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Levels of Multiplicity

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Just thinking aloud here. There are several theories extant about how what we think of as the universe, the totality of spaces you could in principle get to from here, and of moments in time that came before or will come after this one, is only one of many. A multiplicity of multiverse theories, so to speak.

I'll still to three (I'm sure there are more).

1) A multiverse exists because every black hole is also a big bang. I'm told that mathematical modeling of a black hole leads to the inference that a mass of any size may somehowishly be reduced to a single infinitesimal point (meaning: infinite density). Also, that this makes the formation of a black hole look like the big bang postulated as the start of our universe in reverse. From such premises, the italicized inference above seems possible. If every black hole you can get to from here is a big bang, though, then it is the big bang of another universe, one you can't get to from here, one with its own space and time.

On this view, too, the steady-state theory of the universe, long since consigned to the dust heap of scientific history, enjoys a resurrection. The multiverse consisting of all these universe creating universes might well be in a steady state, without a moment of creation and without the prospect of a heat death. Or any other sort of birth or death.  Cosmologist Lee Smolin advocates something like this, although he is not to be held responsible for my bald summary of what I think is his view. I'll call it the Smolin view below, and will continue to do so unless he sues me and gets an injunction.

2) A multiverse exists because some events are quantum mechanical indeterminate, and they cause time-series to diverge. This is probably the most familiar of the three views. It has made a sizeable pop cultural splash since the days of Heisenberg, Schrodinger, etc. If there is a time line in which the infamous cat lives and another in which it doesn't, then there are a heck of a lot more universes than the Smolin view above would entail. This theory may give to some a sort of quasi-religious consolation. Whatever bad decisions Christopher has made in this world, there may have been a quantum mechanical effect involved in his neurons at the time, and if that is so then there may be another universe in which he then made the right call. So miserable Christopher can console himself that there is a happy Christopher in that other (equally actual) universe.

Note that the Smolin sort of multiverse offers no such consolation. I have no reason to identify with any Christopher in any of those other worlds. There might be someone a lot like me in some of them, but if so that fact is entirely accidental and there's nothing consoling about it. This second view, though, with its ordinary-event divergence of universes, strikes close to home. The third one, to which we come now, even more so.

3) A multiverse exists for a purely conceptual reason, because it is impossible to make sense out of counter-factual statements unless every statement about a frustrated possibility is a statement about an actuality in another world.

Another way of putting this point: actuality may just be indexical. Indexical words are words that depend upon the point of view for their truth or falsity. "The book is here," I say, with my hand on the book in question. If you were to say that, in another room, with the same book in mind, you would be wrong. The book (for you) isn't here, it is there. I am bored now. I was excited last Wednesday. Now and then are indexical, like here and there. According to some philosophers, notably David Lewis, we can't make any sense out of the words "actual" or "possible" unless we see them as indexical. And since anything I can conceive of without contradiction is in the relevant sense possible, then any such "possible" world is "actual" in its own here and now, its own universe.

Where do we end up if we believe that each of these arguments for a multiverse is a strong one?  A multiverse-verse? or a multi-multiverse?

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