Empirical evidence for the capacity to detect conflict between biased reasoning and normative principles has led to the proposal that reasoners have an intuitive grasp of some basic logical principles. In two studies, we investigate the boundary conditions of these logical intuitions by manipulating the logical complexity of problems where logical validity and conclusion believability conflict or not. Results pointed to evidence for successful conflict detection on the basic Modus Ponens (MP) inference, but also showed evidence for such a phenomenon on the more complex Modus Tollens (MT) inference. This suggests that both the MP and the MT inferences are simple enough for reasoners to have an intuitive grasp of their logical structure. The boundaries of logical intuition might thus reside in problems of greater complexity than these inferences. We also observed that on the invalid Affirmation of the Consequent (AC) and Denial of the Antecedent (DA) inferences, participants showed higher accuracy on the inference that was expected to be more complex (DA), and no evidence for successful conflict detection was found on these forms. Implications for the logical intuition framework are discussed.