Moreover, analogical inference (qiyās al-tamthīl) can in some situations rise to the level of certainty. Just as the original and the subsidiary case may be joined by identifying their common factor, they may likewise be joined by eliminating any supposed point of difference—by realizing that “this is the same as that” and that they cannot diverge with respect to the ruling in question. Things equal to the same thing are equal to one another, and the mind can know equality and likeness just as revelation can. Once the ruling of one of two identical cases is established, the ruling of the other is necessarily the same—especially when the discussion concerns abstract matters. If one affirms, for example, that a particular patch of blackness is an accident dependent on a substratum, it follows that every instance of blackness is so, indeed every color as well. Likewise, if it is said that the motion of the heavenly bodies occurs successively, one replies that every motion is successive.
To put it briefly, we have shown that every syllogism requires a positive universal proposition, and that the truth of its universality must be known. Whatever establishes that universality simultaneously establishes that the ruling is entailed by the shared universal; that universal may therefore be treated as the common element linking the original and the branch. Hence every inclusive syllogism (qiyās al-shumūl) can be expressed as an analogical inference. If the inclusive form already produces certainty, casting it as an analogy only reinforces that certainty.
When one of the two premises is known from a text of the infallible Lawgiver, employing the inclusive syllogism is preferable.
An analogical inference can indeed be recast as an inclusive syllogism, but demonstrating its soundness may require proving one of its premises—most often the major premise. In such cases the original case to which the branch is compared is easier to establish first, so analogical reasoning is more helpful for exposition. The exception is when the universal proposition itself is known by a text of the infallible or by an infallible consensus; here, arguing from that universal is preferable to arguing by analogy. Yet in such a situation the proof is scriptural, for one of its premises is established solely by the statement of the infallible or by the protected consensus, not by pure reason alone—so the objection is misplaced.
Our discussion is directed to those who take the material of demonstration to be universal propositions known independently of any transmitted statement