Given that the Philosophers believed in the beginninglessness of the world, they could not have used Burhan Al-Huduth to prove God’s existence. Instead, they utilized what is known as the Burhan Al-Imkan (Proof of Contingency):
- If the set of all contingents is contingent, then a necessary being exists.
- The set of all contingents is contingent.
- Therefore, a necessary being exists.
Premise 1: If the set of all contingents is contingent, then a necessary being exists.
A contingent depends on an extrinsic specifier to grant it existence. And an existent that is not part of the set of all contingents, is necessary.
Thus, if the set of all contingents depends on an extrinsic specifier to exist, then this specifier exists necessarily.
Premise 2: The set of all contingents is contingent.
A composite depends on the existence of each of its parts to exist. And if those parts exist contingently, then this composite would exist contingently as well. For that which depends on contingents to exist, is contingent a fortiori.
From there, we realize that the set of all contingents is nothing but a composite of contingents. A composite that would not exist if each of those contingents did not. Thus, the set of all contingents exists contingently.
Therefore, a necessary being exists.
Given the above, there exists a necessary being who the set of all contingents depends on to exist. And since “necessary being” is what is meant by “God”, God exists.
 Since an existent either accepts non-existence, or not. If so, it is a contingent. If not, it is a necessary being.
 For example: a house depends on the existence of its bricks to exist. If those bricks did not exist, then the house would not either.
 For example: if an opponent grants that the bricks that this house is made of are contingent, we say: either the house as a whole exists necessarily, or it exists contingently.
It cannot exist necessarily. This is because those bricks accept non existence by virtue of their being contingent. And the house would not exist if those bricks did not. So since it is possible for those bricks to not exist, it is possible for the house to not exist as well. And that which accepts non-existence, does not exist necessarily.
And since the house does not exist necessarily, it exists contingently.
 The deficiency in this proof, is its failure to identify the necessary being more clearly. An opponent could argue that this necessary being is actually a planet, or an idol, or even the matter and energy of the universe itself. Separate arguments would need to be offered to rule out all those possibilities.
On the other hand, Burhan Al-Huduth, with the aid of Burhan Huduth Al-Ajsam as a sub-argument for the second premise, more directly concludes the existence of an incorporeal and changeless necessary being, who volitionally selected existence for the world.
The above is why most of the Mutakalimun preferred Burhan Al-Huduth over Burhan Al-Imkan, even though they agreed that Burhan Al-Imkan is a valid route to proving the existence of a necessary being.