God's perfection does not imply his existence
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This argument is used in the debate Does God exist?.
This argument is an objection to God's existence is contained in his concept.
Summary
Let's imagine a perfect island that's bigger than all the other islands. Since it's perfect, this island should exist. However, as far as we know, this perfect island does not exist. Similarly, just because God is said to be perfect doesn't mean he exists.