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Is dictum that existence is second-order property core of Frege's objection to ontological argument?

Yes it is, Milos. See *The Foundations of Arithmetic,* p. 65: "Because existence is a property of concepts the ontological argument for the existence of God breaks down."

But Frege goes too far. For if he is right, then 'I exist' is meaningless, and the Cartesian *cogito* 'breaks down' (erreicht sein Ziel nicht) also! A consequence that Carnap drew.

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