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 last thirty years of scholarship in western medieval philosophical historiography have seen a number of reflections on the methodological paradigms, schools, trends, and dominant approaches in the field. As a contribution to this ongoing assessment of the existing methods of studies in medieval philosophy and theology and a supplement to classifications offered by M. Colish, J. Inglis, C. König-Pralong, J. Marenbon, A. de Libera, and others, the article offers another explanatory tool. Here is a description of an imaginary system (...) of methodological coordinates that systematizes the current tendencies by placing them in a three-dimensional system of axes. Every axis corresponds to a certain aspect of the historical and systematic research in medieval thought and symbolizes a possible movement between two extremes representing opposite methodological values and directions. The methods and approaches practiced in recent studies in medieval philosophy and theology might be schematically located inside this general system of argumentational, focal (or objectival), and (con)textual axes with their intersection identified with what some scholars call the “integral” model of study. This explanatory tool allows one to see how current approaches and methods form a panoply of axes that belong together in one complex grid and helps to visualize the tapestry of existing approaches in medieval philosophical historiography. (shrink)

In different parts of Metaphysics, Aristotle presents different views on the nature and subject matter of the discipline in question. These different characterizations led to wide-ranging interpretations of the relation between metaphysics and philosophical theology. Muslim Philosophers adopted two different views. Al-Kindi and al-Farabi endorsed the view that metaphysics is the same as theology as far as its subject matter is the First Cause and it deals essentially with incorporeal entities. After Avicenna, however, a second view became dominant according to (...) which metaphysics has a broader realm that embraces theology as its most noble part. The rationale behind this view is that the subject matter of metaphysics is “being qua being”, or unconditioned existent, in its broad sense so that philosophical theology can be taken as discussing some of the proper accidents of the unconditioned existent. This view requires that metaphysics cannot be a secular discipline and should be totally consistent with theology. It also provides us with a certain interpretation of what is usually called “Islamic philosophy.” * Professor. Department of Philosophy, Tarbiat Modares University, Tehran. Iran. ׀ [email protected]. (shrink)

What is the function of logic in al-Kindī's corpus? What kind of relation does it have with mathematics? This article tackles these questions by examining al-Kindī's theory of categories as it was presented in his epistle On the Number of Aristotle's Books, from which we can learn about his special attitude towards Aristotle theory of categories and his interpretation, as well. Al-Kindī treats the Categories as a logical book, but in a manner different from that of the classical Aristotelian tradition. (...) He ascribes a special status to the categories Quantity and Quality, whereas the rest of the categories are thought to be no more than different combinations of these two categories with the category Substance. The discussion will pay special attention to the function of the categories of Quantity and Quality as mediators between logic and mathematics. (shrink)

Dialetheism is the view that some contradictions are true. Resorting to either metaphysical dialetheism or semantic dialetheism may seem like an appropriate resolve to certain theological contradictions. At least for those who concede to theological contradictions, and take dialetheism seriously. However, I demonstrate that neither of these types of dialetheism would serve to be amenable in resolving an Islamic theological contradiction. This is a theological contradiction that I refer to as ‘the paradox of an unknowable and ineffable God’. As a (...) result of this, I propose an alternative type of dialetheism which aims to resolve the paradox of an unknowable and ineffable God. I call this type of dialetheism, ‘mystical dialetheism’. (shrink)

Originally introduced by Plato and Aristotle, Moderation Theory in Ethics is the most prevalent theory of ethics among Islamic scholars. Moderation Theory suggests that every virtue or excellence of character lies in the mean between two vices: excess or defect. Every ethical virtue comes from moderation in actions or emotions and every ethical vice comes from excess or defect. This paper suggests that while Islamic scholars have been influenced by this doctrine, they have also developed and re-conceptualized it in innovative (...) ways. Kindī, Miskawayh, Avicenna, Rāghib Isfahānī, Nasīr al-Dīn Ṭusī, and others are among the Islamic contributors to the subject. Some of their innovations in this theory are as follows: bringing together Aristotle's doctrine of the mean with Plato's psychology (by Kindī), dividing virtues into four higher genuses, dividing vices into eight higher genuses, setting various kinds of vices and virtues under these higher genuses (by Miskawayh), adding the vice qualitative criteria to Aristotle's vice quantitative criteria (excess and defect) (by Ṭusī), dividing various conceptualizations of justice (by Avicenna), adding religious and mystical virtues into the existing list of virtues (by Rāghib Isfahānī), and proposing a comprehensive model for curing diseases of the soul. This paper seeks to establish the main contributions of these Muslim scholars to Moderation Theory and elaborate on this theory’s evolution within the Islamic world. (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)