  This model theoretic behavior corresponds to expectation-guided reasoning, where the expectations allow certain cases to be neglected. Here is an important difference between common sense and mathematics. Mathematicians are trained to reject a proof by cases unless the cases exhaust all the possibilities; but typical instances of common sense reasoning neglect some alternatives. In fact, it is reasonable to routinely ignore improbable possibilities. Standing in a kitchen in California, wondering if there is time to wash the dishes before leaving for work, one might not take the possibility of an earthquake into account.