The ‘point of intersection’ is a phrase that recurs, albeit infrequently, throughout Eliot’s writings, belonging as much to the language of his verse as to his vocabulary as a critic. This essay argues that Eliot’s notion of the ‘point of intersection’ represents his most extended attempt to conceptualize his own poetics: it is the way in which he thinks about the organizational practices of his verse and the kinds of understanding that these structures make uniquely available. To attend to the ‘point of intersection’ is to discover Eliot’s primary account of how the language of his verse takes us beyond the usual limits of knowledge. But the ‘point of intersection’ has a wider resonance. By demonstrating the ways in which Eliot’s notion of the ‘point of intersection’ emerges from his reading of Karl Barth and Matthew Arnold, this essay shows how Eliot’s account of his own poetics is invested in a series of broader questions about what it is possible to know. In Eliot’s verse this epistemological question is framed in terms of the capacities and limitations of the modern imagination: is it ever possible to know that which transcends the realm of human life or do we extend our knowledge only to find that we are bound forever to inhabit the closed world of secular modernity? In its pursuit of the ‘point of intersection’, this essay recovers Eliot’s neglected account of his own poetics and works with Eliot towards an account of what, as modern readers and writers, we might expect poetry to do for us.