Aristotle on Mathematical Infinity

Book excerpt: Aristotle was the first not only to distinguish between potential and actual infinity but also to insist that potential infinity alone is enough for mathematics thus initiating an issue still central to the philosophy of mathematics. Modern scholarship, however, has attacked Aristotle's thesis because, according to the received doctrine, it does not square with Euclidean geometry and it also seems to contravene Aristotle's belief in the finitude of the physical universe. This monograph, the first thorough study of the issue, puts Aristotle's views on infinity in the proper perspective. Through a close study of the relevant Aristotelian passages it shows that the Stagirite's theory of infinity forms a well argued philosophical position which does not bear on his belief in a finite cosmos and does not undermine the Euclidean nature of geometry. The monograph draws a much more positive picture of Aristotle's views and reaffirms his disputed stature as a serious philosopher of mathematics. This innovative and stimulating contribution will be essential reading to a wide range of scholars, including classicists, philosophers of science and mathematics as well as historians of ideas.