The ontological argument is an attempt at a logical argument for the existence of God.
The argument is:
1 – God is defined as a being whom no greater being could be conceived
2 – A God who actually exists would be greater than one that does not exist
3 – If God did not exist, one could conceive of a greater being (violating #1)
4 – God must therefore exist
Gödel formalized this argument with mathematics, starting from a set of Axioms. The trouble is in the starting definition #1 and the related Axioms. With bad inputs, mathematics provides bad outputs.
The history is somewhat interesting here. In ages past, religious scholars spent a lot of time trying to use mathematics, logic, and science to prove the existence of God. These efforts generally are failures and modern religious movements now prioritize ‘faith’ the believing in absence of proof
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