 In medieval times, dilemma does not seem to have attracted much theoretical reflection, though there was an extensive literature on related genres such as insolubilia and paradoxes, which were generally treated in a logical manner. It is, therefore, interesting to see Valla discussing a whole range of examples of dilemma. The rhetoric textbook by the Byzantine émigré George of Trebizond (1396–1486), composed about 1433, was probably an important source for him. This work might also have led Valla to explore the relevant places in Quintilian, Cicero, the Greek text of Aristotle’s Rhetoric and perhaps other Greek sources. The example Valla discusses most extensively comes from Aulus Gellius and concerns a lawsuit between Protagoras and his pupil Euathlus (Repastinatio, 1:312–319; 2:562–568; DD 2:312–28. Aulus Gellius, Noctes Atticae, 5.10.5–16). The pupil has promised to pay the second installment of the fees as soon as he has won his first case. He refuses to undertake any cases, however, and Protagoras takes him to court, putting the case in the form of a dilemma. If Euathlus loses the case, he will have to pay the rest of the fee, on account of the verdict of the judges; but if Euathlus wins, he will also have to pay, this time on account of his agreement with Protagoras. Euathlus, however, cleverly converts the argument: in neither case will he have to pay, on account of the court’s decision (if he wins), or on account of the agreement with Protagoras (if he loses). Aulus Gellius thinks that the judges should have refrained from passing judgment because any decision would be inconsistent with itself. But Valla rejects such a rebuttal (antistrephon or conversio) of the dilemma and thinks that a response may be formulated as long as one concentrates on the relevant aspects of the case. He carefully considers the perspectives of all parties, the words employed, the feelings of the judges, and all the circumstances of the case. In a highly rhetorical analysis of the case in which Valla makes speeches on behalf of Protagoras, Valla says in the end that Euathlus cannot have it both ways and must choose one or the other alternative, not both: he must comply either with his agreement with Protagoras (and pay the rest of the fees) or with the verdict passed by the judges. If he loses the case, a refusal to obey the sentence of the judges shows contempt; if he wins the case, he has to pay the rest of the fee to Protagoras. At any rate, there is no reason for the judges to despair; Aulus Gellius is, therefore, wrong in thinking that they should have refrained from passing a judgment. In all such cases, Valla argues, the conversion is not a rebuttal, but at best a correction of the initial argument (a correction, however, is not a refutation), and at worst a simple repetition or illegitimate shift of the initial position.