This is the first (of a total of ten) and the strongest proof for the existence of God that Khajeh Nasir al-Din Tusi (d. 1274) adduces in his Treatise on the Proof of the Necessary. Tusi was a close follower of Ibn Sina (d. 1037) so it’s hardly surprising that this proof he presents is essentially a version – nay, almost an exact reproduction – of the Shaykh al-Ra’is’ well-known Burhan al-Siddiqin as contained in his Kitab al-Najat. However, unlike his master’s version, Tusi’s presentation of the argument omits a lot of background and is as a result rather terse and to the point. I’ve tried to retain something of that concision with my own formulations of the steps in the argument here.
From the contingency of essences: Whatever in being is an existent (har che dar wujud mawjud ast) must be of two kinds: (a) necessary existent by its essence, or (b) possible existent by its essence. If (a), the existence of God is established. If (b), then there must be a cause of its existence (given that a contingent existent by definition needs a cause to existentiate it). Now the cause of the existence of (b) is either (c) necessary or (d) contingent. If (c), the existence of God is established. If (d), then, again, it will need a cause. At this point, two options are available; either this process of causation will (e) regress ad infinitum or (f) it will terminate with a being necessary in itself. If (f), the existence of God is established. But if (e), then the actually existing infinite series, considered now as a actually existent totality or set, will either (g) be something that is dependent for its actual state of existence as an actual infinite series on each one of its members or (h) on something outside the entire series. If (h), the existence of God is proven. If (g), then given that each member of the infinite series is contingent, the infinite series as a whole – since, again, it just is the totality of its members existing all together – will be contingent. Consequently, it will be in need of a cause. Now there are three possibilities for what this cause, of which the infinite series is need for its existence, can be; either (i) the cause will be the series itself or (j) it will be a member of the series or (k) it will be something altogether outside the entire series of contingents. If (i), that would mean the series originates itself. That means that it would be prior to itself. And that means that it would be the cause of its own existence prior to existing. But that is a manifest impossibility. If (j), that would mean that the member in question will, in addition to being responsible for the existence of all members other than it, also be the cause of its own existence. But this, again, is a manifest impossibility. If (k), then the existence of God, as a cause outside the entire set of actually infinite series of contingents, is established. For what is outside contingency is not contingent; rather, it is necessary. Thus, the cause of the infinite series is necessary by its essence and this is God. Therefore, God exists.