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.

Este artículo presenta el descubrimiento de un texto hasta ahora desconocido, llamado al-lstidrāk, obra de un astrónomo anónimo andalusí del siglo XI que conoció personalmente a Azarquiel y que planteó sus dudas acerca de la tradición astronómica griega. Sobre la base de este nuevo texto, el artículo pone en cuestión la idea que se ha venido manteniendo de que la tradición astronómica islámica fue sobre todo filosófica en al-Andalus y más matemática en Oriente. Se aducen además datos de ambos lados (...) del Mediterráneo que demuestran que hubo una continuidad y unos contactos entre los dos extremos. El artículo mantiene que la falacia en esta caracterización de la astronomía islámica proviene de una falsa comparación entre las obras de filósofos occidentales con la de astrónomos orientales; cuando se comparan las obras astronómicas del Este y del Oeste queda claro que fueron los mismos problemas los que se plantearon en obras astronómicas en todo el orbe islámico. También se hace evidente que astrónomos orientales como Ibn al-Shāṭir de Damasco estaban sensibilizados a las mismas cuestiones filosóficas que preocupaban a los filósofos andalusíes y respondieron a estas cuestiones con sus propias respuestas filosóficas. (shrink)

According to selective, retentive, scientific realism, past empirical success may be explained only by the parts of past theories that are responsible of their successful predictions being approximately true, and thus theoretically retained, or approximated, by the parts of posterior theories responsible of the same successful predictions. In this article, we present as case study the transit from Ptolemy’s to Kepler’s astronomy, and their successful predictions for Mars’ orbit. We present an account of Ptolemy’s successful prediction of Mars’ orbit (...) from Kepler’s perspective, and scrutinize whether the theoretical elements responsible for Ptolemy’s empirical success are approximately retained in Kepler. In order to give to the realist the best chances, we try different strategies. We conclude that all fail and thereby this case constitutes a prima facie strong anomaly for selective retentive realism. Structural realists may call preservation of structure to the rescue, but the existing notions of structure do not work. In absence of a new notion that works, the burden of the proof lies on the realist side. (shrink)

Some variants in the materials related to the planetary latitudes, including computational procedures, underlying parameters, numerical tables, and so on, may be addressed in the corpus of the astronomical tables preserved from the medieval Islamic period, which have already been classified comprehensively by Van Dalen. Of these, the new values obtained for the planetary inclinations and the longitude of their ascending nodes might have something to do with actual observations in the period in question, which are the main concern of (...) this paper. The paper is in the following sections. In the first section, Ptolemy’s latitude models and their reception in Islamic astronomy are briefly reviewed. In the next section, the medieval non-Ptolemaic values for the inclinations and the longitudes of the nodal lines are introduced. The paper ends with the discussion and some concluding remarks. The derivation of the underlying inclination values from the medieval planetary latitude tables and determining the accuracy of the tables are postponed to “Appendix” in the end of the paper. (shrink)

As early as the ninth century, Muslim astronomers started refining the Ptolemaic astronomy which, by this time, had been fully adopted as the framework of their research. Already, in the early part of this century, refinements were based on improved observational techniques, and included a variety of phenomena such as the length of the seasons, the solar equation, mean motion parameters, and many others.

This book provides the first presentation of the bilingual textual material that illustrates the transmission of Islamic astronomy to scientists of the Indian Sanskritic tradition. It includes editions of the chapter of the _Tadhkira_ in which the mid-thirteenth century Persian astronomer, Nasīr al-dīn al-ṭūsī discussed the new solutions that he devised to overcome certain technical problems in the lunar and planetary models of Ptolemaic astronomy and of the learned commentary composed by al-Birjandī in the early sixteenth century (...) together with the Sanskrit translation of both made by Nayanasukha at Jaipur in 1729. An English translation of the Arabic texts and a commentary discussing their technical meanings and the deviations from them in the Sanskrit version together with a glossary of the Arabic and Sanskrit technical vocabulary conclude the volume. (shrink)

The gravitational influence of Jupiter on Saturn produces, among other things, non-negligible changes in the eccentricity of Saturn that affect the magnitude of error of Ptolemaic astronomy. The value that Ptolemy obtained for the eccentricity of Saturn is a good approximation of the real eccentricity—including the perturbation of Jupiter—that Saturn had during the time of Ptolemy's planetary observations or a bit earlier. Therefore, it seems more probable that the observations used for obtaining the eccentricity of Saturn were done (...) near Ptolemy’s time, and rather unlikely earlier than the first century AD. Even if this is not quite a demonstration that Ptolemy used observations of his own, my argument increases its probability and practically discards the idea that Ptolemy borrowed values or observations from astronomers further back than the first century AD, such as Hipparchus or the Babylonians. (shrink)

ArgumentIn theAlmagest, Ptolemy finds that the apogee of Mercury moves progressively at a speed equal to his value for the rate of precession, namely one degree per century, in the tropical reference system of the ecliptic coordinates. He generalizes this to the other planets, so that the motions of the apogees of all five planets are assumed to be equal, while the solar apsidal line is taken to be fixed. In medieval Islamic astronomy, one change in this general proposition (...) took place because of the discovery of the motion of the solar apogee in the ninth century, which gave rise to lengthy discussions on the speed of its motion. Initially Bīrūnī and later Ibn al-Zarqālluh assigned a proper motion to it, although at different rates. Nevertheless, appealing to the Ptolemaic generalization and interpreting it as a methodological axiom, the dominant idea became to extend it in order to include the motion of the solar apogee as well. Another change occurred after correctly making a distinction between the motion of the apogees and the rate of precession. Some Western Islamic astronomers generalized Ibn al-Zarqālluh's proper motion of the solar apogee to the apogees of the planets. Analogously, Ibn al-Shāṭir maintained that the motion of the apogees is faster than precession. Nevertheless, the Ptolemaic generalization in the case of the equality of the motions of the apogees remained untouchable, despite the notable development of planetary astronomy, in both theoretical and observational aspects, in the late Islamic period. (shrink)

