Computer systems for medical diagnosis based on machine learning are not mere science fiction. Despite undisputed potential benefits, such systems may also raise problems. Two (interconnected) issues are particularly significant from an ethical point of view: The first issue is that epistemic opacity is at odds with a common desire for understanding and potentially undermines information rights. The second (related) issue concerns the assignment of responsibility in cases of failure. The core of the two issues seems to be that understanding and responsibility are concepts that are intrinsically tied to the discursive practice of giving and asking for reasons. The challenge is to find ways to make the outcomes of machine learning algorithms compatible with our discursive practice. This comes down to the claim that we should try to integrate discursive elements into machine learning algorithms. Under the title of "explainable AI" initiatives heading in this direction are already under way. Extensive research in this field is needed for finding adequate solutions.