Possible Worlds and Causal Closure

[Neo-Scholastic]

Many thought problems include ‘possible world’ scenarios, in which if A were otherwise than it actually I was or currently is, then B would have been or currently be otherwise. It seems to me that possible worlds are incompatible with causal closure. Under causal closer the world could be nothing other than what it already is and there could never be another world other than the current one. Therefore if one commits to the idea that things could actually have been or currently be otherwise, then you must also commit to causal closure.

As I see it the validity of a thought problem depends on whether the proposed possible world is, well, actually possible. Since causal closure makes other worlds impossible, it seems to me that those committed to causal closure should refrain from using possible world arguments except to show the impossibility of the imagined alternate universe.

For example, Chalmers proposes a zombie world devoid of mental properties. From this he intends to show the impotency of mental properties. However, is Chalmers’s thought problem instructive in any meaningful way? We do not live in a zombie world, so the argument that mental properties are impotent, simply because it could be otherwise, has no heft.

Do I accurately understand the link between possible worlds and causal closure or am I missing something?

[LostLocke]

Under causal closer the world could be nothing other than what it already is and there could never be another world other than the current one. Therefore if one commits to the idea that things could actually have been or currently be otherwise, then you must also commit to causal closure.

That seems to be a pretty haughty statement.
Where is the rule book that says no other worlds are possible? What's the reason to believe no other worlds are possible?

[Alex K]

Causal closure as a concept to me seems either trivial or wrong depending on how you define physical. Could you elaborate a bit on how you use the term and how your argument goes?