If the two cases share neither the factor that entails the ruling nor that which is entailed by it, the analogy is certainly invalid, for in that situation the operative cause would be confined to the original alone; and unless this is known, the soundness of the analogy cannot be established.

The validity of an analogy may, however, be confirmed simply by the absence of any relevant distinction between the original case and the subsidiary case, even when the precise cause and its supporting evidence remain unknown. The absence of a differentiating factor necessarily implies that both cases fall under the same ruling.

Accordingly, representative analogy is complete only when no distinguishing factor exists, or when a unifying element—a universal that encompasses both cases and entails the ruling—is presented. Either method can be set out as a syllogism of inclusion: the ruling is necessary for the universal, and the universal is necessary for each of its particulars. This is the essence of a syllogism of inclusion; it is not a mere transfer of a ruling from one particular to another.

When it is already known that the common element entails the ruling, the major premise of the syllogism is established. Clarifying the middle term is simply the identification of that shared universal, and affirming its linkage to the major term is the affirmation that the ruling is inextricably tied to that shared universal, as noted earlier.

One may also infer a particular from another particular when the two are mutually entailing, or when one entails the other without the reverse being true. If the entailment is essential, the inference concerns the essence; if it pertains to an attribute or a legal ruling, the inference concerns that attribute or ruling.

It is thus evident how defective their restrictive formulation is. As for their division into three kinds, all of them ultimately reduce to the very principle they cite: that the evidence necessitates what it proves.

Their distinction between the “categorical” (iqtirānī) and the “conditional” (istithnāʾī) syllogism likewise collapses into a single meaning: whatever they present in categorical form can be reformulated in conditional form, and whatever they express conditionally can be recast categorically. In the end, both return to one and the same concept.