Whether observing the behaviour of a photon, diagnosing a patient, or calculating the orbit of a distant planet, scientists face the unavoidable challenge of dealing with data that differ from their models and expectations. However, epistemological categories are not fixed in time. Indeed, there is something fundamentally different in the way an Aristotelian natural philosopher defined a wonder or a “monstrous” birth as “contingent”, a modern scientist defines the unexpected result of an experiment, and a quantum physicist the behavior of a photon. Although to each inquirer these instances appeared self-evidently contingent, each also employs the concept differently. (shrink)

This completes what I think one may state and defend on physical grounds concerning the foundations of Astrology and the coming year 1602. If those learned in matters of Physics think them worthy of consideration, and communicate to me their objections to them, for the sake of eliciting the truth, I shall, if God grants me the skill, reply to them in my prognostication for the following year. I urge all who make a serious study of philosophy to engage (...) in this contest. For it concerns our worship of God and the welfare of the human race. Meanwhile, I pray from the depths of my soul, through Christ our mediator, that for all and for each the coming year may be a very happy one. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 381 Nature and Motion in the Middle.Ages. By FR. JAMES A. WEISHE,IPL. Edited by William E. Carroll. Studies in Philosophy and the History of Philosophy, v. 11. Washington, D.C.: The Catholic University of American Press, 1985. Pp. xii + 292. In this book the editor brings together some articles previously published by Fr. James Weisheipl which deal with various questions relating to Aristotle's natural (...) philosophy along with some medieval interpretations, mainly by St. Thomas Aquinas. The volume was not originally intended to be a posthumous offering, but Fr. James's untimely death has made it into one, and the editor provides a warm ' In Memoriam' at the end. During his fruitful scholarly career in medieval studies Weisheipl devoted much of his efforts to correcting what he took to be some basic modern misunderstandings of Aristotelian and medieval natural philosophy. A long-standing and still commonly held view has it that modern science became possible only after a total and unequivocal rejection of Aristotle's understanding of physical science. According to this theory, science as we now understand it appeared only in the seventeenth century. which is to say long after the close of the Middle Ages (pp. 261 ff.) and therefore, apart from purely historical interest, there remains nothing to be gained from a study of the medieval view of science. In the last century, however, Pierre Duhem argued that heretofore unrecognized linkages exist between modern science and the much earlier efforts by Aristotle and his medieval interpreters. Following Duhem's pioneering work, more recent scholarship has increased still further our knowledge of the relationship between early and modern science, with some (e.g. A. Maier) emphasizing elements of discontinuity and others (e.g. Weisheipl ) pointing out some long neglected but nonetheless philosophically sound and therefore still valuable insights of Aristotle and his medieval disciples. Weisheipl argues that the Aristotelian/medieval notion of nature is perfectly compatible with what he terms the physico-mathematical approach so profitably adopted by modern science. (ch. 11) He rejects the idea that the scientist, after the weleome advances of men like Galileo and Newton, is henceforward correct in replacing the earlier concept of nature with a purely mechanistic model of the universe. The more recent fruitful application of the physico-mathematieal method in science, far from requiring the rejection of Aristotle's concept of nature in favor of a nature-less mechanical model, finds a needed complimentarity with its inclusion as a sure foundation. Taking Aristotle's lead, Albert the Great, Aquinas, and others in fact, Weisheipl argues, were quite well aware of 38~ BOOK REVIEWS the more mathematically grounded method in studying nature. The work they did especially in astronomy, optics, and harmonics, W eisheipl points out, clearly reveals their belief in the heuristic power of mathematics. He readily admits that the earlier attempts to ' save the appearances ' with relatively primitive mathematical tools pale in comparison with the modern achievement, but he thinks the fundamental instinct so remarkably exploited by later scientists is already evident in earlier times. At the core of Weisheipl's exposition of Aristotelian/medieval science is the basic concept of nature, and the frequent failure of scholars to understand this concept conectly is, in his view, the major underlying reason for so much confusion. " For Aristotle..., v. (shrink)

