  We show that, for the transition between any two quantum Hall states, the
semi-circle law and the existence of a duality symmetry follow solely from the
consistency of the law of corresponding states with the two-dimensional scaling
flow. This puts these two effects on a sound theoretical footing, implying that
both should hold exactly at zero temperature, independently of the details of
the microscopic electron dynamics. This derivation also shows how the
experimental evidence favours taking the two-dimensional flow seriously for the
whole transition, and not just near the critical points.
