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A controversial claim in recent dual process accounts of reasoning is that intuitive processes not only lead to bias, but are also sensitive to the logical status of an argument. The intuitive logic hypothesis draws upon evidence that reasoners take longer and are less confident on belief-logic conflict problems, irrespective of whether they give the correct logical response. In this paper we examine conflict detection under conditions in which participants are asked to either judge the logical validity or believability of a presented conclusion, accompanied by measures of eye movement and pupil dilation. The findings show an effect of conflict, under both types of instruction, on accuracy, latency, gaze shifts and pupil dilation. Importantly these effects extend to conflict trials in which participants give a belief-based response (incorrectly under logic instructions, or correctly under belief instructions) demonstrating both behavioural and physiological evidence in support of the logical intuition hypothesis.