Scholars from a range of disciplines including medicine, sociology, psychology, and philosophy have addressed the concepts of ambiguity and uncertainty in medical practice and training. Most of this scholarship has been descriptive, focusing on defining and measuring ambiguity and uncertainty tolerance or tracking clinicians’ responses to ambiguous and uncertain situations. Meanwhile, scholars have neglected some fundamental normative questions: Is tolerance of uncertainty good; if so, to what extent? Using a philosophical approach to these questions, we show that neither tolerance nor intolerance of uncertainty is necessarily a good or bad trait. Rather, both tolerance and intolerance of uncertainty can give physicians advantages while at the same time exposing them to pitfalls in clinical practice. After making this case, we argue that cultivating certain virtues—like courage, diligence, and curiosity—could help clinicians avoid the dangers of excessive tolerance and intolerance of uncertainty. Finally, we suggest that medical educators develop curricula and career counseling beginning with matriculation and proceeding through specialty choice and residency training that explicitly address trainees’ responses to clinical uncertainty. These programs should encourage trainees, students and residents, to be mindful of their reactions to uncertainty and help them develop virtues that will allow them to avoid the hazards of extreme tolerance or intolerance of uncertainty.