Avicenna on Mathematical Infinity

Archiv für Geschichte der Philosophie 102 (3):379-425 (2020)
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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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Mohammad Saleh Zarepour
University of Manchester

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References found in this work

The Complete Works: The Rev. Oxford Translation.Jonathan Barnes (ed.) - 1984 - Princeton, N.J.: Princeton University Press.
The Child's Conception of Number.J. Piaget - 1953 - British Journal of Educational Studies 1 (2):183-184.
Aristotle’s Philosophy of Mathematics.Jonathan Lear - 1982 - Philosophical Review 91 (2):161-192.
Aristotle on Geometrical Objects.Ian Mueller - 1970 - Archiv für Geschichte der Philosophie 52 (2):156-171.

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