Teaching is a paradoxical activity, beset by ironies and apparent contradictions: •Educated people are autonomous and self-directed, but schooling generally involves expert direction of compliant and dependent students. •Empathy, imagination, and creativity characterize fully actualized people, but these qualities seem at odds with mastering received bodies of material.•Societies value testable facts and abilities, but these are of little use, and can even be dangerous, without maturity of character. •Educators rightly value teaching for maturity, but risk in the process indoctrination or natural resistance. •Modeling forthrightness would seem indispensable to character development, but some of the most effective teachers induce learning by good-natured trickery.These are genuine paradoxes, in that even when we work out credible resolutions for them they tend not stay solved. Their tensions continue to bedevil us in each new class, with each new student, and at each phase of learning. The insights and conclusions of this conversation are neither inflexible doctrines nor a compendium of abstract disputes unrelated to actual teaching practices. Rather, the reader at once witnesses and participates in the philosophy of education as a vital process, experiencing the kind of passionate and imaginative conversations that good teachers often have, and from which they learn to understand and engage the elusive art of teaching.