ABSTRACT: The new rationalists – BonJour and Bealer – have characterized one type of a priori justification as based on intellectual intuitions or seemings. I argue that they are mistaken in thinking that intellectual intuitions can provide a priori justification. Suppose that the proposition that a surface cannot be red and green all over strikes you as true. When you carefully consider it, you couldn’t but realize that no surface could be both red and green all over. Ascertaining the truth of what you believe (when you believe that a surface cannot be red and green all over) requires conscious experiences of thinking. The character of such experiences (propositions’ striking you as true, and the sense of incoherence you would experience were they to be false) is what justifies your belief. It should follow that the justification for such propositions (and your believing them) is a posteriori, i.e., based on conscious experience. Your cognitive phenomenology plays a constitutive role in justifying your belief. Hence your belief is not a priori justified, contra the new rationalists.