Data involving epistemic modals suggest that some classically valid argument forms, such as reductio, are invalid in natural language reasoning as they lead to modal collapses. We adduce further data showing that the classical argument forms governing the existential quantifier are similarly defective, as they lead to a de re–de dicto collapse. We observe a similar problem for disjunction. But if the classical argument forms for negation, disjunction and existential quantification are invalid, what are the correct forms that govern the use of these items? Our diagnosis is that epistemic modals interfere with hypothetical reasoning. We present a modal first-order logic and model theory that characterizes hypothetical reasoning with epistemic modals in a principled manner. One upshot is a sound and complete natural deduction system for reasoning with epistemic modals in first-order logic.