In this essay, we reconsider two themes particularly discussed by the interpreters of Ockham: that of divine omnipotence and the hypothesis of the intuitive cognition of non-existent things. The purpose is to show that the hypothetical case considered by Ockham was subjected to opposite interpretations. For theological reasons, Ockham attributes not only to God but also to human beings the possibility of having acts of intuitive cognition of things that do not exist; nonetheless, he holds that it is contradictory for God to give us the evident cognition of things that appear to be present when they are actually absent. Walter Chatton opposes this conclusion, arguing that no contradiction ensues from that hypothesis. Instead, he believes that it is impossible for God to give us the intuition of things that absolutely do not exist or are in no way present to us. Ockham’s arguments include some difficulties that Chatton acutely sees and discusses. In particular, Chatton calls into question Ockham’s missed distinction between the existence and the presence of the intuited thing.