So, something about BioShock Infinite's ending has been bugging me....
First, let's set some ground assumptions so that this doesn't get too unwieldy.
1. Elizabeth has powers because a piece of her resides in another reality (her pinky). So in effect she can bridge the gap between multiple realities. Let's just pretend this makes sense.
2. Comstock could see alternate versions of reality using Lutece field-generated tears in the fabric of his reality. He sees a version of the future that appeals to him and his perverse plans (which came about because baptisms can make you into a self righteous prick bent on world domination). In one of these visions, he sees himself with a daughter. Comstock tries to have his own, but he shoots blanks because tears give you physical side effects. So the twins set out to find an alternate reality where Comstock has a daughter, takes that child, and gives it to their Comstock.
3. Cue pinky accident, girl has powers, self fulfilling prophecy. Okay.
4. Comstock discovers her powers to bring realities together and make stuff from one appear in another. Presumably he wants to use this power to further his plans?
Here's where things get confusing for me.
5. When Booker kills himself in Comstock-form, Elizabeth says it's meaningless because Comstock/Booker still exists in many other realities (presumably an infinite number of them). Because of this, we can conclude there's an infinite number of "bad" Bookers.
6. Presumably this is bad, because in some of these realities Booker still has Elizabeth's power in essence because he either utilizes it somehow (the siphon) or he brainwashes her into carrying out his will. This would allow him to not just screw up his own reality, but also other realities. And really "some" in this case is an infinite number, as a subset of infinity. So there's an infinite number of Bookers out there who are "bad" and can potentially screw up the multiverse.
7. If Booker is to stop this, he must "stop himself" and die before he undergoes the trigger event of a baptism (the event where presumably the infinite number of bad Booker permutations results from). A few problems with this to my mind. If we're talking about infinite possibility, then there's an infinite number of trigger events. The baptism would be just one in an infinite series, each one resulting in another infinite of infinites. Wouldn't there be other potentially worse Bookers resulting from entirely different events? Like a Booker hell bent on giving everyone herpes because he's resentful over sleeping with a prozzy after Wounded Knee?
8. Furthermore, why would a single permutation of Booker dying as an adult result in all possible Bookers dying? Would you literally have to kill him as a baby? I get that killing him before the trigger event leads to all *those* trigger-event specific Bookers going bye-bye. However see point #7. Other potential trigger events, potentially worse Bookers or Comstocks.
9. Furthermore, as the twins say, when you're dead you're really not dead because time is more of an ocean and not a river. So how is Booker "erased?"
10. The only explanation I can think of is Elizabeth using her tear-powers to bring "dead Booker" into other realities. Basically Booker would be dead in each of those possible worlds.
11. But it seems to me like you HAVE to allow for possible worlds where Booker is alive. Indeed, the game implies this is so by showing a Booker who never sold his daughter (...to himself). Going beyond this, what about the possible world where Elizabeth decides to save Booker by fighting her other possible selves who don't want to save him? All possible Elizabeths seem to want to go along with this plan, as the game shows, but that seems to be giving her too much power. She's not like the twins who basically exist outside of spacetime.