Levi ben Gerson (1288–1344) was a medieval astronomer who responded in an unusual way to the Ptolemaic tradition. He significantly modified Ptolemy’s lunar and planetary theories, in part by appealing to physical reasoning. Moreover, he depended on his own observations, with instruments he invented, rather than on observations he found in literary sources. As a result of his close attention to the variation in apparent planetary sizes, a subject entirely absent from the Almagest, he discovered a new phenomenon of (...) Mars and noticed a serious flaw in Ptolemy’s treatment of the Moon. (shrink)

ArgumentThe present paper is an attempt to understand how medieval astronomers working within the Ptolemaic astronomical context in which the annular eclipse is an unjustified and impossible phenomenon, could know, define, justify, and later make attempts that led to success in predicting annular solar eclipses. As a context-based study, it reviews the situation of annular eclipses with regard to the medieval hypotheses applied to the calculation of the angular diameters of the sun and the moon, which was basic for (...) contemplating the possibility of annular eclipses. This gives the premises and the preliminary insights that were necessary to clarify the complex situation of the annular eclipse in the late medieval Islamic period and to explain the historical mechanisms leading to justifying the phenomenon during that period. This was, first due to a convincing and efficient observational evidence which, of course, was available only to a number of medieval astronomers and significantly for only a limited time period, and, second, the result of an amazing interaction amongst various astronomical traditions available to them. At a more general level, the research aims to inspect or, at least, to give some impressions of the essential conditions, i.e., identification of phenomenon, empirical evidence, and the justifying underlying tradition, under which it became possible in the tradition-based science of the `medieval period to permit a not-already-defined and tradition-opposed phenomenon to be posed and justified. (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)

Antonino Saliba, a sixteenth century cartographer hailing from the Maltese island of Gozo, published a map in 1582 espousing his cosmology. Its popularity at the time is attested via the multiple editions and copies that were produced in Europe. Numerous sky phenomena, amongst them comets, are portrayed in the map. This study presents a detailed analysis of Saliba's treatment of these phenomena, following the first comprehensive translation of the map's text to English. It elucidates the sources that Saliba used, clarifying (...) and shedding further light on the views he held. Where possible, the comets mentioned by Saliba are identified and explained. Besides showing how Saliba wholly conformed to the Aristotelian and Ptolemaic representation of the world, in which respect he was quite orthodox, it is also shown for the first time that his work is significantly derived from previous and contemporary sources. (shrink)

As a leading scientist of the 13th century C. E. Quṭb al-Dīn Shīrāzī wrote three substantial works on hay'a (or the configuration of the celestial orbs): Nihāyat al-idrāk fī dirāyat al-aflāk ("The Limits of Attainment in the Understanding of the Heavens"), al-Tuḥfa al-shāhīya fī 'ilm al-hay'a ("The Royal Offering Regarding the Knowledge of the Configuration of the Heavens"), and Ikhtīyārāt-i Muẓaffarī ("The Muẓaffarī Elections"). Completed in less than four years and written in two of the classical languages of the Islamic (...) world, Arabic and Persian, these works provide a fascinating window to the astronomical research carried out in Ilkhanid Persia. Shīrāzī and his colleagues were driven by their desire to rid Ptolemaic astronomy from its perceived shortcomings. An intriguing trail of revisions and emendations in Shīrāzī's hay'a texts serves to highlight both those features of Shīrāzī's astronomy that were inherited from his predecessors, as well as his original contributions to this branch of astronomical research. As a renowned savant, Shīrāzī spent a large portion of his career near centers of political power in Persia and Anatolia. A study of his scientific output and career as a scholar is an opportunity, therefore, for an examination of the patronage of science and of scientific works within the Ilkhanid realms. Not only was this patronage important to the work of scholars such as Shīrāzī but it was critical to the founding and operation of one of the foremost scientific institutions of the medieval Islamic world, the Marāgha observatory. The astronomical tradition in which Shīrāzī carried out his research has many links, as well, to the astronomy of Early Modern Europe, as can be seen in the astronomical models of Copernicus. (shrink)

In a recent article, Okasha challenges Kuhn’s claim that there is no ‘neutral’ algorithm for theory choice. He argues using Arrow’s ‘impossibility’ theorem that — except under certain favourable conditions concerning the measurability and comparability of theoretical values — there are no theory choice algorithms at all, neutral or otherwise. But Okasha’s argument does not apply to important theory choice problems, among them the case of Copernican and Ptolemaic astronomy that much occupied Kuhn. The reason is that Kuhn’s (...) choice criteria can rank rival theories in only a few ways, which makes the analogue of Arrow’s domain assumption inappropriate. It is hard to see any consequences for Kuhn’s claim, or threat to the rationality of science. (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)

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)

