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PhilGoetz comments on A simple counterexample to deBlanc 2007? - Less Wrong
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The problem with my counterexample was that the set S_I is much larger than the set I tried to define it as.
But I think this reveals a fatal flaw in the paper. The environment is described by a function h: N->N. S_I is the set of functions that match h on a finite number of examples.
This means that S_I will have cardinality N^N - the cardinality of the reals. But this makes it impossible to satisfy the precondition that there exists a probability distribution over S_I such that every element is > 0, and the total sums to 1.
Nope. S_I has cardinality N, because it's a subset of S, which is the set of computable functions, which has cardinality N.