Muslim logicians have concluded in two different ways from the conditional syllogism, whose middle term is incomplete. In this paper, Kashshi's method is investigated.
By examining disagreements about types, conditions of validity, conclusive moods, and the reason for the validity of this syllogism, we find that the validity of this syllogism is based on a syllogism whose middle term is complete and the components of categorical syllogism in the deduction system of conditional syllogism have made it difficult to understand clearly the structure of conditional syllogisms.
In order to reveal the deduction system concealed in this method, two basic syllogisms have been identified first: the syllogism whose middle term is part of the consequent in both the premises and the syllogism whose middle term is part of the minor consequent and the major antecedent. And then we introduce the rules that are used to prove non-basic syllogisms.