Ŷābir b. Aflaḥ al-Išbīlī, conocido como Geber filius Afflay Hispalensis en la Europa medieval, fue un matemático y astrónomo teórico que probablemente floreció en Sevilla durante el primer cuarto del s. XII. Ŷābir b. Aflaḥ es un astrónomo medieval importante gracias a su obra principal, IIṣlāḥ al-Maŷisṭī, traducida al latín y al hebreo. Con el IIṣlāḥ al-Maŷisṭī, su autor pretende reescribir el Almagesto a la vez que introduce algunas correcciones. En 1984, A.I. Sabra, en su importante artículo «The Andalusian revolt (...) against Ptolemaic astronomy» llama la atención sobre un grupo de filósofo andalusíes, contemporáneos de Ŷābir b. Aflaḥ o que florecieron poco después que él —como Ibn Baŷŷa, Ibn Ṭufayl, Ibn Rušd, Maimónides y al-Biṭrūŷī —, quienes criticaron, desde un punto de vista cosmológico, los modelos astronómicos descritos en el Almagesto al no ser coherentes con la física aristotélica. La finalidad de este artículo es describir el tipo de críticas que hace Ŷābir b. Aflaḥ a Ptolomeo con el objeto de dilucidar si cabe considerarlo uno de los miembros de la rebelión andalusí contra la astronomía ptolemaica. La conclusión final es que las críticas de Ŷābir b. Aflaḥ no son de carácter cosmológico —si bien puedan tener consecuencias cosmológicas—, sino que son de carácter matemático y técnico. Así pues, no cabe considerarlo un miembro de la rebelión andalusí contra la astronomía ptolemaica. (shrink)

This article elaborates on McShea and Brandon’s idea that drift is unlike the rest of the evolutionary factors because it is constitutive rather than imposed on the evolutionary process. I show that the way they spelled out this idea renders it inadequate and is the reason why it received some objections. I propose a different way in which their point could be understood, that rests on two general distinctions. The first is a distinction between the underlying mathematical apparatus used to (...) formulate a theory and a concept proposed by that theory. With the aid of a formal reconstruction of a population genetic model, I show that drift belongs to the first category. That is, that drift is constitutive of population genetics in the same sense that multiplication is constitutive in classical mechanics, or that circle is constitutive in Ptolemaic astronomy. The second distinction is between eliminating a concept from a theory and setting its value to zero. I will show that even though drift can be set to zero just like the rest of the evolutionary factors, eliminating drift is much harder than eliminating those other factors, since it would require changing the entire mathematical apparatus of standard population genetic theory. I conclude by drawing some other implications from the proposed formal reconstruction. (shrink)

Ŷābir b. Aflaḥ al-Išbīlī, conocido como Geber filius Afflay Hispalensis en la Europa medieval, fue un matemático y astrónomo teórico que probablemente floreció en Sevilla durante el primer cuarto del s. XII. Ŷābir b. Aflaḥ es un astrónomo medieval importante gracias a su obra principal, IIṣlāḥ al-Maŷisṭī, traducida al latín y al hebreo. Con el IIṣlāḥ al-Maŷisṭī, su autor pretende reescribir el Almagesto a la vez que introduce algunas correcciones. En 1984, A.I. Sabra, en su importante artículo «The Andalusian revolt (...) against Ptolemaic astronomy» llama la atención sobre un grupo de filósofo andalusíes, contemporáneos de Ŷābir b. Aflaḥ o que florecieron poco después que él —como Ibn Baŷŷa , Ibn Ṭufayl , Ibn Rušd , Maimónides y al-Biṭrūŷī —, quienes criticaron, desde un punto de vista cosmológico, los modelos astronómicos descritos en el Almagesto al no ser coherentes con la física aristotélica. La finalidad de este artículo es describir el tipo de críticas que hace Ŷābir b. Aflaḥ a Ptolomeo con el objeto de dilucidar si cabe considerarlo uno de los miembros de la rebelión andalusí contra la astronomía ptolemaica. La conclusión final es que las críticas de Ŷābir b. Aflaḥ no son de carácter cosmológico —si bien puedan tener consecuencias cosmológicas—, sino que son de carácter matemático y técnico. Así pues, no cabe considerarlo un miembro de la rebelión andalusí contra la astronomía ptolemaica. (shrink)

This dissertation is about human knowledge of reality. In particular, it argues that scientific knowledge is bounded by historically available instruments and theories; nevertheless, the use of several independent instruments and theories can provide access to the persistent potentialities of reality. The replicability of scientific observations and experiments allows us to obtain explorable evidence of robust entities and properties. The dissertation includes seven chapters. It also studies three cases – namely, Higgs bosons and hypothetical Ϝ-particles (section 2.4), the Ptolemaic (...) and Kepler model of the planets (section 6.7), and the special theory of relativity (chapter 7). -/- Chapter 1 is the introduction of the dissertation. Chapter 2 clarifies the notion of the real on the basis of two concepts: persistence and resistance. These concepts enable me to explain my ontological belief in the real potentialities of human-independent things and the implications of this view for the perceptual and epistemological levels of discussion. On the basis of the concept of “overlapping perspectives”, chapter 3 argues that entity realism and perspectivism are complementary. That is, an entity that manifests itself through several experimental/observational methods is something real, but our knowledge of its nature is perspectival. Critically studying the recent views of entity realism, chapter 4 extends the discussion of entity realism and provides a criterion for the reality of property tokens. Chapter 5, in contrast, develops the perspectival aspects of my view on the basis of the phenomenological-hermeneutical approaches to the philosophy of science. This chapter also elaborates my view of empirical evidence, as briefly expressed in sections 2.5 and 4.5. Chapter 6 concerns diachronic theoretical perspectives. It first explains my view of progress, according to which current perspectives are broader than past ones. Second, it argues that the successful explanations and predictions of abandoned theories can be accounted for from our currently acceptable perspectives. The case study of Ptolemaic astronomy supports the argument of this chapter. Chapter 7 serves as the conclusion of the dissertation by applying the central themes of the previous chapters to the case study of special relativity theory. I interpret frame-dependent properties, such as length and time duration, and the constancy of the speed of light according to realist perspectivism. (shrink)

