The term "paradox" signifies a contradiction of some sort. Modern health care appears to be rich in contradictions, and it is claimed to be paradoxical in a number of ways. In particular health care is held to be a paradox itself: it is supposed to do good, but is accused of doing harm. The objective of this article is to investigate whether the concept of paradox can serve as a framework for analysing pressing problems in modern health care. To pursue this, three distinctive levels of paradox are identified: resolvable paradoxes, antinomies and aporias. The analysis reveals that when facing the challenges of modern health care the focus of attention should be to resolve the resolvable paradoxes, to acknowledge the antinomies and to learn to live with the aporias.