In his Essay concerning Human Understanding, John Locke explicitly refers to Newton’s Philosophiae naturalis principia mathematica in laudatory but restrained terms: “Mr. Newton, in his never enough to be admired Book, has demonstrated several Propositions, which are so many new Truths, before unknown to the World, and are farther Advances in Mathematical Knowledge” (Essay, 4.7.3). The mathematica of the Principia are thus acknowledged. But what of philosophia naturalis? Locke maintains that natural philosophy, conceived as natural science (...) (as opposed to natural history), would give us demonstrations of the necessary connection between the (ultimately, simple) ideas constitutive of our complex ideas of various natural kinds of substances (e.g., gold). Indeed Locke goes so far as to suggest that a completely adequate natural science would also realize (perhaps, per impossibile) the goal of transforming the corpuscularian hypothesis into knowledge by demonstrating the necessary connection between the ‘microstructure’ (primary qualities of insensible corpuscles) of a particular natural kind of substance (e.g., gold) and the ideas of secondary qualities constitutive of the complex idea of that kind of substance. Locke’s conclusion concerning the possibility of the development of a natural science thus conceived is pessimistic: In vain therefore shall we endeavor to discover by our Ideas, (the only true way of certain and universal knowledge,) what other Ideas are to be found constantly joined with that of our complex Idea of any Substance: since we neither know the real Constitution of the minute Parts, on which their Qualities do depend; not, did we know them could we discover any necessary connexion between them, and any of their Secondary Qualities: which is necessary to be done, before we can certainly know their necessary co-existence (Essay, 4.3.14). It is understandable that, with such a conception of the science of nature, Locke found little of it in Newton’s Principia. In this paper, I further explore what might, perhaps with some hyperbole, be termed Locke’s ‘disappointment’ with the Prinicipia as a contribution to natural science. In particular, I argue that Locke’s adherence to the idealist epistemology of the Way of Ideas entails that mathematics cannot lend its certainty as a scientia to natural philosophy. Consequently, he finds more mathematics than natural philosophy in the Principia. (shrink)

This book describes how and why the early modern period witnessed the marginalisation of astrology in Western natural philosophy, and the re-adoption of the cosmological view of the existence of a plurality of worlds in the universe, allowing the possibility of extraterrestrial life. Founded in the mid-1990s, the discipline of astrobiology combines the search for extraterrestrial life with the study of terrestrial biology – especially its origins, its evolution and its presence in extreme environments. This book offers a (...) history of astrobiology's attempts to understand the nature of life in a larger cosmological context. Specifically, it describes the shift of early modern cosmology from a paradigm of celestial influence to one of celestial inhabitation. Although these trends are regarded as consequences of Copernican cosmology, and hallmarks of a modern world view, they are usually addressed separately in the historical literature. Unlike others, this book takes a broad approach that examines the relationship of the two. From Influence to Inhabitation will benefit both historians of astrology and historians of the extraterrestrial life debate, an audience which includes researchers and advanced students studying the history and philosophy of astrobiology. It will also appeal to historians of natural philosophy, science, astronomy and theology in the early modern period. (shrink)

Although the mathematization of nature is a distinctive and crucial feature of the emergence of modern science in the seventeenth century, this volume shows that it was a far more complex, contested, and context-dependent phenomenon than the received historiography has indicated.0.

The article presents philosophical views on music in the context of the transformations of the worldview from Antiquity to the Modern Time. In this research author also mentions the contemporary issues, and uses her own philosophical concept of the music, which can be described as following: the value of music as a substance and the way of the valuable interaction of a person with the world affirm the essence of musical being, in which the invariable principle of Harmony, the principle (...) of Chaos-Form movement, is preserved. Music expresses the fluid essence of the world and changes of being in space and time. Philosophy of music as a field of philosophical knowledge considers music from ontological-epistemological and phenomenological-axiological prospectives, as something more than just a form of art. It explores the deep, ultimate foundations of the existence of music as such and the philosophical and aesthetic foundations of musical art. Since ancient times music has been a representation of the world in the human conscience and served as the harmonic equivalent of cosmological philosophy, mathematics, astronomy, and astrophysics. The scientific view on music was enriched in the Modern Time by the expanded view on the cosmo-sound space reflected in musical art, which at the same time transforms the mathematical ideas of geometricity, squareness etc. The tendency to create integral world music in the musical practice of the XX-XXI centuries explains the attempt of mankind to present music by modern methods of composing musical art as an expression of fear towards the secret Harmony of universal existence, and, on the other hand - as a form of search for salvation and mental balance, intuitively reflecting what is happening in natural science, which more and more points to the abyss of unknowable universe, and the unstable place of man in the world. (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)

