Mixed Ḥaqīqī-Khārijī Syllogisms: The Productive Moods and Their Conclusions

In both of his logical books, Qisṭās al-afkār</em> and its self-commentary Sharḥ al-Qisṭās</em>, Shams al-Dīn Samarqandī presents two versions of mixed ḥaqīqī-khārijī syllogisms. In previous papers, we discussed these two versions and demonstrated that both contain numerous errors. As a result, neither version provides a correct and comprehensive analysis of mixed ḥaqīqī-khārijī syllogisms. In this paper, we aim to present the accurate conclusions of mixed syllogisms. By adhering to the principles accepted by Arabic logicians, including Samarqandī, our version should be beyond objection and can be considered a wholly correct interpretation of mixed ḥaqīqī-khārijī syllogisms. We will examine the khārijī-ḥaqīqī and ḥaqīqī-khārijī mixes separately within each of the four traditional figures of syllogism. We will determine the sterile and productive mood-mixes on a case-by-case basis and elucidate the true conclusions of each productive mood-mix individually. The systematic study of counterexamples for the sterile mood-mixes will be deferred to future research.