I am referring to this paper https://github.com/FormalTheology/GoedelGod/blob/master/GodProof-ND.pdf which has formalized the ontological argument.
If I am not mistaken, watered down, the argument should be that we can define existence as a property by saying it's exemplification of essential properties of a thing, and then take a set of properties (here he takes 'positive properties') to include it. Once we accept existence as a property, the rest kind of naturally follows. Once we establish existence as a property we can simply in different terms define something in whose essence is to have that property, and then the very possibility of that thing would imply its necessary existence.
I'm aware why ontological arguments have historically failed, and why they must fail, but that doesn't show me the error of this argument, and that's what I'm interested in. I would prefer not to reach outside of the argument to search for the fact that there must be an error, but attempt to point at the error. Where does it exactly go wrong?
The only thing that crosses my mind right now is to refer to the equivalence made by the property of existence and the exemplification of essential properties made by the argument. If the complete sum of all essential properties is exemplified, then a thing has the property of existence. If we use existence defined in such a way as an essential property of something, we are inferring a complete sum of all properties, but we're doing it from within the essence of a thing, which is still not complete, so the reference to it is not justified. This is the only thing I could think of so far, aside from rejecting the notion of essence.
How do we answer this paper? Is there shakiness of some axiom that I'm missing?