A characteristic hallmark of medieval astronomy is the replacement of Ptolemy’s linear precession with so-called models of trepidation, which were deemed necessary to account for divergences between parameters and data transmitted by Ptolemy and those found by later astronomers. Trepidation is commonly thought to have dominated European astronomy from the twelfth century to the Copernican Revolution, meeting its demise only in the last quarter of the sixteenth century thanks to the observational work of Tycho Brahe. The present article seeks to (...) challenge this picture by surveying the extent to which Latin astronomers of the late Middle Ages expressed criticisms of trepidation models or rejected their validity in favour of linear precession. It argues that a readiness to abandon trepidation was more widespread prior to Brahe than hitherto realized and that it frequently came as the result of empirical considerations. This critical attitude towards trepidation reached an early culmination point with the work of Agostino Ricci, who demonstrated the theory’s redundancy with a penetrating analysis of the role of observational error in Ptolemy’s Almagest. (shrink)

Scholarly attempts to analyze the history of science sometime suffer from an imprecise use of terms. In order to understand accurately how science has developed and from where it draws its roots, researchers should be careful to recognize that epistemic regimes change over time and acceptable forms of knowledge production are contingent upon the hegemonic discourse informing the epistemic regime of any given period. In order to understand the importance of this point, I apply the techniques of historical epistemology to (...) an analysis of the place of the study of astrology in the medieval and early modern periods alongside a discussion of the “language games” of these period as well as the role of the “archeology of knowledge” in uncovering meaning in our study of the past. In sum, I argue that the term “science” should never be used when studying approaches to knowledge formation prior to the seventeenth century. (shrink)

In order to get rid of the contradictions he had identified in Ptolemy’s Astronomy, Ibn al-Haytham abandons cosmology and develops a purely kinematic description of the movement of the wandering stars. This description culminates with the proof that such a star, during its daily movement, reaches exactly one time a maximum height above the horizon and that any inferior height is reached exactly twice. The proofs of these facts necessitates new mathematical tools and Ibn al-Haytham is led to establish (...) very sophisticated statements concerning the variation of certain ratios of arcs of circles on the sphere. He also introduces the fruitful idea of assimilating a very small spherical triangle to a plane triangle. (shrink)

The Ikhwan al-Safa (Brethren of Purity), the anonymous adepts of a tenth-century esoteric fraternity based in Basra and Baghdad, hold an eminent position in the history of science and philosophy in Islam due to the wide reception and assimilation of their monumental encyclopaedia, the Rasa'il Ikhwan al-Safa (Epistles of the Brethren of Purity). This compendium contains fifty-two epistles offering synoptic accounts of the classical sciences and philosophies of the age; divided into four classificatory parts, it treats themes in mathematics, (...) logic, natural philosophy, psychology, metaphysics, and theology, in addition to didactic fables. Epistles 32 to 36 comprise the first five treatises in the third division of the Rasa'il, on the sciences of the soul and intellect. Combining Islamic revelation with Hellenistic philosophy, the Ikhwan delineate herein their metaphysical system. Epistles 32 and 33 present adaptations of the Pythagorean doctrines, and of Neo-Platonist leitmotifs, whereby a numerical analogy is applied to the unique and transcendent God, or the One, from whom all existence emanates. Epistle 34 takes up the pervasive theme of the correspondence between microcosm and macrocosm, situating the human being as the central link between the celestial and terrestrial realms. In Epistle 35, we find an explanation of the intellectual faculties of the individual human soul, whose ultimate aim is ascension to the timeless reality of pure intellect. Finally, Epistle 36 presents itself as the astrological epistle par excellence of the Rasa'il; from the coming-to-be of worms, to the emergence of religions and empires, nothing in the sub-lunar sphere escapes the determining influence of the celestial cycles. (shrink)

