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  1. Zeno Beach.Jacob Rosen - 2020 - Phronesis 65 (4):467-500.
    On Zeno Beach there are infinitely many grains of sand, each half the size of the last. Supposing Aristotle denied the possibility of Zeno Beach, did he have a good argument for the denial? Three arguments, each of ancient origin, are examined: the beach would be infinitely large; the beach would be impossible to walk across; the beach would contain a part equal to the whole, whereas parts must be lesser. It is attempted to show that none of these arguments (...)
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  • Avicenna on Mathematical Infinity.Mohammad Saleh Zarepour - 2020 - Archiv für Geschichte der Philosophie 102 (3):379-425.
    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 (...)
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