and upward; yet that, most certainly, is not what they meant, so only the first sense remains.
If it is objected that they nevertheless commit themselves to the view that “the minimum make-up of a syllogism is two premises, though it may contain more,” the reply is, first, that this contradicts their own manuals: there they accept only two—and nothing but two—premises. Indeed, they state explicitly that the syllogism which yields the desired conclusion, whether categorical (iqtirānī) or hypothetical (istithnāʾī), is never fewer than two premises and never more.
Their reason is that the single sought proposition does not exceed two parts, a subject and a predicate. If the syllogism is categorical, each of those two parts must correspond to one of the premises, appearing in it as either subject or predicate, without itself being the entire premise. Because the conclusion has no more than two parts, it needs no more than two premises. If the syllogism is hypothetical, it must include one conditional premise—conjunctive or disjunctive—covering the whole conclusion or its negation, together with an exceptive premise; a third premise is unnecessary.
They add that a statement in excess of the two canonical premises may sometimes be inserted—either unrelated to the syllogism or connected with it. When connected, it is introduced either to make the discourse more persuasive and elegant, or to spell out one or both premises. Such an argument they call a “compound syllogism.” In essence, it reduces to several syllogisms marshalled to establish a single conclusion, one of which alone proves the point directly, while the rest serve to clarify its premises.
They may also omit some premises, relying either on the listener’s mind to supply them or on the wish to pass off a sophism whose falsehood would become evident if the premises were plainly stated. If the auxiliary syllogisms that explain the premises have their own conclusions explicitly mentioned, the argument is called “separated”; if not, it is “connected.”
They illustrate the connected type with the example: “Every human being is an animal; every animal is a body; every body is a substance; therefore every human being is a substance.”
The separated type they exemplify by saying: “Every human being is an animal; every animal is a body; therefore every human being …”