Theoretical astrophysics emerged as a significant research programme with the construction of a series of stellar models by A. S. Eddington. This paper examines the controversies surrounding those models as a way of understanding the development and justification of new theoretical technologies. In particular, it examines the challenges raised against Eddington by James Jeans, and explores how the two astronomers championed different visions of what it meant to do science. Jeans argued for a scientific method based on certainty and completeness, whereas Eddington called for a method that valued exploration and further investigation, even at the sake of secure foundations. The first generation of stellar models depended on the validity of Eddington's approach – the physics and many of the basic facts of stars were poorly understood and he justified his models through their utility for future research and their robustness under challenging use. What would become theoretical astrophysics depended heavily on this phenomenological outlook, which Jeans dismissed as not even science. This was a dispute about the practice of theory, and it would be this methodological debate (rather than the emergence of new facts or the incorporation of new theory) that made theoretical astrophysics viable.