Avicenna on Mathematical Infinity

Zarepour, Mohammad Saleh (2020): Avicenna on Mathematical Infinity. In: Archiv für Geschichte der Philosophie, Vol. 102, No. 3: pp. 379-425

Abstract

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.

• Item Type: Journal article
• Faculties: Philosophy, Philosophy of Science and Religious Science
• Subjects: 100 Philosophy and Psychology > 100 Philosophy
• ISSN: 0003-9101
• Language: English