We examined the particular cases and found them otherwise; it may therefore be retorted to him:
“The crocodile moves the upper jaw.”
They then say that syllogism is divided into the categorical (iqtirānī) and the conditional (istithnāʾī). A conditional syllogism is one in which the conclusion—or its negation—is explicitly stated; a categorical syllogism contains the conclusion only potentially, as in a chain of categorical propositions, for example: “Every nabīdh is intoxicating, and every intoxicant is unlawful.”
The conditional syllogism is built from conditional propositions and is of two kinds.
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The connected (muttasil), as in: “If the prayer is valid, then the worshipper is in a state of purification.” Affirming the antecedent yields the consequent, while denying the consequent yields the denial of the antecedent.
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The disjunctive (munfasil), which itself falls into three classes:
a. Exclusive of both conjunction and separation, e.g. “A number is either even or odd.” The two cannot coexist, nor can the number be devoid of both.
b. Exclusive of conjunction only, e.g. “This object is either white or black.” Whiteness and blackness cannot be combined, though the subject may lack both.
c. Exclusive of separation only, where the simultaneous absence of both alternatives is impossible, but their coexistence is not.
They sometimes maintain that the disjunction exclusive of both conjunction and separation is the genuine conditional, for it corresponds exactly to contradictories in scope. The disjunction that bars conjunction only is narrower than contradictories, for contraries cannot coexist yet may both be absent. The disjunction that bars separation is broader than contradictories, and they often struggle to supply examples of it—unlike the first two kinds, whose examples are plentiful. One illustration they give is: “This man is either sailing on the sea or he does not drown in it,” meaning that one of the two must hold. He does not drown unless he is at sea, so either he is not drowning—thus not sailing—or he is sailing, and it is also possible that he both sails and drowns.
Many other examples can be cited, such as: “This being is alive, or it is not knowledgeable, or powerful, or hearing, or…”