This article examines three passages of De caelo in order to discuss Aristotle’s epistemological attitude towards the theories advanced by him and towards the possibility of progress in the scientific research of the celestial world. I argue that, although the possibility of progress in scientific investigation is not central in Aristotle’s reflections, progress is not ruled out either as impossible or as undesirable.

ArgumentThis article is the sequel to an article published in the previous issue ofScience in Contextthat dealt with homeomeric lines (Acerbi 2010). The present article deals with foundational issues in Greek mathematics. It considers two key characters in the study of mathematical homeomery, namely, Apollonius and Geminus, and analyzes in detail their approaches to foundational themes as they are attested in ancient sources. The main historiographical result of this paper is to show thatthere wasa well-establishedmathematicalfield of discourse in “foundations of (...) mathematics,” a fact that is by no means obvious. The paper argues that the authors involved in this field of discourse set up a variety of philosophical, scholarly, and mathematical tools that they used in developing their investigations. (shrink)

Archimedes’ Sand-Reckoner presents a system for naming extraordinarily large numbers, larger than the number of grains of sand that would fill the cosmos. Curiously, Archimedes addresses the treatise not to another specialist but to King Gelon II of Syracuse. While the treatise has thus been seen as evidence for the dynamics of patronage, difficulties in both Archimedes’ treatment of Gelon and his discussion of astronomical models make it fit incongruously within contemporary court and scientific contexts. This article offers a new (...) reading of the Sand-Reckoner based on a reconsideration of the relationship between author and addressee: deferring assumptions about the historicity of that relationship, it analyzes Gelon’s role in the treatise with respect to both the stylistic features of Archimedes’ prose and a broader tradition of narratives about a variety of cultural actors who engage with kings, speaking not so much truth as wit to power. Such a reading resolves the social and scientific difficulties of the treatise, and develops the literary-experimental qualities of Hellenistic science. In turn, the article proposes a revised approach, sensitive to broader patterns of authorship, to understanding ancient scientific authors’ relationship to royal authority. It concludes, finally, that the royal patronage seemingly exemplified by the Sand-Reckoner had greater significance as a cultural trope than as a social institution. (shrink)

An interesting question arises in the context of the typically medieval description of the universe presented at the beginning of Maimonides' great law code, the Mishneh Torah. What was Maimonides' own attitude towards that account? Was it meant only as a statement of the best description of nature available at the time matters which make up the bulk of the Mishneh Torah) or was it meant to be a description of the true nature of the universe as it really is, (...) not subject to revision in the light of new paradigms or new models ? Answering this question will lead us to a better understanding of Maimonides' understanding of the nature of science and of what I shall call, for lack of a better term, scientific progress. Maimonides will be shown to hold that while sublunar science can reach perfection and completion such is not possible for superlunar science and that to the extent that the scientific matters in the Mishneh Torah deal with the latter they could not have been presented as the final description of the universe as it truly is. (shrink)

ArgumentThe purpose of this paper is to provide an analysis of Giordano Bruno’s conception of mathematics. Specifically, it intends to highlight two aspects of this conception that have been neglected in previous studies. First, Bruno’s conception of mathematics changed over time and in parallel with another concept that was central to his thought: the concept of infinity. Specifically, Bruno undertook a reform of mathematics in order to accommodate the concept of the infinitely small or “minimum,” which was introduced at a (...) later stage. Second, contrary to what Héléne Védrine claimed, Bruno believed that mathematical objects were mind-dependent. To chart the parallel development of the conceptions of mathematics and infinity, a seven-year time span is considered, from the publication of Bruno’s first Italian dialogue (La cena de le ceneri,1584) to the publication of one of his last Latin works (De minimo, 1591). (shrink)

Duhem has generally been understood to have maintained that the major Greek astronomers were instrumentalists. This view has emerged mainly from a reading of his 1908 publication To Save the Phenomena. In it he sharply contrasted a sophisticated Greek interpretation of astronomical models (for Duhem this was that they were mathematical contrivances) with a naive insistence of the Arabs on their concrete reality. But in Le Système du monde, which began to appear in 1913, Duhem modified his views on Greek (...) astronomy considerably; his more subtle understanding included the recognition that many Greeks subordinated mathematical astronomy to physical theory. But he could not completely repudiate his earlier views about Greek astronomy in part because his extreme nineteenth century prejudices led him to continue to insist on a clear-cut demarcation between Greek and Arabic astronomy. The inevitable result is a certain unevenness in the Système and some glaring inconsistencies. (shrink)

Journal Name: Apeiron Issue: Ahead of print.

