Similar to Meinong, Abū Hāšim al-Ğubbāī held the view that some objects do not exist. This paper is a comparative study between Meinong’s object theory and Abū Hāšim’s theory of nonexistent objects. Our comparative study is mostly done through three topics: the characterization principle, objecthood, and the ontological status of existence. Moreover, Abū Hāšim’s theory of nonexistent objects is based on his theory of states, according to which some things, namely states, which among other things include existence, are neither existent (...) nor nonexistent. In this paper, we have also discussed two arguments on behalf of this claim and then we have examined them from a Meinongian perspective. (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)

Abzj proposed, in a fragment established and translated herein, two methods to build a parabolic mirror. The lack of demonstration, particularly for the first method, raises a difficult question of interpretation. To understand this method, O. Neugebauer used, in an unpublished article translated herein, concepts of descriptive geometry. He then eliminated the space construction used, to keep only simple geometrical considerations known by the Greeks. The second interpretation, given by R. Rashed, is based on the geometrical practices of al-Bnhzj from (...) Ibn Sinān seems to support this last interpretation. (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.