In limmī demonstration, the middle term both grounds the conclusion in reasoning and causes the relevant predication in reality. In innī demonstration, it grounds the inference but does not cause the fact; it may even be an effect of its real cause.
The textbook's fever-and-humors illustration represents these two directions within a historical theory. The enduring logical lesson is to distinguish evidence from causation and to assess the argument's form and premises independently.
The following section is dialectical syllogism (al-qiyās al-jadalī), which uses commonly accepted or conceded premises rather than the certain foundations of demonstration.