In this paper, I argue that major elements of Hume’s metaphysics and epistemology are not only directed at the inductive argument from design which seemed to follow from the success of Newton’s system, but also have far larger aims. They are directed against the authority of Newton’s natural philosophy; the claims of natural philosophy are constrained by philosophic considerations. Once one understands this, Hume’s high ambitions for a refashioned ‘true metaphysics’ or ‘first philosophy’, that is, (...) Hume’s ‘Science of Human Nature’, can be seen and evaluated in their proper light. Hume has three motives for his attack on Newton: his work is informed by and gives cover to superstitious beliefs; his project is not useful to the public; and its success generates a challenge to the independent authority of philosophy. This essay consists of five sections. First, I discuss Hume’s attitude toward Newton. Newton claims that natural philosophy should be the foundation for other sciences, while in the ‘Introduction’ to the Treatise Hume asserts the supremacy of the ‘science of man’. For Hume the human sciences can attain the high epistemic status of ‘proof’, while much of the physical sciences must do with lower forms of ‘probability’. Furthermore, Hume’s ‘rules by which to judge of causes and effects’ do not replicate Newton’s fourth Rule; this opens a gap between the ontologies and methodologies of Newton and Hume. Moreover, Hume’s account of causation is designed to undercut the reductionist bias of natural philosophy. According to Hume the parts of natural sciences that go beyond common life can be evaluated from the point of view of the science of man. I end with remarks on the philosophic origins and significance of Hume’s attack on Newton’s natural philosophy. I depart from two independent traditions of interpreting Hume. One tradition makes many references to Newton’s influence on Hume. On a more detailed level, proponents of this view may call attention to Hume’s ‘rules’, his ‘Experiments’ and ‘Anatomy’, his method of investigation, the application of Newtonian metaphors works (e.g., an ‘attraction’ in the ‘mental world’ on a par with that in the ‘natural world’ – the principles of association are, then, analogous to the laws of motion). Hume’s ‘science of man’ is said to be inspired by Newton’s science of nature. Hume wants his readers to feel that he is modeling his project on the successes of natural philosophy, exemplified by Newton. In the ‘Introduction’ to the Treatise and more explicitly in the opening pages of EHU, Hume suggests that his ‘science of man’ can parallel recent achievements in natural philosophy (especially planetary astronomy). Thus, my claim is not that Newton did not figure importantly in Hume’s philosophy, but, instead, that Hume’s project is in many respects more hostile to Newton’s achievements – as available to well-informed eighteenth-century readers – than many recent interpreters have realized. There is a different tradition that argues Hume simply did not understand Newton. Hume’s philosophy, thus, cannot do justice to Newtonian science. Hume’s lack of mathematical competence is said to be a barrier to his understanding of Newton’s mathematical natural philosophy. One finds this attitude behind the cranking of Bayesian machinery in John Earman’s attack on Hume’s treatment ‘Of Miracles’. However, this tradition begs the question; it takes the authority of ‘science’ for granted in Hume. Against this second tradition I argue that Hume did understand salient features of Newton’s methodology and position, although in ways often unappreciated by the first tradition mentioned above. For example, in his comments on Newton in the History of England, Hume discerns the (broad) outlines of Newton’s commitment to the method of analysis and synthesis (see Newton’s Opticks, Query 31) and how it differs from Boyle’s methodology. So, Hume has a subtle understanding of Newton’s methodology – even if one were to grant that he lacks appreciation of the role of mathematics in Newton’s natural philosophy. Leaving open the question whether Hume understood all the details of Newton’s system, Hume’s departures from Newton are best interpreted not as ‘ironic’, but as philosophically motivated. (shrink)

The discrepancy between the Aristotelian and the Ptolemaic astronomies led many medievals to regard the latter (and mathematical astronomy generally) as no more than a calculational device. This was the challenge that Copernicus and Kepler had to meet: How was one to show that a mathematically expressed astronomy could indicate that the earth really moves? Copernicus pointed to features of the planetary motions that he could explain but that Ptolemy could not. Kepler went much further. His account of the (...) planetary system yields a passable theory of why the planets move as they do; the geocentric account (now without the support of carrier spheres) most certainly cannot. The basic hypothesis that the sun is really at the center and the earth really in motion, he claims, is thus likely to be true. (shrink)

The Jesuit C.F. Milliet Dechales, author of one of the most famous early modern mathematical encyclopedias, Cursus seu mundus mathematicus, wrote a hundred-folio-page long treatise devoted to the “progress of mathematics,” which was published in the second, enlarged edition of his encyclopedia. His historical treatise covers the gamut of mixed mathematics—including astronomy, mechanics, optics, music, geography and navigation, ars tignaria, and architecture. The early modern historical narratives about the mathematical sciences, from Regiomontanus’s Oratio onwards, have been aptly characterized (...) by their literary form and goals rather than their historical content. Rhetoric, humanistic topoi, and philosophical filiation turned the histories of mathematics into powerful tools for different purposes. My account of Dechales’ tract on the “progress of mathematics” analyzes the ways in which it dovetails with Jesuit approaches to mathematics, provides legitimation to the mathematical sciences as well as to their authors, and contributes to define the role and boundaries of the discipline, in particular vis-à-vis natural philosophy. (shrink)

In this paper I present an alternative reading and interpretation of the cuneiform tablet BM 76829. I suggest that the obverse of the tablet contains a simple astrological scheme linking the sign of the zodiac in which a child is born to the maximum length of life, and that the reverse contains a copy of a scheme relating parts of the body to the signs of the zodiac.

At the end of the last century Paul Tannery published an article on geometry in eleventh-century Europe, which he began with the following statement:“This is not a chapter in the history of science; it is a study of ignorance, in a period immediately before the introduction into the West of Arab mathematics.”.