Siegel claimed that teachers are obliged to provide grounds whenever demanded, as a result of which they must be able to subject to scrutiny whatever they teach. In this paper, however, and taking as a reference Wittgenstein's "On Certainty," it is shown that such a demand cannot work for second language teachers because their main task consists in transmitting ungrounded certainties. To clarify this point, I begin by presenting Wittgenstein's conception of 'certainty', and explaining why I think he was right to provide examples of teachers who refuse to answer their students' doubts concerning certainties. Thereafter, I analyze two kinds of grounds -- i.e. historical and practical -- with which a second language teacher might reply to the students' queries about the certainties that he aims to transmit to them. This will enable me to reveal the consequences of such replies and, by extension, the scenario that would result from allowing students to decide whether they accept whatever is taught to them. In this way, I will show not only that Siegel's demand is unfeasible, but also why second language teaching provides a clear example that the acquisition of certainties constitutes a final goal in education.