If, then, you class reasoning from one particular to another as “analogy,” your list is still far from exhaustive. There yet remains the reasoning that proceeds from one universal to another that is inseparably linked to it—equal to it in scope—as well as the reasoning that proceeds from a particular to the particular that necessarily accompanies it, so that the presence of the one entails the presence of the other and its absence entails the other’s absence. This mode belongs to none of the three you have named—syllogism, induction, or analogy. These, in fact, are the very “signs” (āyāt).

Reasoning from a universal to a universal and from a particular to its concomitant particular:

Take, for example, inferring the presence of day from the rising of the sun, and the rising of the sun from the presence of day. Here one may infer a specific sunrise from a specific day—that is particular to particular—or infer the class of days from the class of sunrises—that is universal to universal. It is not a universal-to-particular inference at all.

Similarly, determining the direction of the Kaʿbah by means of the stars is an instance of particular-to-particular reasoning: one may rely on al-Jady, on Banāt Naʿsh (the Plough), or on the small star near the celestial pole that some people call al-Quṭb (the Pole Star), just as others call al-Jady the Pole—even though the true pole is actually a point of the celestial sphere situated close to that tiny star.

The same applies to inferring the rise of one star from the rise of another that shares its latitude, or inferring