Gödel's Ontological Proof
Let K be a class of sets such that whenever x is in K and x is a subset of y, then y is also in K. It follows that if the empty set is in K, then every set is in K. Let's rule this out by stipulating that some set is not in K. Thus every set that is in K is not empty. So instead of saying outright that some set is not empty we can instead say that it is in K, which sounds less controversial but really comes down to the same thing.
I think this is the trick in Gödel's ontological proof of god. His class K is the class of 'positive' properties, where properties are individuated intensionally. Gödel claims 1) that whenever some property Q is necessarily implied by a positive property P, then property Q is also positive (which is just the closure principle above), and 2) that not all properties are positive. On these assumptions saying that a property is positive means saying that it is not empty, that is, not necessarily uninstantiated. Hence when Gödel says that 3) necessary existence is a positive property he in effect says that a necessary being possibly exists, which in turn means that a necessary being actually exists.
The fallacy is to assume that there is any class of ('positive') properties satisfying (1)-(3).