In an influential article, A. I. Sabra identified an intellectual trend from twelfth and thirteenth-century Andalusia which he described as the ‘‘Andalusian revolt against Ptolemaic astronomy.” Philosophers such as Ibn Rushd, Ibn Tufayl, and Maimonides objected to Ptolemy’s theories on philosophic grounds, not because of shortcomings in the theories' predictive accuracy. Sabra showed how al-Bitrūjī's Kitāb al-Hay'a attempted to account for observed planetary motions in a way that met the philosophic standards of those philosophers and others. In Nūr (...) al-‘ālam, the subject of this article, Joseph ibn Joseph ibn Nahmias endeavoured to improve upon al-Bitrūjī’s models. Levi Ben Gerson's Hebrew writings on astronomy criticized al-Bitrūjī, but Ibn Nahmias did not mention them. Nūr al-‘ālam deserves attention, too, because it is the first Arabic text on theoretical astronomy by a Jewish author to come to light. In the body of this article, I will describe and analyze Ibn Nahmias’ theory, from Nūr al-‘ālam, for the motion of the sun. (shrink)

Averroes defended philosophy by returning to the true Aristotle. For this purpose, Aristotle's book in which he explained the eternity, uniqueness and movement of the universe, occupied a place of special importance. But the Aristotelian philosopher had a hard time holding his own in the face of contradictions within the book and with respect to Aristotle's later works. In his early Compendium, later Paraphrase, and final Long Commentary of De Caelo, Ibn Rushd continued the efforts of the Hellenistic commentators in (...) order to integrate all the elements of his doctrine into a unified system, to harmonize his early cosmology with his later Metaphysics and to uphold his models of homocentric planetary spheres against the mathematical paradigm of Ptolemaic astronomy. By insisting throughout on demonstrative arguments based on rational principles, he asserted the philosophers' claim to irrefutable truth. (shrink)

Earlier than the Arabic-Latin transfer of Ptolemaic astronomy via the Iberian peninsula, a serious occupation with Arabic astronomy by Latin scholars took place in crusader Antioch in the first half of the twelfth century. One of the translators of Arabic science in the East was Stephen of Pisa, who produced a commented Latin version, entitled Liber Mamonis, of Ibn al-Haytham’s cosmography, On the Configuration of the World. Stephen’s considerations about the physical universe in relation to the doctrines (...) of Ptolemaic astronomy have hitherto received but little attention. The present paper discusses Stephen of Pisa’s treatment of the planetary spheres in regard to Ptolemy’s theory of oscillating deferents. Emphasis is given to geometric arguments in Stephen’s criticism of Ibn al-Haytham’s spherical model of the inner planets and to Stephen’s own attempt at an improved theory based on additional spheres. The paper argues that astronomical studies in Antioch were of an advanced level, involving independent judgement as well as an influence of contemporary trends in Arabic astronomy. (shrink)

Inhaltsverzeichnis/Table of Contents: Rudolf HALLER: Investigating Hintikka. David PEARS: Hintikka's Interpretation of Wittgenstein's Treatment of Sensation-Language. Allan JANIK: How Did Hertz Influence Wittgenstein's Philosophical Development? Ilkka NIINILUOTO: Hintikka and Whewell on Aristotelian Induction. Jan von PLATO: Illustrations of Method in Ptolemaic Astronomy. Peter SIMONS: New Categories for Formal Ontology. Henri LAUENER: How to Use Proper Names. Matti SINTONEN: Knowing and Making: Kantian Themes in Hintikka's Philosophy. Paul WEINGARTNER: A Note on Jaakko Hintikka's "Knowledge and Belief". Nenad MIŠ_EVI_: Naturalism (...) and Modal Reasoning. Ulrike LEOPOLD-WILDBURGER: Induction as a Connection between Philosophy, Psychology and Economics. A Plea for Experimental Research. John PASSMORE: Editing Russell's Papers: A Fragment of Institutional History. Rudolf HALLER: From Archives to Editions. (shrink)

Inhaltsverzeichnis/Table of Contents: Rudolf HALLER: Investigating Hintikka. David PEARS: Hintikka's Interpretation of Wittgenstein's Treatment of Sensation-Language. Allan JANIK: How Did Hertz Influence Wittgenstein's Philosophical Development? Ilkka NIINILUOTO: Hintikka and Whewell on Aristotelian Induction. Jan von PLATO: Illustrations of Method in Ptolemaic Astronomy. Peter SIMONS: New Categories for Formal Ontology. Henri LAUENER: How to Use Proper Names. Matti SINTONEN: Knowing and Making: Kantian Themes in Hintikka's Philosophy. Paul WEINGARTNER: A Note on Jaakko Hintikka's "Knowledge and Belief". Nenad MIŠ_EVI_: Naturalism (...) and Modal Reasoning. Ulrike LEOPOLD-WILDBURGER: Induction as a Connection between Philosophy, Psychology and Economics. A Plea for Experimental Research. John PASSMORE: Editing Russell's Papers: A Fragment of Institutional History. Rudolf HALLER: From Archives to Editions. (shrink)

