Now (8) asserts not just that it's possible that a G exist, but that it's possible that a G exist
necessarily. What this means, in terms of our boxes, is that a G is in one box, and in that
box, it's true of the G that it exists in all the boxes (more precisely, all the boxes possible
relative to it, which in S5 are all the boxes). So if (8) is true, G is in W1, and in W1 it's
true that if G is in W1, it is also in W2–4, so that we have
Thus, given an S5 system of relations among the boxes, (8) does entail (9): G exists
necessarily (in all boxes). Now if W1–4 are all the worlds there are, then one of them will
turn out to be actual. G is in all of them, so no matter which one is actual, G will be actual
with it. So (9) entails (10). In S5, this modal argument from perfection is valid.