Gödel does the usual Gödel thing - he just breaks modal logic. Modal logic is higher order, but there's logic above modal, and property "exists in all possible

Gödel does the usual Gödel thing - he just breaks modal logic. Modal logic is higher order, but there's logic above modal, and property "exists in all possible worlds" is such supermodal property that doesn't obey modal logic and is supposed to be output of modal logic, but Gödel uses it as input as a normal modal property. Modal property should be limited to one world and circumstances around it should be a priori variable across worlds, then we can expect those circumstances to vary by switching between worlds, but supermodal properties aren't like that and shouldn't be used like that. Anseml's argument isn't really an argument, but a hypothesis: it concludes with "a greater thing can be thought to exist in reality", which is obviously a hypothesis.