I doubt on exegetical grounds that Anselm actually means to give this argument. But as
Proslogion 3 has led some to this argument, we can discuss it here.
(6)–(10) is a valid argument in the S5 system of modal logic. Systems of modal logic—
the logic of inferences involving “possibly” and “necessarily”—differ in the claims they
make about the relations between possible worlds. The distinctive feature of the S5
system of modal logic is that in it, every world is possible relative to every other world:
no matter which world were actual, the same set of worlds would be possible. To see how
(6)–(10) works in such a set of worlds, let the boxes below represent all the worlds that
are possible:
Let existing in at least one box represent being possible, and existing in all the boxes
represent existing necessarily. (6) asserts that possibly a G exists. To represent this, we
enter a G in one box: