In his influential paper “Grasping the Third Realm,” John Bengson raises the question of how we can non-accidentally grasp abstract facts. What distinguishes successful intuition from hallucinatory intuition? Bengson answers his “non-accidental relation question” by arguing for a constitutive relationship: The intuited object is a literal constituent of the respective intuition. Now, the problem my contribution centers around is that Bengson’s answer cannot be the end of the story. This is because, as Bar Luzon and Preston Werner have recently pointed (...) out, this answer leads to the follow-up question of why certain intuitional experiences are constituted by the facts, but others are not. My objective is to answer this question by specifying precisely what is epistemically defective about intellectual hallucinations. My result is that, in stark contrast to perception, intellectual hallucinations are epistemically defective in the sense that something is overlooked. In successful intuition, by contrast, all relevant possibilities/scenarios are considered/imagined. This has crucial epistemological implications. In particular, I argue that intuitions exhibiting a certain phenomenology cannot fail to successfully grasp abstract facts. I call this the non-accidental correctness thesis, which constitutes the main thesis of this paper. (shrink)