Ockham on the Parts of Continuum

This paper argues that, for Ockham, the parts of the continuum exist in act in the continuum: they are already there before any division of the continuum. Yet, they are infinitely many in that no division of the continuum will exhaust all the existing parts of the continuum taken conjointly. This reading of Ockham takes into account the crucial place of his new concept of the infinite in his analysis of the infinite divisibility of the continuum. Like many of his fellow anti-atomists, Ockham stresses that the concept of a potential infinite seems to contradict Aristotle’s modal logic, in particular the central assumption that there is no potency that will never be realized. Ockham, like other fourteenth-century anti-atomists, tried not only to refute atomism, but also to propose an analysis of the infinite divisibility of the continuum that is not incompatible with their modal logic.