Clinical judgement is a central and longstanding issue in the philosophy of medicine which has generated significant interest over the past few decades. In this article, we explore different approaches to clinical judgement articulated in the literature, focusing in particular on data-driven, mathematical approaches which we contrast with narrative, virtue-based approaches to clinical reasoning. We discuss the tension between these different clinical epistemologies and further explore the implications of big data and machine learning for a philosophy of clinical judgement. We argue for a pluralistic, integrative approach, and demonstrate how narrative, virtue-based clinical reasoning will remain indispensable in an era of big data and predictive analytics.