This paper explores the use of irony in narratives that focus on the problem of knowing what we do not know. Sometimes issues arise on a grand scale, as in the literature of Socrates, Pascal, and Descartes, where the question really is whether we can know anything at all or whether all that we can know is that there is nothing worth knowing that we do know. The grand level does not apply only to philosophy, but also to mathematics and theoretical physics. They are disciplines that seek to state truths about the structure of the universe. Examples are Newton's laws; absolute space and time and Einstein's denial of absolute space and time; Maxwell's Equations and Heisenberg' Uncertainty Principle. There are problems about the nature of knowledge that arise on a smaller scale, at the petite level, for example where ignorance of a protagonist's own epistemic condition leads to tragedy, as in narratives from Sophocles, Shakespeare and Flaubert. These personal issues pertain to introspective knowledge, but not all petite issues deal with the intensely personal. Some deal with problems that cry out for statistical analysis, as in the medical sciences or in the social sciences more generally. Other more general issues do not attempt to generalize about the "deep structure" of nature and thought, but often take the form of "statistically significant" correlations. The paper argues that ironies about knowing test the limits of rational deliberation about what to do and what to believe, which in turn accounts for much that is perplexing in intellectual life, tragic in personal life and confused in public life. All this, it is concluded, encourages more humble assessments of the extent of human knowledge and therefore a greater commitment to intellectual and moral toleration.