All of the ontological arguments are basically word salads attempting to trick the listener into accepting the argument. That makes them about the most dishonest arguments as well.
As for Godel, his Axioms are a big problem. First of all he never defines what he means by "positive." Some who defend his argument sometimes claim that this doesn't matter but most people disagree. Something that is so central to the argument has to be defined.
Axiom 1: If property A is positive, and if property A entails property B, then B is positive.
Why? Does there never exist a trade-off where one "positive" property requires the acceptance of a "negative" one? How about a military tank with light armor which allows it to move quickly but makes it vulnerable to armor piercing shells?
Axiom 2: If property A is positive, then the property not-A is not positive. So is the property "Red" "positive?" Some people would say so (especially given that Godel never defines "positive), does that make "non-Red" not positive? Or are the property of "Red" and "non-Red" simply neutral? How do we tell if properties are "positive" or simply neutral.
Axiom 3: The property G is a positive property. (G is the property of being "God-like"; an object with property G has all positive properties)
This is total gibberish. Define "God-like" and why must someone with this property have all "positive" properties? Is jealousy a positive property? What about vengefulness?
Axiom 4: If a property is positive, then it is positive in all possible worlds.
Why? There are probably possible worlds where the property of being a Nazi is considered positive because the Germans won WW II while in most worlds the property of being not-Nazi is positive.
Axiom 5: Necessary existence is a positive property.
Again, define "necessary existence" and demonstrate that it must be "positive" whatever the hell positive may be.
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