Guglielmo da Ockham e gli infinita in actu

The article analyses the concept of actual infinity in William of Ockham’s thought, thanks to a close reading of his writings, first those on physics, where he argues more than once the existence of the actual infinity, intended as a set of infinite parts in act present in a continuum. By virtue of this representation of infinity, Ockham also states that two sets with infinite parts are not necessarily equal, but one of the two can be greater than the other, as would happen with the revolutions of the moon and the sun in an endless time. Nonetheless, in the theological works, the Franciscan seems to have apparently a different position, since he denies the possibility of the actual infinity, either as a set of infinite entities existing all simultaneously, or as an infinite entity, since in both cases a limit would be placed on God’s omnipotence. Ockham instead demonstrates that he has a double vision of the actual infinity, similar to that of Cantor, as already proposed by Annaliese Maier. The essay will therefore show the compatibility of Ockham’s physics and theological writings by virtue of the different meanings of infinity.