You have a minor ailment. You wonder to yourself if it's going to clear up by itself within a week. Suddenly you receive utterly conclusive evidence that an omniscient and perfectly honest being is speaking with you. Now consider the following case:
- The being informs you that there is a twin-earth, where everything has hitherto been exactly like on earth. In particular, twin-earth contains a duplicate of you, whose life has hitherto been exactly like yours. In particular, your twin has the same minor ailment you do. Moreover, the being informs you that exactly one of you and your twin will have their ailment clear up within a week.
- Just like (1), except that the being also gives you some additional information afterwards. He tells you that on both earth and twin-earth, superb medical studies of the ailment have been done, and they have concluded that in the vast majority of cases like yours, the ailment clears up within a week.
- Just like (2), except that instead of the being telling you about the studies, you knew ahead of the communication from the being about these studies in your world, and after the being told you about the twin, you inferred that there must be such studies on twin-earth, too, since twin-earth has up to now been just like earth.
- Just like (3), except now the being informs you that there is an infinite number of such twin-earths, and if we let E be the set whose elements are earth and these twin-earths, then on infinitely many members of E, you or your twin (as the case might be) recovers within a week, and on an equal infinity of members of E, you or your twin does not recover.
- Just like (4), except that the twin-earths have not been exactly alike, but extremely similar, with any differences being far several orders of magnitude below the ability of our scientific experiments to discriminate between.
Now, if we are justifiably sure that there are infinitely many universes, then we should expect that there are universes that contain near twins like in (5), and we should expect that infinitely many of them your near twin recovers and on an infinity of them your near twin does not recover, and you should not be confident that you'll recover in a week. And if you aren't sure about there being infinitely many universes, but you simply assign a high probability to that hypothesis, then you should significantly lower your confidence that you will recover, below the confidence given by our best medical studies.
This applies to David Lewis's plurality of worlds. It seems to apply to scientific multiverse theories. And it applies to theistic versions of Lewis's theory, like those by Donald Turner or Klaas Kraay, on which only universes worthy of being created exist, since there plausibly is a just as big infinity of worlds worthy of creation where you don't recover in a week as ones where you do. (This is clear if our universe is far enough above the cut-off line that your failing to recover in a week will not push it below the cut-off line. If our universe is too close to the cut-off, then to ensure worthiness, some kind of a compensating good would also have to be present.)
Thus, infinite multiverse theories should sap our confidence in scientific predictions. This is particularly problematic for scientific multiverse theories.
I think the controversial move will be the transition from (3) to (4) actually.