Avoiding Modal Collapse

Consider the following:

Let,

g ≝ God

a ≝ God’s act of creation Now, according to the argument from Modal Collapse:

1. ☐(∃x)(x = g) (premise)

2. ☐(a=g) (premise)

Therefore

3. ☐(∃x)(x = a)

The fear, is that if God’s act of creation exists of necessity, then all contingent facts become necessary. However, I would propose the following:

C<x,p,ω> ≝ x creates the fact of p in world ω
a* ≝ (ɿx)(∀p)[(♢p ∧ ♢~p) →(∃ω)(C<x,p,ω>)]

However, this does not cause modal collapse, it seems to me.

As (3) above would really just mean:

4. ☐(∃x)(∀p){[(♢p ∧ ♢~p) → (∃ω)(C<x,p,ω>) ∧ (∀y)[(♢p ∧ ♢~p) → (∃ω)(C<y,p,ω>) → (y=x)]}

The act of creation could even involve an index of all possible worlds, e.g.: (∀p){(♢p ∧ ♢~p) →[(C<x,p,ω1> ∨ C<x,p,ω2>) ∨… C<x,p,ωn>

Necessitating that the act of creation is that which creates contingent facts in all of the possible worlds does not necessitate those facts. Rather, this is akin to thinking ☐♢p, and ☐♢p → ♢p, not ☐p.

Note, that a* can rigidly designate and be identified with God across all possible worlds, thus the very same act of creation does the explanatory work for why contingent facts vary across possible worlds. The same act is true in every world, but the results are a unique set of contingent facts in that world, and a set of contingent facts true in other possible worlds as they relate to that world.