The erotetic, or question-based, theory of reasoning has been developed from an account of utterance interpretation but moves beyond interpretation to a general account of human reasoning with multiple premises that covers both ideal valid reasoning as well as fallacious reasoning. The core idea of the erotetic theory of reasoning is that reasoners treat premises as questions and maximally strong answers, which can be made mathematically precise using tools from philosophy and linguistics. We present three experiments showing new fallacious inferences predicted by the erotetic theory, some of which are so frequently endorsed to be akin to cognitive illusions. The results suggest that similar phenomena discussed in the literature are more general and systematic than had been thought.