seeing or speaking; for if life is present, then the being falls under one of the two divisions, and if life is absent these attributes disappear as well—though someone may be alive yet not described by them. Likewise, when it is said, “This person is either in a state of purification or he is not praying,” then if prayer is absent, purification is also absent; and if purification is present, the statement belongs to the other division. In either case, the matter cannot escape one of the two alternatives.
The same reasoning applies whenever the absence of a condition is set against the existence of what depends on it. If the alternatives are framed as either the existence of the conditioned or the absence of its condition, no third option remains, for the matter is never devoid of the condition’s being present or absent. And once the absence of the condition itself is ruled out, the statement is reduced to two possibilities: the existence of the conditioned or the absence of the condition.
They then divide the categorical syllogism into four figures according to the position of the middle term. If the middle term is the predicate in the major premise and the subject in the minor, this is the natural (first) figure, and it yields all four kinds of conclusions—universal and particular, affirmative and negative. If the middle term is predicate in both premises, that is the second figure, which yields only negative conclusions. If it is subject in both premises, that is the third figure, which yields only particulars. The fourth figure produces particulars and universal negatives, yet it is far removed from what is natural.
When they wish to demonstrate the conclusions of the second and third figures—or other required conclusions—they must appeal to the contradictory, the converse, and the contrapositive. The truth of a proposition necessitates the falsity of its contradictory and the truth of its equipollent converse and contrapositive. Thus, if the statement “None of the pilgrims is an unbeliever” is true, then “None of the unbelievers is a pilgrim” is also true. And if “Every pilgrim is a Muslim” is valid, then “Some Muslims are pilgrims,” and “Whoever is not a Muslim is not a pilgrim,” are both valid.
Refutation of their statements concerning proof and syllogism: we say that what they have advanced is either outright false or an unduly lengthy detour that only postpones the attainment of truth.