A mixed syllogism (qiyās mukhtalaṭ) is a syllogism that has various modalities in its premises. Regarding mixed syllogisms of the first figure, Aristotle, Al-Fārābī, Ibn Sīnā, and Fakhr al-Dīn al-Rāzī correctly maintain that a syllogism can yield a conclusion from a possible minor premise. On this basis, they even regard negative minor premises as productive, despite the fact that affirmation of the minor premise is a condition of the first figure. An important consequence of this view is the expansion in the number of productive mixed syllogisms within this figure. However, logicians such as Khūnjī, Athīr al-Dīn al-Abharī, Najm al-Dīn al-Kātibī, and Al-Taftāzānī, by introducing the condition of the actuality of the minor premise, considered not only mixed syllogisms with a negative minor premise and a possible minor premise to be non-productive, but also regarded Ibn Sīnā’s position as inconsistent with his own theory concerning the ʿaqd al-waḍʿ (“subject nexus”). Consequently, at least twenty-six forms among the mixed syllogisms of the first figure were judged invalid solely on this basis. Among later scholars, however, Quṭb al-Dīn al-Rāzī rose in strong defense of Ibn Sīnā and explicitly accused Khūnjī of failing to understand Ibn Sīnā’s words. Accordingly, the main question is whether such mixed syllogisms are productive or not. In order to answer this question, the present study seeks to examine the arguments of both sides and evaluate Khūnjī’s reasoning and criticisms. It seems that Khūnjī’s argument, while resting upon disputable presuppositions, suffers from several fundamental problems and improper generalizations, some of which are pointed to by Quṭb al-Dīn al-Rāzī.