This is one of the methods followed by people of this kind: they set out categories conceived in the mind, without proving either the possibility or the existence of each category. They merely posit them, then build upon that supposition as though they had established it in external reality, although they have not. We have mentioned similar cases elsewhere.
The point here is that the statement, “Every existent, when considered in respect of its essence without reference to anything else, is either necessary or contingent,” is valid only if it is known that what exists in external reality has an essence that can be considered without reference to anything else. Only then can it be said that this essence is either necessary, or that existence is necessary for it, or that existence is not necessary for it.
But if there is nothing in external reality except what exists—either through itself or through another—then what exists through another, when considered without reference to that other, has no essence that can be considered such that one might say, “It is contingent, capable of existence and nonexistence.” Rather, this entity posited as existing through another has no reality whatsoever when that other is left out of consideration: neither existence nor anything else. Nor is there anything there that could possibly exist at all.
Thus, this interpretation cannot serve as the basis of an argument until an actual essence has been established in external reality, distinct from the existence found in external reality. Since this category has not been established, the argument is invalid.