Authors
Mohammad Saleh Zarepour
University of Manchester
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.
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DOI 10.1515/agph-2017-0032
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References found in this work BETA

The Child's Conception of Number.J. Piaget - 1953 - British Journal of Educational Studies 1 (2):183-184.
Aristotle on Geometrical Objects.Ian Mueller - 1970 - Archiv für Geschichte der Philosophie 52 (2):156-171.
Al-Kindī.Peter Adamson - 2006 - Oxford University Press.

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