The Second Day of Galileo's Dialogue was concerned mainly with the removal of objections raised against daily rotation of the earth. His novel doctrine of motion was preceded by twenty pages of preliminary conversation about cosmological aspects of the Copernican and Ptolemaic astronomies. About forty pages were then devoted, directly or indirectly, to the tower argument, and another fifty pages followed on matters relating to fall.

Ptolemy´s astronomy and the Galileo case: two historical and epistemological considerations The Galileo case is the most famous example of the encounter betwen science and Faith. The debate was centered, among others, in the field of epistemology and the history of science. The paper shows that the Galilean pretentions of interpreting the heliocentric hypothesis in a realistic way did not constituted a novelty, but rather it was a continuation of the most important Ptolemaic astronomical tradition. It also argues (...) that the Copernican hypothesis did not inaugurate, because of the introduction of the Earth´s motion, a new phase of conflict between astronomy and physics. This conflict already existed, at least, since the times of Ptolemy. (shrink)

The idea of reconciling Ptolemaic planetary theory with Aristotelian natural philosophy by imagining epicycles and eccentric deferents as three-dimensional orbs or orb-segments within larger spheres is frequently associated with Georg Peurbach and his widely read astronomy textbook, the Theoricae novae planetarum (1454). This article cautions against existing tendencies to overstate the originality or revolutionary force of this work by taking a closer look at the early history of the same Ptolemaic-Aristotelian compromise in a Latin European context. Using (...) previously unpublished or unused source material from the twelfth to early fourteenth centuries, it documents the gradual spread and acceptance of an orbicular interpretation of Ptolemy’s planetary models among astronomers and university teachers. (shrink)

In Paradigms and Barriers Howard Margolis offers an innovative interpretation of Thomas S. Kuhn's landmark idea of "paradigm shifts," applying insights from cognitive psychology to the history and philosophy of science. Building upon the arguments in his acclaimed Patterns, Thinking, and Cognition, Margolis suggests that the breaking down of particular habits of mind—of critical "barriers"—is key to understanding the processes through which one model or concept is supplanted by another. Margolis focuses on those revolutionary paradigm shifts— such as the switch (...) from a Ptolemaic to a Copernican worldview—where challenges to entrenched habits of mind are marked by incomprehension or indifference to a new paradigm. Margolis argues that the critical problem for a revolutionary shift in thinking lies in the robustness of the habits of mind that reject the new ideas, relative to the habits of mind that accept the new ideas. Margolis applies his theory to famous cases in the history of science, offering detailed explanations for the transition from Ptolemaic to cosmological astronomy, the emergence of probability, the overthrow of phlogiston, and the emergence of the central role of experiment in the seventeenth century. He in turn uses these historical examples to address larger issues, especially the nature of belief formation and contemporary debates about the nature of science and the evolution of scientific ideas. Howard Margolis is a professor in the Harris Graduate School of Public Policy Studies and in the College at the University of Chicago. He is the author of Selfishness, Altruism, and Rationality and Patterns, Thinking, and Cognition, both published by the University of Chicago Press. (shrink)

From the early ninth century until about eight centuries later, the Middle East witnessed a series of both simple and systematic astronomical observations for the purpose of testing contemporary astronomical tables and deriving the fundamental solar, lunar, and planetary parameters. Of them, the extensive observations of lunar eclipses available before 1000 AD for testing the ephemeredes computed from the astronomical tables are in a relatively sharp contrast to the twelve lunar observations that are pertained to the four extant accounts of (...) the measurements of the basic parameters of Ptolemaic lunar model. The last of them are Taqī al-Dīn Muḥammad b. Ma‘rūf’s trio of lunar eclipses observed from Istanbul, Cairo, and Thessalonica in 1576–1577 and documented in chapter 2 of book 5 of his famous work, Sidrat muntaha al-afkar fī malakūt al-falak al-dawwār. In this article, we provide a detailed analysis of the accuracy of his solar and lunar observations. (shrink)

This paper is a technical study of the systematic observations and computations made by Muḥyī al-Dīn al-Maghribī (d. 1283) at the Maragha observatory (north-western Iran, c. 1259–1320) in order to newly determine the parameters of the Ptolemaic lunar model, as explained in his Talkhīṣ al-majisṭī, “Compendium of the Almagest.” He used three lunar eclipses on March 7, 1262, April 7, 1270, and January 24, 1274, in order to measure the lunar epicycle radius and mean motions; an observation on April (...) 20, 1264, to determine the lunar eccentricity; an observation on August 29, 1264, to test the model; and another on March 15, 1262, for measuring the lunar parallax. In the second period of activity at the Maragha observatory, Shams al-Dīn Muḥammad al-Wābkanawī (c. 1254–1320) adopted all of al-Maghribī’s parameter values in his Zīj, but decreased his value for the mean longitude of the moon at epoch by 0;13,11∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\circ }$$\end{document}. By comparing the times of the new moons and lunar eclipses in the period of 1270–1320 as computed from the astronomical tables of the Maragha tradition with the true modern ones, it is argued that this correction was very probably the result of actual observations. (shrink)

