Can the Best-Alternative-Justification solve Hume's Problem?
On the Limits of a Promising Approach
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1 Introduction
In a recent article on “The Meta-inductivist's Winning Strategy
in the Prediction Game: A New Approach to Hume's Problem” (Schurz 2008)
Gerhard Schurz proposes the Best-Alternative-Justification
as a new approach to the problem of induction. As acknowledged by Schurz,
the original idea goes back to Hans Reichenbach (Reichenbach 1935, Reichenbach 1938).
But Schurz furnishes this idea with a new technical approach relying
on a certain class of prediction strategies which he calls “meta-inductivists”.
Given that all attempts to solve the problem of induction have hitherto
failed (Howson 2000),
what should induce us to reconsider the sceptical conclusion that there
is no solution to the problem of induction? Prima facie, Gerhard Schurz
has a convincing answer to this question: Most of the proposed solutions
to the problem of induction tried to prove the reliability
of the inductive procedure. But Schurz, following Reichenbach, merely
tries to show the optimality of a specific inductive strategy,
namely his “meta-inductivist” strategy. Demonstrating the
optimality of an inductive prediction strategy is a less ambitious
task than demonstrating its reliability, because for an inductive strategy
to be reliable one would have to prove that it works in any possible
world. But an inductive strategy that is merely optimal is allowed
to fail in some possible worlds, as long as in the worlds where it
does not work all other possible prediction strategies are bound to
fail, too. Schurz does not raise the claim that he has solved the problem
of induction literally, but the closing paragraph of his article suggests
that he believes that he has at least provided a very good candidate
for a solution to the problem of induction (Schurz 2008, p. 304).[1]
Schurz discusses the problem of induction within the technical framework
of prediction games, where a number of players have to predict the
next event in a series of binary valued (0 or 1) or real valued (any
real number from 0.0 to 1.0) world events. By proving two theorems
regarding the optimality of the prediction strategies of the “weighted
meta inductivist” and the “collective weighted meta inductivist”,
Schurz is at least able to give a partial solution for the problem
of induction that accounts for the case of finitely many prediction
strategies. But, as shall be demonstrated in the following, Schurz'
technical approach meets insurmountable limits once one tries to pass
from a finite number to an infinite number of prediction strategies.
This raises the philosophical question whether an optimality result
demonstrated for a finite number of prediction strategies might suffice
to answer the problem of induction. If not, then providing a full solution
to Hume's problem remains an open challenge.
In the following, I am going to briefly restate Schurz' central results
and then demonstrate that the results for prediction games with finitely
many strategies cannot be extended to prediction games with infinitely
many strategies. Finally, there will be a brief discussion of open
questions regarding Schurz' answer to Hume's problem.
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