Philosophy of Medicine seeks to answer two questions: (1) what is medicine? and (2) what should we think of it? The first question is motivated by the observation that medicine has existed and continues to exist in many different forms in different times and places. There is no activity or belief that is common to all medical traditions in all times and places. What, if anything, makes us count these activities as varieties of the same thing—namely, medicine? The book distinguishes the goal and business of medicine, arguing that the goal is cure, while the business of medicine cannot be, because medical traditions have been too hit-and-miss at achieving cure. The core medical competence is identified as engaging with the project of understanding the nature and causes of disease. A model of health is also required to say what medicine is, since health is part of its subject matter, and a novel theory of health as a secondary property is offered. In the second part of the book, the proper epistemic attitude to medicine is considered. Contrary to much contemporary work, the book argues against positions setting very rigid constraints on what counts as admissible evidence in forming beliefs either about whole traditions or about specific interventions. Thus both Evidence-Based Medicine and Medical Nihilism are rejected. Instead a view called Medical Cosmopolitanism is developed from Appiah’s corresponding work in ethics. The view is applied to alternative and non-Mainstream traditions, as well as to the project of decolonizing medicine.