This chapter offers a brief historical survey of attempts to fathom the physical mechanisms of mind as computational systems, followed by a consideration of some of the concrete versions of underdetermination in contemporary neuropsychology. In the conception of Hermann Helmholtz and his associates, Ernst Brucke and Emil du Bois Reymond and their students, mental phenomena were ultimately a piece of physiology, like breathing, and the ambition of psychology should be to unravel their physical mechanisms, as with any other physiological process. The work of Ramon y Cajal invited the view of the functioning brain as a kind of signaling system, what we would, but they did not, call a computational information processing system. What was needed to reduce structural underdetermination and allow the kind of theory of mind Helmholtz envisioned was a way to see inside the box, to acquire data that would bring theories of cognition closer to physiology and to the neural mechanisms of computation.