In his Metrica, Hero provides four procedures for finding the area of a circular segment (with b the base of the segment and h its height): an Ancient method for when the segment is smaller than a semicircle, $$(b + h)/2 \, \cdot \, h$$ ( b + h ) / 2 · h ; a Revision, $$(b + h)/2 \, \cdot \, h + (b/2)^{2} /14$$ ( b + h ) / 2 · h + ( b / 2 (...) ) 2 / 14 ; a quasi-Archimedean method (said to be inspired by the quadrature of the parabola) for cases where b is more than triple h, $${\raise0.5ex\hbox{$\scriptstyle 4$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 3$}}(h \, \cdot \, b/2)$$ 4 / 3 ( h · b / 2 ) ; and a method of Subtraction using the Revised method, for when it is larger than a semicircle. He gives superficial arguments that the Ancient method presumes $$\pi = 3$$ π = 3 and the Revision, $$\pi = {\raise0.5ex\hbox{$\scriptstyle {22}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 7$}}$$ π = 22 / 7. We are left with many questions. How ancient is the Ancient? Why did anyone think it worked? Why would anyone revise it in just this way? In addition, why did Hero think the Revised method did not work when $$b > 3\;h$$ b > 3 h? I show that a fifth century BCE Uruk tablet employs the Ancient method, but possibly with very strange consequences, and that a Ptolemaic Egyptian papyrus that checks this method by comparing the area of a circle calculated from the sum of a regular inscribed polygon and the areas of the segments on its sides as determined by the Ancient method with the area of the circle as calculated from its diameter correctly sees that the calculations do not quite gel in the case of a triangle but do in the case of a square. Both traditions probably could also calculate the area of a segment on an inscribed regular polygon by subtracting the area of the polygon from the area of the circle and dividing by the number of sides of the polygon. I then derive two theorems about pairs of segments, that the reviser of the Ancient method should have known, that explain each method, why they work when they do and do not when they do not, and which lead to a curious generalization of the Revised method. Hero’s comment is right, but not for the reasons he gives. I conclude with an exploration of Hero’s restrictions of the Revised method and Hero’s two alternative methods. (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)

At the end of the sixteenth century astronomers and others felt compelled to choose among different cosmologies. For Tycho Brahe, who played a central role in these debates, the intersection of the spheres of Mars and the Sun was an outstanding problem that had to be resolved before he made his choice. His ultimate solution was to eliminate celestial spheres in favour of fluid heavens, a crucial step in the abandonment of the Ptolemaic system and the demise of Aristotelian (...) celestial physics. These debates involved issues that had not previously been part of astronomy, and had the effect of undermining the traditional hierarchy of the sciences. While this complicated story involves many scientific personalities of the sixteenth and seventeenth centuries, in the present paper we will concentrate on one figure who has been assigned an unnecessarily minor role in most histories of science: Christoph Rothmann. In the present paper we show that ‘the dissolution of the celestial spheres’ depends on arguments about the substance of the heavens, following a mistaken argument of Gemma Frisius, elaborated by Joannes Pena and appropriated by Rothmann. We next consider the status and origin of the doctrine, as presented by Brahe, that the heavenly spheres are solid, and the impact on Brahe of Rothmann's treatise on the comet of 1585. Rothmann provided several key ideas that enabled Brahe to develop his system, and we suggest in passing that Rothmann may also have precipitated Brahe's re-evaluation of his attempt to detect the parallax of Mars during the opposition of 1582–83. We offer a new account of this central piece of evidence for the Tychonic system. (shrink)

The book of Aristarchus of Samos, On the distances and sizes of the sun and moon, is one of the few pre-Ptolemaic astronomical works that have come down to us in complete or nearly complete form. The simplicity and cleverness of the basic ideas behind the calculations are often obscured in the reading of the treatise by the complexity of the calculations and reasoning. Part of the complexity could be explained by the lack of trigonometry and part by the (...) fact that Aristarchus appears unwilling to make some simplifications that could be simply taken for granted. But an important part of the complexities is due to some unnecessary inconsistencies, as recently discovered by Berggren and Sidoli (Arch Hist Exact Sci 61:213–254, 2007). In the first part of this paper, I will try to show that some of these inconsistencies are just apparent. But the complexity of the calculations and reasoning is not the only reason that could disturb a reader of the treatise. The great inaccuracy—even for the measurement methods and instruments available at those times—of one of the three input values of the treatise is really astonishing. In the sixth and last hypothesis, Aristarchus states that the moon’s apparent size is equal to 2∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\circ }$$\end{document}, while the correct value is one-fourth of that. Some attempts have been made in order to explain such a big value, but all of them have problems. In the second part of this paper, I will propose a new speculative but plausible explanation of the origin of this value. (shrink)

In this article, we report the discovery of a new type of astronomical almanac by Joseph Ibn Waqār (Córdoba, fourteenth century) that begins at second station for each of the planets and may have been intended to serve as a template for planetary positions beginning at any dated second station. For background, we discuss the Ptolemaic tradition of treating stations and retrograde motions as well as two tables in Arabic zijes for the anomalistic cycles of the planets in which (...) the planets stay at first and second stations for a period of time (in contrast to the Ptolemaic tradition). Finally, we consider some medieval astrological texts where stations or retrograde motions are invoked. (shrink)

