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The problem of infinity in medieval philosophy is located at the crossroad of mathematics, history, and philosophy. In order to understand this problem, which shows extremely complicated features in the active interaction among the diverse disciplines, we need a map. This survey article aims at pr...

The problem of infinity in medieval philosophy is located at the crossroad of mathematics, history, and philosophy. In order to understand this problem, which shows extremely complicated features in the active interaction among the diverse disciplines, we need a map. This survey article aims at providing the readers with such a map by reporting Murdoch’s and Sylla’s studies. Though Murdoch enumerated five features as medieval philosophers’ innovation, we discuss these under two categories, i.e., the problem of the equalities of infinities and the problem of the infinite divisibility of continua. Focus of our discussion, in particular, is laid on Henry of Harclay, who played a central role in the medieval debates on the problem of infinity, and his critic William of Alnwick. Finally, by drawing attention to a case shere medieval theory of supposition was applied in order to refute indivisibilism, and the two geometrical arguments used by Duns Scotus in the context of addressing angelic motion, it is pointed out that some aspects of medieval discussions of the problem of infinity might be interesting even to modern mathematicians.

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