Lukowski has argued that, if it is the case that there are actual non-monotonic inferences, they are very hard to find. In this paper, a representative kind of inference that is often considered to be non-monotonic is addressed. Likewise, certain arguments provided by Lukowski to demonstrate that that type of inference is not really non-monotonic are reviewed too. Finally, I propose an explanation of why, despite the fact that the arguments given by him seem to be convincing, it is usually thought that those inferences are not monotonic. In this way, I also try to account for the role that disjunction has in this issue and argue in favor of the idea that we can continue to suppose that the human mind does not ignore the essential requirements of classical logic.