It is argued that the origins of modern science can be revealed due to joint account of external and internal factors. The author tries to keep it in mind applying his scientific revolution model according to which the growth of knowledge consists in interaction, interpenetration and even unification of different scientific research programmes. Hence the Copernican Revolution as a matter of fact consisted in realization and elimination of the gap between the mathematical astronomy and Aristotelian qualitative physics in (...) class='Hi'>Ptolemaic cosmology. Yet the very realization of the contradictions became possible because at the first stages European science was a result of Christian Weltanschaugung evolution with its gradual elimination of pagan components. Key words: modern European science, Christian Weltanschaugung. (shrink)

After a chapter which is an introduction to and summary of the rest of the book, chapter 2 begins by criticizing various attempts to do away with theories, such as the Reichenbach-Salmon conception of theoretical truth in terms of observational consequences, and the Ramsey strategy of replacing first-order theoretical sentences by second-order nontheoretical ones; it then argues against hypothetico-deductivist theories of confirmation on the grounds that they are unable to handle the relevance of evidence to theory, whether or not other (...) formal constraints or even nonformal ones such as simplicity and explanatory power are added to those theories; it ends with an exposition of the Reichenbach-Carnap conventionalist thesis that the confirmation of hypotheses with evidence presupposes analytic principles connecting hypothetical and empirical concepts. Chapter 3 criticizes Bayesian theories of confirmation on such grounds as that the a priori arguments for Bayesian restrictions on beliefs are insufficient; that the Bayesian explanations of notions like variety of evidence, ad hocness, and simplicity are inadequate; and that they cannot account, without drastic revisions, for the relevance of evidence to theory, especially old evidence to new theory. Chapter 4 is an unsympathetic account of historically oriented philosophies of science; Lakatos’s notion of progressive research programs and Laudan’s theory of problem-solving effectiveness are found to be insufficiently precise and dubbed examples of "new fuzziness", while the Sneed-Stegmüller dynamics of theories is regarded as "a paradigm of misplaced rigor" ; and all three are criticized as unable to explicate the concept of evidential relevance. Chapter 5 is a formal and informal elaboration of the basic idea in Glymour’s account of theory and evidence, namely that confirmation or support is a three-term relation among evidence, hypothesis, and theory, so that evidence confirms an hypothesis only relative to a theory, and such that evidence e confirms hypothesis h relative to T if T with e implies, but T without e does not imply, an instance of h, and T with e does not imply a comparable hypothesis h’ different from h; the most interesting part of this chapter is a series of discussions showing how such an idea makes sense of the "methodological truisms" that it is possible selectively to test certain parts of a theory but not others, that a theory is supported better by a greater variety of evidence, that redundant or physically meaningless quantities are an undesirable feature of theories, that there are no inviolable rules, that a "white shoe" does not confirm "all ravens are black," that a theory is more useful and better supported than the set of its observational consequences, and that the hypothetico-deductive method often works. Since Glymour claims no originality for the conception of this general account, but only for its description, he plausibly thinks it necessary to apply it to some important historical cases of actual science; he does so in the next chapter by discussing at some length the structure and merits of Ptolemaic and Copernican astronomy, of Newton’s universal gravitation, of nineteenth century atomism, of Freud’s Rat Man, and of general relativity. For example, he argues convincingly that Copernicanism was better supported by the evidence available even before the telescope because it alone, and not the Ptolemaic theory, can determine some planetary properties which are presupposed by both theories, can test and confirm some common hypotheses, and can be confirmed in an essential rather than incidental manner; and though Glymour admits that the Copernicans tended to argue in terms of explanatory rather than confirmatory superiority, he sketches an interesting account of the relation between explanation and confirmation which strengthens his case. He also analyzes the text at the beginning of book 3 of Newton’s Principia and compiles a reconstruction of the intricate details of the inferential structure of the argument to universal gravitation; his impressive reconstruction clearly shows that Newton’s method is neither the inductivist one he himself thought he was following, nor the one attributed to him by Pierre Duhem, but rather one in accordance with Glymour’s so-called "bootstrap strategy" of repeatedly using the evidence from Kepler’s second and third laws, from lunar data, and from falling bodies, together with the theory consisting of the second and third laws of motion, to arrive at increasingly general instances of the principle of universal gravitation. Glymour’s account of arguments for and against the atomic theory from Thomson to Cannizzaro is his longest historical example, but he himself admits that this illustration of the bootstrap strategy is "certainly not the neatest", and rather "diffuse, and perhaps disconnected". Chapter 7 is a detailed application of the same principles to the technique known among social scientists as "causal modeling"; since such "causal models" are essentially systems of algebraic equations, Glymour’s account shows indirectly that the bootstrap strategy is applicable to any scientific theory presented as a set of algebraic equations; this, of course is not surprising, since the formal considerations with which Glymour begins the exposition of his theory in chapter 5 involve systems of algebraic equations. Chapter 8 is an attempt to apply Glymour’s theory of evidence to the very common scientific practice of curve-fitting, where one measures values of two or more quantities and then infers a functional relationship; Glymour argues that simpler polynomials are preferred because they are tested more frequently and more severely by the data and because they are more informative; but then he criticizes his own explanation and concludes that "the bootstrap procedures of chapter 5 do not seem to help the problem much more than a whit" ; this is admirably honest, but if one wants an additional logical or methodological rationale, then one would perhaps have to go to the meta-level and say that Glymour is here testing his own theory, and he is more interested in a further illustration of the bootstrap methodology even with a failed test, than he is to claim universal or exclusive validity for it. In chapter 9 Glymour uses his bootstrap theory of confirmation to criticize geometrical conventionalism; he considers the alternative theories of space or space-time proposed by conventionalists to show the radical undetermination of geometries by evidence, for example, a non-Euclidean geometry with no universal force instead of Newtonian gravitation with Euclidean geometry; he argues that such alternatives are simply not as well tested as the originals and that their equivalence to the originals is questionable. The last chapter is a brief discussion of further problems worthy of future investigation. (shrink)

