In summary, if a boundary is posited in an infinite series, such as the time of the Flood, and a later boundary is posited, such as the time of the Hijrah, and both series are assumed to extend without limit, then the greater must equal the lesser; if they differ in magnitude, this entails a difference in magnitude between infinite series.
This is the crux of the argument. Their opponents allowed such differences when what is infinite is not something existent with a beginning and an end, and countered their argument with the case of an endless future. This occurs when something infinite in one direction is taken to be finite in the other. For example, one may consider the events ending at the time of the Flood, and then those ending at the time of the Hijrah: although they have no limit in the earlier direction, they have a limit in the direction nearest to us.
Thus, if someone says:
“If we match these two series point by point, then, if they are equal, the greater must be equal to the lesser, or the presence of the additional portion must be equivalent to its absence. If they differ in magnitude, this entails a difference in magnitude between infinite series.”
They have two answers to this.
The first is:
“We do not concede that point-by-point matching is possible between series of different magnitudes. Such matching is possible only between equal series, not unequal ones.”
The second answer is:
“This entails a difference at the finite end, not at the infinite end, and there is nothing objectionable in that.”
Some people have a third answer: point-by-point matching is possible only with what exists, not with what does not exist.
Many groups among those who affirm the temporal origination of the celestial spheres—including the Muʿtazila, the Ashʿarīs, the philosophers, the scholars of hadith, and others—agreed with these people that what is infinite can exist both in the past and in the future. For they allowed a beginningless succession of events while maintaining that Allah brought into existence the heavens