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@AndersA:
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As I have already said, if you add other axioms, you may show that there are several gods or no god at all. You talk about proofs, but you don't like me to talk about logic which is the mother of proof theory.


Nothing wrong with proofs, but you can only come to a valid conclusion if you start with valid axioms.


My point exactly. And the axiom "god exists" is neither more nor less valid than any of mine.

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Borrowing your notations, fastlane made the following statements:
1) R(x) := x is a god and
2) x
The question then is what is required to show that either
(x).(y).R(x) ^ R(y) -> x==y or
(x).(y).R(x) ^ R(y) -> x!=y



Also true, but my point is that this is logically impossible without a definition for the property god. In other words, you have to add more axioms which I did. I probably didn't add the same axioms that fastlane would have, but I added some at least

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It comes down to figuring out what the existence of one or many gods entails, i.e. what other predicates can we deduce from x ^ R(x) ? The answer to this lies outside of predicate logic.


And again you are right and the consequence is that there is no proof.