Since the time of Plato, relativism has been attacked as a self-refuting theory. Today, there are two basic kinds of argument that are used to show that global relativism is logically incoherent: first, a direct descendent of the argument Plato uses against Protagoras, called the peritrope; and, second, a more recent argument that relativism leads to an infinite regress. Although some relativist theories may be formulated in such a way as to be susceptible to these arguments, there are other versions of relativism that are impervious to these charges of incoherence. First the arguments against relativism will be stated. Next, a radical form of global relativism with assessment sensitivity is introduced, RR. Finally, it is shown how RR can be defended against the challenges of the peritrope and the regress. No attempt is made to defend RR as a plausible theory; however, the usual attempts to show the logical incoherence of radical forms of global relativism fail.