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What are the arguments of the mathematicians who objected against the ontological proof Gödel offered?

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0 4 $begingroup$ Q: What are the arguments of the mathematicians who objected against the ontological argument/proof Gödel offered? $$ begin{array}{rl} text{Ax. 1.} & left{P(varphi) wedge Box ; forall x[varphi(x) to psi(x)]right} to P(psi) \ text{Ax. 2.} & P(neg varphi) leftrightarrow neg P(varphi) \ text{Th. 1.} & P(varphi) to Diamond ; exists x[varphi(x)] \ text{Df. 1.} & G(x) iff forall varphi [P(varphi) to varphi(x)] \ text{Ax. 3.} & P(G) \ text{Th. 2.} & Diamond ; exists x ; G(x) \ text{Df. 2.} & varphi text{ ess } x iff varphi(x) wedge forall psi left{psi(x) to Box ; forall y[varphi(y) to psi(y)]right} \ text{Ax. 4.} & P(varphi) to Box ; P(varphi) \ text{Th. 3.} & G(x) to G text{ ess } x \ text{Df. 3.} & E(x) iff forall varphi[varphi text{ ess } x to Box ; exis...