If this is correct, then Anselm's second version of the argument also fails. The targets might be undergraduate philosophy students, and the goal might be to give them some sufficiently frustrating examples on which to cut their critical teeth.
Those who take themselves to have good independent reason to deny that there are any gods will take themselves to have good independent reason to deny that there are God-properties that form a non-trivial collection that is closed under entailment.
Conflating the concept with its object, this gives us the belief that than which no greater can be conceived possesses the property of existing in the understanding. If so, then a being cannot be perfectly just and perfectly merciful.
Chambers, T. Premise Hence There is a being x existing in the actual world such that for no world w and being y does the greatness of y in w exceed the greatness of x in the actual world.
Hence God exists. Trying to support most of these claims merely in order to beat up on ontological arguments is like using a steamroller to crack a nut in circumstances in which one is unsure that one can get the steamroller to move! Malcolm goes on to claim that it is unreasonable to hold that a believer in the Ontological Argument is required to show that his conception of God is sound since, although he may respond to specific claims that the notion of a being than which no greater can be conceived is self-contradictory and defend his definition of God on that ground, it cannot be shown in general that the concept is not self-contradictory.
Descartes attempts to prove God's existence by arguing that there "must be some one thing that is supremely good, through which all good things have their goodness". Accordingly, the trick is to show that a maximally great being exists in some world W because it immediately follows from this claim that such a being exists in every world, including our own.