Can the Best-Alternative-Justification solve Hume's Problem?
On the Limits of a Promising Approach
Summing it up, what can be achieved with prediction games with respect
to inductive inferences is a non-trivial result which shows that if
only a finite number of prediction strategies are involved there exists
with the “(collective) weighted average meta-inductivist”
a strategy that is an approximately best strategy in all possible worlds.
However, it can also be demonstrated that no approximately best strategy
exists if an infinite number of alternative prediction strategies is
involved. And there is some reason to believe that for a full solution
to the problem of induction the restriction to a finite number of alternative
prediction methods is insufficient. If this is true, then the best
alternative justification cannot offer a full solution to the problem