This paper offers a comprehensive interpretation of Aristotle’s theoretical account of the infinity of such infinite things as he holds actually exist in nature: number, time, and spatial magnitudes. On the interpretation presented, number and time for Aristotle are infinite not because there exists an actual infinity of numbers or of past or future times in relation to any ‘now’, but rather because, given the nature of the physical world, as he argues it actually exists, nature is such that for any number of things or any stretch of past or future time, however large/long, another finite one, precisely one unit larger/longer, can always be generated by some well-defined process of division.
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