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)

Al-Ghazālı̄ famously claims in the Incoherence of the Philosophers that al-Fārābī and Avicenna are unbelievers because they hold philosophical positions that conflict with Islam. What is less well-known, however, is that Averroës claims in the Decisive Treatise that al-Fārābī and Avicenna are not unbelievers; rather, al-Ghazālı̄ is the true unbeliever for writing the Incoherence of the Philosophers. In this paper, my aim is to present a sustained reconstruction of Averroës’ legal and philosophical argument for why al-Ghazālı̄ is an unbeliever. The (...) crux of Averroës’ argument is that al-Ghazālı̄ has expressed false allegorical interpretations of scripture to unqualified persons, which has led them into unbelief. By being causally responsible for other people’s unbelief, al-Ghazālı̄ is an unbeliever as well. (shrink)

This dissertation examines Avicenna's theory of efficient causation in light of his approach to central problems in metaphysics, from the proof of the Necessary Existent to his emanative cosmology. Avicenna provides an internally coherent metaphysical account of efficient causation. A metaphysical account of the efficient cause explains the existence of the effect or essence in a way that is not explained by the causes of motion, as investigated in physics. That is, a full explanation of the cause of the existence (...) of an essence is not found in the four causes of natural change and motion. Avicenna aims to clarify what the explanatory division of labor is between the account of the natural philosopher and that of the metaphysician. In so doing, Avicenna develops a theory of causation that ties his innovative concepts of the contingent in itself and necessary in itself to the concept of efficient causation. A central distinction that Avicenna advances in relation to the efficient cause is that between the cause of the effect qua species and the cause of the effect qua individual. The distinction is relevant to understanding his view of the role of the causes of the essence, including the Active Intellect. Drawing on the above theory of efficient causation, the study reexamines Avicenna's famous proof for the Necessary Existent. The analysis shows that his metaphysical account of efficient causation is at the heart of his proof for a Necessary Existent. The "cause of persistence", in particular, is argued to have a more critical role than previously acknowledged, and is explicated in the context of his theory of efficient causation in metaphysics. (shrink)