The forma fluens/fluxus formae debate concerns the question as to whether motion is something distinct from the body in motion, the flow of a distinct form identified with motion , or nothing more than the successive states of the body in motion, the flow of some form found in one of Aristotle's ten categories . Although Albertus Magnus introduced this debate to the Latin West he drew his inspiration from Avicenna. This study argues that Albertus misclassified Avicenna's position, since Albertus (...) could not conceptualize motion at an instant, whereas it is claimed here this was the very position Avicenna adopted. The paper includes an overview of Albertus's discussion and a brief survey of the Avicennan sources upon which Albertus drew. The heart of the paper treats Avicenna's analysis of motion at an instant. Avicenna's general argument was that since spatial points have no extremities, nothing in principle prevents a moving object from being at a spatial point for more than an instant, understood as a limit. It is then argued that Avicenna had the philosophical machinery to make sense of a limit, albeit not in mathematical terms, but in terms of an Aristotelian potential infinite. (shrink)

Avicenna believed in mathematical finitism. He argued that magnitudes and sets of ordered numbers and numbered things cannot be actually infinite. In this paper, I discuss his arguments against the actuality of mathematical infinity. A careful analysis of the subtleties of his main argument, i. e., The Mapping Argument, shows that, by employing the notion of correspondence as a tool for comparing the sizes of mathematical infinities, he arrived at a very deep and insightful understanding of the notion of mathematical (...) infinity, one that is much more modern than we might expect. I argue, moreover, that Avicenna’s mathematical finitism is interwoven with his literalist ontology of mathematics, according to which mathematical objects are properties of existing physical objects. (shrink)

The twelfth century philosopher-theologian Fakhr al-Dīn al-Rāzī is well known for his critique of Avicennan metaphysics. In this paper, I examine his critique of Avicenna's physics, and in particular his rejection of the Avicennan and Aristotelian theory of place as the inner boundary of a containing body. Instead, Fakhr al-Dīn defends a definition of place as self-subsisting extension, an idea explicitly rejected by Aristotle and Avicenna after him. Especially in his late work, theMaṭālib, Fakhr al-Dīn explores a number of important (...) philosophical issues with reference to this theory of place, including the principle that two indiscernible things must be identical and the idea that motion and rest are always relative.RésuméLe philosophe-théologien du XIIesiècle Fakhr al-Dīn al-Rāzī est bien connu pour sa critique de la métaphysique avicennienne. Nous examinons, dans cet article, sa critique de la physique d'Avicenne, et en particulier son rejet de la théorie avicennienne et aristotélicienne du lieu – lieu comme limite interne du corps englobant. Alternativement, Fakhr al-Dīn défend une théorie du lieu comme extension auto-subsistante, doctrine explicitement révoquée par Aristote et Avicenne à sa suite. En particulier dans son œuvre tardive, lesMaṭālib, Fakhr al-Dīn explore plusieurs questions philosophiques importantes en rapport avec cette théorie du lieu, dont: le principe voulant que deux choses indiscernables soient identiques, et l'idée selon laquelle mouvement et repos sont toujours relatifs. (shrink)

Aristotle's account of place in terms of an innermost limit of a containing body was to generate serious discussion and controvery among Aristotle's later commentators, especially when it was applied to the cosmos as a whole. The problem was that since there is nothing outside of the cosmos that could contain it, the cosmos apparently could not have a place according to Aristotle's definition; however, if the cosmos does not have a place, then it is not clear that it could (...) move, but it was thought to move, namely, in its daily revolution, which was viewed as a kind of natural locomotion and so required the cosmos to have a place. The study briefly outlines Aristotle's account of place and then considers its fate, particularly with respect to the cosmos and its motion, at the hands of later commentators. To this end, it begins with Theophrastus' puzzles concerning Aristotle's account of place, and how later Greek commentators, such as Alexander of Aphrodisias, Themistius and others, attempted to address these problems in what can only be described as ad hoc ways. It then considers Philoponus' exploitation of these problems as a means to replace Aristotle's account of place with his own account of place understood in terms of extension. The study concludes with the Arabic Neoplatonizing Aristotelian Avicenna and his novel introduction of a new category of motion, namely, motion in the category of position. Briefly, Avicenna denies that the cosmos has a place, and so claims that it moves not with respect to place, but with respect to position. (shrink)

“Before the sun of Eli had set the sun of Samuel had risen.” Before the voice of the prophets had ceased to guide the people, the Interpreters of the Law, the Doctors of the Talmud, had commenced their labours, and before the Academies of Sura and of Pumbadita were closed, centres of Jewish thought and learning were already flourishing in the far West. The circumstances which led to the transference of the head-quarters of Jewish learning from the East to the (...) West in the tenth century are thus narrated in the Sefer ha-kabbalah of Rabbi Abraham ben David: “After the death of Hezekiah, the head of the Academy and Prince of the Exile, the academies were closed and no new Geonim were appointed. But long before that time Heaven had willed that there should be a discontinuance of the pecuniary gifts which used to be sent from Palestine, North Africa and Europe. Heaven had also decreed that a ship sailing from Bari should be captured by Ibn Romahis, commander of the naval forces of Abd-er-rahman al-nasr. Four distinguished Rabbis were thus made prisoners—Rabbi Ḥushiel, father of Rabbi Ḥananel, Rabbi Moses, father of Rabbi Ḥanok, Rabbi Shemarjahu, son of Rabbi Elḥanan, and a fourth whose name has not been recorded. They were engaged in a mission to collect subsidies in aid of the Academy in Sura. The captor sold them as slaves; Rabbi Ḥushiel was carried to Kairuan, R. Shemarjahu was left in Alexandria, and R. Moses was brought to Cordova. These slaves were ransomed by their brethren and were soon placed in important positions. When Rabbi Moses was brought to Cordova, it was supposed that he was uneducated. In that city there was a synagogue known at that time by the name of Keneset ha-midrash, and Rabbi Nathan, renowned for his great piety, was the head of the congregation. The members of the community used to hold meetings at which the Talmud was read and discussed. One day when Rabbi Nathan was expounding the Talmud and was unable to give a satisfactory explanation of the passage under discussion, Rabbi Moses promptly removed the difficulty and at the same time answered several questions which were submitted to him. Thereupon R. Nathan thus addressed the assembly:—‘I am no longer your leader; that stranger in sackcloth shall henceforth be my teacher, and you shall appoint him to be your chief.’ The admiral, on hearing of the high attainments of his prisoner, desired to revoke the sale, but the king would not permit this retraction, being pleased to learn that his Jewish subjects were no longer dependent for their religious instruction on the schools in the East.” Henceforth the schools in the West asserted their independence, and even surpassed the parent institutions. The Caliphs, mostly opulent, gave every encouragement to philosophy and poetry; and, being generally liberal in sentiment, they entertained kindly feelings towards their Jewish subjects. These were allowed to compete for the acquisition of wealth and honour on equal terms with their Mohammedan fellow-citizens. Philosophy and poetry were consequently cultivated by the Jews with the same zest as by the Arabs. Ibn Gabirol, Ibn Ḥasdai, Judah ha-levi, Ḥananel, Alfasi, the Ibn Ezras, and others who flourished in that period were the ornament of their age, and the pride of the Jews at all times. The same favourable condition was maintained during the reign of the Omeyades; but when the Moravides and the Almohades came into power, the horizon darkened once more, and misfortunes threatened to destroy the fruit of several centuries. Amidst this gloom there appeared a brilliant luminary which sent forth rays of light and comfort: this was Moses Maimonides. (shrink)