  Haag's theorem cries out for explanation and critical assessment: it sounds
the alarm that something is (perhaps) not right in one of the standard way of
constructing interacting fields to be used in generating predictions for
scattering experiments. Viewpoints as to the precise nature of the problem, the
appropriate solution, and subsequently-called-for developments in areas of
physics, mathematics, and philosophy differ widely. In this paper, we develop
and deploy a conceptual framework for critically assessing these disparate
responses to Haag's theorem. Doing so reveals the driving force of more general
questions as to the nature and purpose of foundational work in physics.
