The decisive factor is that it diverts people from the remembrance of God and from prayer; this quality is present in it, the revealed text identifies it as the very cause of the prohibition, and once the cause is present, the prohibition necessarily follows.
When, in a universal syllogism (qiyās al-shumūl), one seeks to establish the major premise—whose role parallels the identification of the shared element that links the original case to the subsidiary—evidence must be produced to show that the ruling applies to every instance covered by that premise by virtue of the single, universal attribute common to them all. That attribute is the "common denominator" (jāmiʿ) in analogical reasoning; the universal (kullī) is the jāmiʿ, and the jāmiʿ is the universal.
Some later dialecticians—such as Abū al-Maʿālī, Abū Ḥāmid, al-Rāzī, and Abū Muḥammad—maintained that in purely rational matters there is no qiyās and that one need only consider the direct evidence. Although this view runs contrary to the great majority of logicians and their masters, the disagreement is essentially terminological. They argue that rational questions do not require designating one case as the “original” and the other as the “subsidiary,” for neither designation is more rightful than its opposite; what counts is the proof that encompasses both cases.
The reply is that, in both rational and revealed disciplines, contention never concerns every instance of the general meaning known as the common denominator; it only concerns some instances, while the rest are agreed upon. Labeling one case the original and the other the subsidiary is therefore a relative matter. If, for example, a person learned the ruling of the so-called subsidiary from an explicit text while the ruling of the supposed original was unknown to him, he would reverse the designations, treating the original as the subsidiary and vice-versa. The two cases are connected either by eliminating the purported difference or by presenting the shared cause—and this operates in rational matters, whether with certainty or with probability, just as it operates in Sharīʿa-based matters.