This article makes two claims. The first is that Archimedes’ On Floating Bodies included a punning reference, in its key diagrammatic figure AΠΟΛ: the precise purpose of the pun may not be recovered by us, but even so it remains a powerful example of the playful in Archimedes’ writing. The second is that Apollonius could have been Archimedes’ younger contemporary. The outcome could be that we find Archimedes addressing a playful, hidden message to Apollonius, providing us with a unique insight (...) into the communication of Greek mathematics. (shrink)

RésuméLa théorie avicenienne du mouvement des orbes célestes représente un aspect important de sa cosmologie qui n'a cependant pas encore été l'objet d'une étude approfondie. Cet article compte combler ce manque en fournissant une analyse des différents principes à l'origine du mouvement céleste, ainsi qu'une réflexion sur le rôle des disciplines astronomique, physique, et métaphysique dans les explications que fournit Ibn Sīnā à ce sujet. L'accent est mis sur le rapport des intelligences aux orbes et sur la problématique du passage (...) de l'intellectif au physique, un moment charnière dans la cinématique avicenienne. En outre, l'étude remet en question l'adhésion d'Ibn Sīnā à la théorie farabienne des dix intelligences et entreprend une reconstitution de son modèle cosmologique. (shrink)

Pierre Duhem rejected unambiguously the strong version of realism that he believed was held by Copernicus. In fact, although Copernicus believed that his theory was clearly superior to Ptolemy's, he seems to have recognized that his theory was at best only approximately true. Accordingly, he recognized that his arguments were not demonstrative in the traditional sense but probable and persuasive. Duhem regarded even the belief in probably true explanations as misguided. Nevertheless, Duhem recognized that, even if metaphysical intuition does not (...) enter into the content of physical theories, the rejection of hypotheses could be explained only by appeal to common sense. Hence, Duhem held a qualified instrumentalism according to which physical theories are not realist, but the terms of ordinary experience and empirical laws are realist. Accordingly, Duhem rejected the complete subordination of science to philosophy as well as the complete separation of science from philosophy. Duhem's history of cosmological doctrines reflects his belief in the origin of the subordination of science to philosophy and of the struggle to achieve the proper balance without being driven to the opposite extreme of their complete separation. (shrink)

The theology as enabler of a more human science Paul Karl Feyerabend conceives religion as a possible way to infuse meaning and humanity to the science. He asserts that when it has taken place historically a unity between science and religion, science has been able to transcend values of utility and efficiency. This happens because the religion confers meaning to scientific results within an image of the world that involves the person as a whole. In this context, the Viennese invites (...) to establish a dialogue with the science of ancient Greece in order to know more about more human ways of doing science and to be able to judge in perspective the achievements of scientific materialism. Our objective in this work will be to attend to this invitation of Viennese studying the relation that exists between mathematics and theology in the Ptolemaic writings. We believe that the Alexandrian is an emblematic case of this communion between science and theology and –in this sense– allows us to rethink contemporary science as a cognitive task more attentive to the human and existential implications of its theories and models. (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)

The author examines the question of Galen's affinity with astrology, in view of Galen's extended astrological discussion in the De diebus decretoriis . The critical passages from Galen are examined, and shown to be superficial in understanding. The author performs a lexical sounding of Galen's corpus, using key terms with astrological valences drawn from the Critical Days, and assesses their absence in Galen's other works. He compares Galen's astrology with the astrology of Ptolemy's Tetrabiblos, and evaluates their respective strategies of (...) scientific reasoning. Three types of inference are introduced and applied to Galen's astrology. Finally, he concludes that the empirical side of Galen's science does not depend upon astrological methods or concepts, but that these were introduced for their rhetorical effect in presenting his new medical methodology. It is suggested that continued attention to Galen's astrology has obscured the truly important empirical scientific method that Galen developed. (shrink)

It is well known that heliocentrism was proposed in ancient times, at least by Aristarchus of Samos. Given that ancient astronomers were perfectly capable of understanding the great advantages of heliocentrism over geocentrism—i.e., to offer a non-ad hoc explanation of the retrograde motion of the planets and to order unequivocally all the planets while even allowing one to know their relative distances—it seems difficult to explain why heliocentrism did not triumph over geocentrism or even compete significantly with it before Copernicus. (...) Usually, scholars refer to explanations of sociological character. In this paper, I offer a different explanation: that the pre-Copernican heliocentrism was essentially different from the Copernican heliocentrism, in such a way that the adduced advantages of heliocentrism can only be attributed to Copernican heliocentrism, but not to pre-Copernican heliocentrism proposals. (shrink)

