  There has been a long-standing and sometimes passionate debate between
physicists over whether a dynamical framework for quantum systems should
incorporate not completely positive (NCP) maps in addition to completely
positive (CP) maps. Despite the reasonableness of the arguments for complete
positivity, we argue that NCP maps should be allowed, with a qualification:
these should be understood, not as reflecting 'not completely positive'
evolution, but as linear extensions, to a system's entire state space, of CP
maps that are only partially defined. Beyond the domain of definition of a
partial-CP map, we argue, much may be permitted.
