Let's say that W1 is actual, and relative to W1, W2 is possible. Our G, God, exists only in
W2. So actually, God does not exist. But W2 is possible. So it's possible that God exist.
Now suppose that W2 had been actual instead of W1. In that case, God would have been
actual. But if relative possibility is symmetric, then because W2 is possible relative to
W1, had W2 been actual, W1 would have been possible. So had W2 been actual, a world
would have been possible in which God did not exist. So had W2 been actual, God would
have existed contingently: which is to say that if our G possibly exists and does not, it
would exist contingently if it did exist, assuming what the Brouwer system says about
relations among possible worlds.
It's also worth noting that (6) and (12) suffice on their own to prove God's existence if the
correct system of modal logic for metaphysical possibility includes Brouwer. To see this,
suppose that these boxes represent all the possible worlds there are:
If W4 is actual, of course, God exists. Suppose instead that W3 is actual. Then if possibly
God exists, God exists in at least one box possible relative to W3, and so God exists in
W4. Per (12), God exists necessarily in W4. So if W4 were actual, God would exist
necessarily, that is, in every world possible relative to W4. Per Brouwer, if W4 is
possible relative to W3, W3 is also possible relative to W4. So God is necessary in W4
only if God also exists in W3. So if W3 is actual, God actually exists. So whether W3 or
W4 is actual, God exists, and so given (6), (12), and Brouwer, God exists.
Modulo the change from (11) to (17), then, we can credit Anselm with the first valid
modal argument from perfection.
Modal arguments from perfection face two difficulties. One lies in showing that the
modal systems they invoke really are the correct logics for real metaphysical possibility.
The other is epistemological. Consider Plantinga's (1974a) attribute of no-maximality, or
being such that one does not coexist with a G. If this attribute is possibly exemplified,
then given (12) and S5, being a G is not. A modal argument gives one reason to become a
theist only if its proponent offers one not just the argument but some reason to believe the
claim that being a G is possibly exemplified rather than the claim that no-maximality is.
Many claim that modal arguments from perfection “beg the question” by asserting that
being a G rather than no-maximality is possibly exemplified. They do not. Every
argument asserts rather than justifies its own premises. If we need reason to believe in
being a G rather than no-maximality, this shows not that a modal argument begs the
question, but merely that another argument is needed, on behalf of one of its premises.