A passage in Copernicus's De Revolutionibus regarding the rotation of the Earth provides evidence that he was aware, whether directly or indirectly, of an Islamic tradition dealing with this problem that goes back to Na[sdotu]īr al-Dīn al-[Tdotu]ūsī. The most striking similarity is the use of comets by both astronomers to discredit Ptolemy's “proofs” in the Almagest that depended upon observational evidence. The manner in which this question was dealt with by Copernicus, as an astronomical rather than natural philosophical matter, also (...) argues for his being within the tradition of late medieval Islamic astronomy, more so than that of medieval Latin scholasticism. This of course is bolstered by his use of non-Ptolemaic models, such as the [Tdotu]ūsī couple, that have a long history in Islam but virtually none in medieval Europe. Finally, al-Qūshjī, who was in Istanbul just before Copernicus was born, entertained the possibility of the Earth's rotation; this also opens up the possibility of non-textual transmission. (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)

The margravial court astronomer Simon Marius, was involved in all of the new observations made with the recently invented telescope in the early part of the seventeenth century. He also discovered the Moons of Jupiter in January 1610, but lost the priority dispute with Galileo Galilei, because he missed to publish his findings in a timely manner. The history of astronomy neglected Marius for a long time, finding only the apologists for the Copernican system worthy of attention. In contrast (...) the papers presented on the occasion of the Simon Marius Anniversary Conference 2014, and collected in this volume, demonstrate that it is just this struggle to find the correct astronomical system that makes him particularly interesting. His research into comets, sunspots, the Moons of Jupiter and the phases of Venus led him to abandon the Ptolemaic system and adopt the Tychonic one. He could not take the final step to heliocentricity but his rejection was based on empirical arguments of his time. This volume presents a translation of the main work of Marius and shows the current state of historical research on Marius. (shrink)

The publication in 1632 of Galileo’s Dialogue on the Two Chief World Systems, Ptolemaic and Copernican marked a crucial moment in the ‘scientific revolution’ and helped Galileo become the ‘father of modern science’. The Dialogue contains Galileo’s mature synthesis of astronomy, physics, and methodology, and a critical confirmation of Copernicus’s hypothesis of the earth’s motion. However, the book also led Galileo to stand trial with the Inquisition, in what became known as ‘the greatest scandal in Christendom’. In The (...) Routledge Guidebook to Galileo's Dialogue , Maurice A. Finocchiaro introduces and analyzes: the intellectual background and historical context of the Copernican controversy and Inquisition trial; the key arguments and critiques that Galileo presents on both sides of the ‘dialogue’; the Dialogue ’s content and significance from three special points of view: science, methodology, and rhetoric; the enduring legacy of the Dialogue and the ongoing application of its approach to other areas. This is an essential introduction for all students of science, philosophy, history, and religion wanting a useful guide to Galileo’s great classic. (shrink)

In this article, we aim at presenting a thorough and comprehensive explanation of the mathematical and theoretical relation between all the aspects of Ptolemaic planetary models and their counterparts which are built according to Kepler’s first two laws. Our article also analyzes the predictive differences which arise from comparing Ptolemaic and these ideal Keplerian models, making clear distinctions between those differences which must be attributed to the structural variations between the models, and those which are due to the (...) specific parameters Ptolemy determined in the Almagest. We expect that our work will be a contribution for a better understanding not only of the Ptolemaic theories for planetary longitudes through a clearer perception of the way in which Keplerian features are present—or absent—in Ptolemy’s models, but also for a more balanced judgement of different aspects of the contribution of the first two laws of Kepler to the modern astronomical revolution. (shrink)

I argue that Gilles-Gaston Granger (1920–2016) broadly incorporates the central affirmations of Jean Cavaillès’s (1903–44) philosophy of the concept into his own epistemological program. Cavaillès and Granger share three interrelated epistemological commitments: they claim (1) that mathematics has its own content and is therefore autonomous from and irreducible to logic, (2) that conceptual transformations in the history of mathematics can only be explained by an internal dialectic of concepts, and (3) that the objectivity of mathematics is an effect of the (...) productive form of its rationality—that is, they claim that mathematical objectivity is the result of a generative process internal to mathematics. Mathematical objectivity, as I demonstrate, requires Cavaillès and Granger to modify the limits of epistemological critique as envisioned by Kant. For Cavaillès, this modification requires the elimination of the transcendental in favor of a dialectic of concepts. For Granger, the philosophy of the concept remains a genre of transcendental critique, but in a radically revised “Ptolemaic” style. I initially demonstrate how Granger extracts each of these claims from Cavaillès. I then follow Granger as he develops these claims in the service of a novel description of the content and structure of mathematical objectivity. (shrink)