They then say that syllogisms are divided into “conjunctive” and “exceptive.” An exceptive syllogism explicitly contains either its conclusion or the contradictory of its conclusion, whereas a conjunctive syllogism contains it implicitly. An example of the latter is a syllogism composed of categorical propositions, such as: “All nabīdh (infused drink) is intoxicating, and everything intoxicating is forbidden.”

An exceptive syllogism is composed of conditional propositions and is of two types:

The first employs an “if–then” proposition, such as: “If the prayer is valid, then the person praying is ritually purified.” Affirming the antecedent yields the consequent, while denying the consequent yields the denial of the antecedent.

The second employs a disjunctive proposition. This may preclude both joint truth and joint falsity, as when we say: “A number is either even or odd.” These two cannot both apply, nor can a number be neither.

Alternatively, it may preclude joint truth alone, as when we say: “This is either black or white,” meaning that blackness and whiteness cannot coexist, although the subject may possess neither.

As for a proposition that precludes joint falsity, it is one in which both alternatives cannot be absent together, although they may coexist.

They sometimes call the proposition that precludes both joint truth and joint falsity the genuine conditional proposition. It is coextensive with a pair of contradictories. A proposition that precludes joint truth has a narrower scope than a pair of contradictories: two contraries cannot coexist, but both may be absent, and they are narrower in scope than a pair of contradictories. A proposition that precludes joint falsity, by contrast, has a broader scope than a pair of contradictories. They may find it difficult to give an example of this, unlike the first two types, for which examples abound.

They illustrate it by saying: “This man has gone to sea, or he does not drown in it”; that is, he cannot be without