It is often supposed that an infinite regress of existents undermines any proof for God’s existence. Put simply, on this view it is argued that there has always been some ‘thing’ causing another, the former itself being caused by something prior, and the latter in turn causing yet another thing and so on ad infinitum. Usually, arguments for God’s existence in one way or another rule out such a premise by appealing to the principle of infinitum actu non datur (i.e. an actual infinite is impossible) which the First Teacher put forth in both his Physics and Metaphysics. Interestingly however, the Shaykh al-Ra’is in his famous proof for God’s existence, known as the Burhan al-Siddiqin (the Proof of the Veracious) makes no use of such a principle and grants the assumption of an infinite series of existents for the sake of argument. Even if allowing such an assumption, still it would not, he argues, disprove in the least the existence of a necessary being, namely, God. The entire argument, consisting of various interrelated premises, is complex and intricate, but I’d just like to focus on one part of it here, namely, how the Shaykh arrives at his conclusion i.e. the existence of God, despite the assumption of an actual infinite series of existents.
This is my formulation, in syllogistic format, of the relevant part of the Shaykh’s argument as it is found in the Ilahiyyat of his Kitab al-Najat. He argues, with respect to the entire series of possible existents considered as a totality/aggregate, thus:
The totality/aggregate (jumla) of such an infinite series of contingents must exist, at any given moment, either (a) necessarily in itself or (b ) possibly in itself.
But it cannot exist (a) necessarily in itself.
Proof of the Major: given that necessity and contingency (or possibility) are the two primary divisions of existence, and given that, as per the present assumption, an infinite series actually exists, this division is hence applicable to it.
Proof of the Minor: the totality/aggregate cannot exist necessarily in itself, for it only subsists through its members, all of which are merely possible/contingent in themselves. Hence in this case the totality that is necessary through itself would be so only through the existence of its members – but this is a contradiction, for a thing necessary in itself cannot at the same time be necessary through another. And the conclusion follows.
Given the above conclusion, then,
The totality/aggregate that exists possibly in itself needs a cause of its existence, and this cause will be either (c ) internal to it or (d) external to it.
But the cause cannot be internal to the totality/aggregate.
Therefore, etc; and this external cause is the Necessary Existent.
Proof of the Major: that which is contingent (or possible) in itself needs a cause of its existence.
Proof of the Minor: if the cause were internal to the totality/aggregate, a contradiction would result; for something internal to the aggregate would be a member of it and hence merely possible/contingent in itself – and as such it can’t exist necessarily, the assumption at the moment being that the aggregate only includes the mumkinat i.e. contingent existents. Hence if we now supposed that the cause of the aggregate was internal to it and necessary in itself, a contradiction would result. Thus, the internal cause of the totality/aggregate cannot be both i.e. internal to the aggregate (for then it would be merely contingent) and necessary in itself (for then, contrary to our assumption, it wouldn’t be a member of the series, which includes all and only contingents). Furthermore, such a cause cannot be both internal to the aggregate and contingent (possible) in itself either; for then it, being a member of the aggregate, would be the cause of its own existence. But self-causation, i.e., for one thing to be a cause and an effect in the same respect, is an impossibility. Hence this option is false also. But let the assumption of self-causation, per impossibile, be granted; in that case such a member would exist necessarily in itself. But against this the initial assumption was that the aggregate consists of members only contingent (possible) in themselves – and hence a contradiction results again, namely, the member in question this time now being both contingent (possible) in itself (for presumably it is a member of the aggregate) and necessary in itself (but being a member of the aggregate exludes it from being necessary). But all that is false; hence the member in question cannot be both i.e., internal to the aggregate and possible in itself. And the conclusion follows.