ABSTRACT W.L. Craig has argued that the universe has a beginning because (1) the infinitude of the past entails the existence of actual infinite multitudes of past intervals of time, and (2) the existence of actual infinite multitudes is impossible. Puryear has rejected (1) and argued that what the infinitude of the past entails is only the existence of an actual infinite magnitude of past time. But this does not preclude the infinitude of the past, Puryear claims, because there can (...) be no justification for the claim that actual infinite magnitudes are impossible. I argue, against Puryear, that there can be such a justification. I claim, nevertheless, that, for reasons entirely different from Puryear’s, the finitude of the past cannot be established based either on the impossibility of actual infinite multitudes or on the impossibility of actual infinite magnitudes. My arguments in this paper draw on insights from al-Kindī and Avicenna. (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)

It is widely known that Aristotle rules out the existence of actual infinities but allows for potential infinities. However, precisely why Aristotle should deny the existence of actual infinities remains somewhat obscure and has received relatively little attention in the secondary literature. In this paper I investigate the motivations of Aristotle’s finitism and offer a careful examination of some of the arguments considered by Aristotle both in favour of and against the existence of actual infinities. I argue that Aristotle has (...) good reason to resist the traditional arguments offered in favour of the existence of the infinite and that, while there is a lacuna in his own ‘logical’ arguments against actual infinities, his arguments against the existence of infinite magnitude and number are valid and more well grounded than commonly supposed. (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)

The study begins with the language employed in and the psychological basis of thought experiments as understood by certain medieval Arabic philosophers. It then provides a taxonomy of different kinds of thoughts experiments used in the medieval Islamic world. These include purely fictional thought experiments, idealizations and finally thought experiments using ingenious machines. The study concludes by suggesting that thought experiments provided a halfway house during this period between a staunch rationalism and an emerging empiricism.