The growing presence of 'New Atheism' in recent decades has brought with it a fairly commonplace argumentative strategy: first, the New Atheist will lay claim to be 'rational', 'reasonable', or 'justified' in their beliefs. The New Atheist will then usually proffer a number of theologically, philosophically and factually questionable arguments that the theist lacks any reasons, evidence or justification, or theism contradicts a position that has reasons, grounds, evidence or justification. The New Atheist concludes the theist is therefore delusional or 'irrational'; the theist must rely on 'faith' rather than reason. Oftentimes, this argumentative strategy moves one more step: the New Atheist claims theists are, by relying solely on 'faith', deserving of public derision, invective or opprobrium. Thus move the iron chains of logic. Case closed. But is this argumentative strategy appropriate? These New Atheists have played a weak hand, for the existence of many different theories of rationality raise a second-order question of interest to theists and atheists alike:What standards should be adopted when choosing between conflicting theories of rationality? Presumably, we should rationally choose our standards--yet this produces a feeling like floating on air: we are faced with two problems, namely what should count as the rational adoption of some standard? and which standards should be rationally adopted? The first requires a standard of rational adoption; the second requires the rational adoption of standards. Each question demands the answer to the other, with no obvious starting-point with which to 'bootstrap' to an answer. This is but to restate briefly the traditional problem of the criterion. I focus on three proposed attempts at jointly solving the problem of the criterion and preserving the possibility of the rational adoption of a theistic stance: (1) Alvin Plantinga's reformed epistemology, (2) the radical form of presuppositionalism developed by Karl Barth and Paul Tillich, and (3) comprehensively critical rationalism, a theory of rationality developed by W.W. Bartley that abandoned the assumption that rationality and justification were one in the same. I explain the philosophic problem-situation that lead to developing these three theories of rationality, compare their respective approaches, and conclude that comprehensively critical rationalism provides the most principled approach for both resolving the problem of the criterion and permitting the possibility of the rational adoption of a theistic stance. I then provide historical evidence that there exist versions of theistic stances that are compatible with comprehensively critical rationalism.