The Logic of Port-Royal, first published in 1662 by the Jansenists Antoine Arnauld and Pierre Nicole, is a work that underlines the inadequacies of the traditional logic. Traditional logic, which included the texts of Aristotle's Organon and the works of the scholastics, was experiencing a mild renaissance in the seventeenth century following its outright and brutal discrediting by the humanists of the previous two centuries. Arnauld and Nicole introduce a fairly original system of logic that attempts to remedy the shortcomings (...) of the revived tradition; they dismiss the Aristotelian "Categories", "Predicables", and "Topics", ignore the scholastic "Doctrine of Terms and Consequence", and suggest a single "General Principle" by means of which the validity of all arguments can be decided. The Principle is based on a notion of containment, divided into entendue and comprehension , which applies to all terms. Because the notion of containment is linked to the objective reality of Cartesian ideas, the authors can claim that their system of logic properly describes reality. The General Principle also suggests that terminist logic is logically and epistemologically prior to sentential logic because, Arnauld and Nicole claim, it governs the Dictum de Omni et Nullo and the Nota Notae. The self-evidence of the two dicta confirmed the validity of all syllogisms of the first figure; furthermore, all syllogisms of other figures could be reduced to one of the first figure. With the General Principle, however, there is no need for such reduction to the first figure. This additional result makes the theorem of sentential logic, "$\supset$r)$\approx$$\supset$-q)", which was needed for the reductions of Baroco and Bocardo, unnecessary. The fact that no theorem of sentential logic is needed to underline term logic guarantees the autonomy of the latter. (shrink)

From Bernard Boxill, professor of philosophy at the University of North Carolina at Chapel Hill and editor of Race and Racism, comes a tightly-argued, very illuminating book that will be essential reading for anyone interested in ...

Kant claimed that we have a duty to seek peace, and encouraged a hope for peace to support that duty. To encourage that hope he argued that peace was reasonably likely. He thought that peace was reasonably likely because he believed that historical trends would create opportunities to implement his plan for peace. But authorities claim that globalization is undermining such opportunities. Consequently Kant's arguments can no longer sustain our hope for peace. We can sustain that hope by devising a (...) new plan for peace that globalization will give us opportunities to implement. But in order to devise such a plan we need to sustain our hope for peace. We can sustain such a hope by reflecting on the value of peace because hope is sustained not only by the belief that the object of hope is likely, but also by the conviction that it is valuable. In this way we can perhaps sustain a hope for peace that will support our duty to seek peace. But the fear of war and compassion for the victims of war may also support the duty to seek peace. Kant ignored these opportunities to support the duty to seek peace because they could support only the duty to avoid war. But Kant never showed that the duty to seek peace—as he saw it—outweighed the duty to avoid war. I conclude that Kant's arguments lead us to endless war rather than to peace. (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)

In this paper, we analyze the astronomical tables in al-Zīj al-Muqtabis by Ibn al-Kammād (early twelfth century, Córdoba), based on the Latin and Hebrew versions of the lost Arabic original, each of which is extant in a unique manuscript. We present excerpts of many tables and pay careful attention to their structure and underlying parameters. The main focus, however, is on the impact al-Muqtabis had on the astronomy that developed in the Iberian Peninsula and the Maghrib and, more generally, on (...) the transmission and diffusion of Indian astronomy in the West after the arrival of al-Khwārizmī’s astronomical tables in al-Andalus (Muslim Spain) in the tenth century. This tradition of Indian origin competed with the Greek tradition represented by al-Battānī’s astronomical tables and was much more alive in the Iberian Peninsula and the Maghrib than previously thought. From Spain, the Indian tradition entered mainstream European astronomy, where we find echoes of it in all versions of the Alfonsine Tables, both in manuscript and in the printed editions (beginning in 1483), as well as in Copernicus’s De Revolutionibus, published in 1543. (shrink)

This study of the concept of orbit is intended to throw light on the nature of revolutionary concepts in science. We observe that Kepler transformed theoretical astronomy that was understood in terms of orbs [Latin: orbes] and models , by introducing a single term, orbit [Latin: orbita], that is, the path of a planet in space resulting from the action of physical causes expressed in laws of nature. To demonstrate the claim that orbit is a revolutionary concept we pursue three (...) lines of argument. First we trace the origin of the term; second, we document its development and specify the meaning of the novel term as it was introduced into astronomy by Kepler in his Astronomia nova . Finally, in order to establish in what sense the concept is revolutionary, we pay attention to the enduring impact that the concept has had on the relevant sciences, in this case astronomy and indeed physics. We claim that orbit is an instance of a revolutionary concept whose provenance and use can provide the insights we are seeking. (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)

Abraham ibn Ezra d'Espagne (m. 1167) fut l'un des plus importants savants ayant contribué à la transmission de la science arabe à l'Occident. Ses ouvrages en astrologie et en astronomie, rédigés en hébreu puis traduits en latin, étaient considéréd comme faisant autorité par de nombreux savants juifs et Chrétiens. Parmi les ouvrages qu'il a traduits de l'arabe en hébreu, certains sont perdus dans leur langue originale et ses propres ouvrages renferment certaines informations concernant des sources anciennes mal ou pas du (...) tout connues par ailleurs. Ibn Ezra semble être le premier a avoir consigne l'une des sept méthodes pour dresser les maisons astrologiques. Cette méthode avait par la suite été utilisée par Lévi ben Gershom (m. 1344) dans le Midi de la France. (shrink)

Philosophers have long distinguished various interpretations of the principle of equal opportunity and argued over their implications and justifications. But they have almost always tacitly assumed that the context was a national one. They have not, in particular, considered whether some interpretation of the principle could apply and be justified globally, that is, to all people without regard to their nationality or citizenship. Yet, such an investigation is clearly demanded. The leading moral theories seem to support a case for at (...) least some interpretation of the equal opportunity principle, and it is not obvious that they can support it only domestically.Consider, first, those moral theories which place great value on negative liberty, for example, libertarianism. Libertarianism supports a standard interpretation of the equal opportunity principle – “formal” equality of opportunity; formal equality of opportunity requires that legal restrictions j on the taking of opportunities be lifted, and such restrictions diminish negative liberty. But libertarianism would also seem to support a global. version of formal equality of opportunity, for example, that laws be rescinded which require that candidates for jobs in a country be citizens of that country, or which restrict emigration or immigration. Such laws also diminish negative liberty.Or consider those moral theories which place great value on efficiency, for example, utilitarianism. Utilitarianism probably supports formal equality of opportunity because legal restrictions on the taking of opportunity not only diminish negative liberty, but also often prevent talent and skill from going where it can best be used and thus reduce efficiency. (shrink)

A table in five columns for the radii of the Sun, the Moon, and the shadow is included in sets of astronomical tables from the fifteenth to the early seventeenth century, specifically in those by John of Gmunden (d. 1442), Peurbach (d. 1461), the second edition of the Alfonsine Tables (1492), Copernicus (d. 1543), Brahe (d. 1601), and Longomontanus (d. 1647). The arrangement is the same and the entries did not change much, despite many innovations in astronomical theories in this (...) time period. In other words, there is continuity in presentation and, from the point of view of the user of these tables, changes in the theory played no role. In general, the methods for computing the entries are not described and have to be reconstructed. In this paper, we focus on the users of these tables rather than on their compilers, but we refer to modern reconstructions where appropriate. A key issue is the treatment of the size of the Moon during a solar eclipse which was not properly understood by Tycho Brahe. Kepler’s solution and that of his predecessor, Levi ben Gerson (d. 1344), are discussed. (shrink)