... to acknowledging that our universe is contingent? Matter doesn't have to be this way: in fact, the matter called "our universe" doesn't have to be at all... (see Aquinas's 3rd way for more).
And don't the various hypothetical universes have to be individuated in some way? (I dunno, but it seems so). That is, don't they have to have something different about them: otherwise, there would be no explanatory gain in positing them.
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But suppose they exist. I wouldn't say that means we're any more or less contingent that before, simply because the "black box" is from quantum mechanics to begin with (regardless of whether we interpret QM in terms of multiverses or not). Measurements don't have deterministic outcomes. That seems to suggest contingency. In a way, multiverses make for less of a need for causal input - everything that can happen does happen.
ZZZZ
This is a hunch that I haven't worked out, but if you pursue your questions it will help me to think it out ore.
But as for the multiverses - with different laws of physics in different "regions" - it's a different issue. Can you explain more what you mean by contingent in this context?
"Doesn't multi-verse theory open the door a bit wider... to the acknowledgment that our universe is contingent? Matter doesn't have to be this way: in fact, the matter called 'our universe' doesn't have to be at all... (see Aquinas's 3rd way for more)."