Pretendemos averiguar como Aristóteles concebe a passagem do nosso conhecimento prévio do mundo ao conhecimento científico, avaliando os pressupostos e consequências de sua resposta ao paradoxo de Mênon e atentando para a metodologia científica defendida nos Segundos Analíticos. Quanto ao conhecimento preliminar necessário à edificação da ciência, procuraremos caracterizar seus tipos e também os meios pelos quais ele pode vir a ser adquirido por nós. Buscaremos estabelecer também as propriedades que o conhecimento científico deve possuir em relação à sua necessidade, (...) universalidade e caráter explanatório. Buscaremos marcar, com precisão, a natureza da conclusão científica segundo a teoria científica aristotélica, argumentando que, nas conclusões, o atributo demonstrado, em relação com seu substrato, representa uma propriedade por si concomitante. Pretendemos averiguar como os diferentes tipos de demonstração e definição respondem a diferentes estágios de organização do saber prévio e a diferentes estágios na estruturação das demonstrações propriamente científicas, e, por conseguinte, como esses se organizam de modo a responder as quatro perguntas que toda investigação científica deve abarcar em seus dois estágios. (shrink)

Our purpose is to study Aristotle?s solution, in the second book of the Posterior Analytics, for the problem of the apprehension of the principles of science. We attend to the relations between the concepts of induction (epagoge) and intelligence (nous) found in the chapter 19, which seems to confirm that the acquisition of the principles is reached by a process of empirical observation. We examine the method, proposed in chapters 13 to 17, for the right formulation of definitions, which seems (...) to attribute to dialectics the task of finding the principles. Aristotle seems to indicate two different methods ? on one hand, the empirical observation followed by intelligence, on other, the dialectics ? for the apprehension of the principles. Our purpose is to study possible solutions for the problem of the concurrence between these two methods in order to refute as much a strictly empiricist interpretation as a strictly dialectical one. (shrink)

This dissertation offers a new and comprehensive analysis of Abū Naṣr al-Fārābī's cosmology by focusing on various important issues that have been largely neglected by the modern scholarship. It provides an examination of the physical, metaphysical, and astronomical aspects of al-Fārābī's cosmology by adopting a multidisciplinary approach that takes into account the history of philosophy and the history of astronomy. Accordingly, my dissertation explores how al-Fārābī attempted to reconcile features of Ptolemaic astronomy with Aristotelian and Neoplatonic theories, an endeavor which (...) resulted in the formulation of innovative cosmological ideas. Chapters I and II provide background information on al-Fārābī's activity as a commentator and his relation to the Greek commentatorial tradition and assess the relevant primary sources. In addition, they examine al-Fārābī's approach to cosmology and his scientific method in terms of both the Ptolemaic astronomical tradition and the Aristotelian corpus. Chapter III addresses problems related to the structure of al-Fārābī's cosmology, especially the origin of his ennadic cosmological model and his spherology. Particular attention is devoted to the question of how Aristotle's unmoved movers and Ptolemy's astronomical theories are reconciled. Chapters IV, V, and VI analyze the place of celestial matter, intellect, and motion respectively in al-Fārābī's cosmology and attempt to redefine the second teacher's relation to the various trends of Greek philosophy. The study stresses al-Fārābī's connection with the Neoplatonic and Peripatetic currents, particularly with thinkers such as Alexander of Aphrod. (shrink)

Thesis (Ph. D.)--University of Hawaii at Manoa, 1996.

One of the hardest questions to answer for a (Neo)platonist is to what extent and how the changing and unreliable world of sense perception can itself be an object of scientific knowledge. My dissertation is a study of the answer given to that question by the Neoplatonist Proclus (Athens, 411-485) in his Commentary on Plato’s Timaeus. I present a new explanation of Proclus’ concept of nature and show that philosophy of nature consists of several related subdisciplines matching the ontological stratification (...) of nature. Moreover, I demonstrate that for Proclus philosophy of nature is a science, albeit a hypothetical one, which takes geometry as its methodological paradigm. I also offer an explanation of Proclus’ view of what is later called the mathematization of physics, i.e. the role of the substance of mathematics, as opposed to its method, in explaining the natural world. Finally, I discuss Proclus’ views of the discourse of philosophy of nature and its iconic character. (shrink)