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endoself comments on A simple counterexample to deBlanc 2007? - Less Wrong
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Let J be the constant set that I is currently equal to. Your agent's set of hypotheses then does not contain the computable function f(k) =
(2(1-1/2^k))^4 for all K in J
-k for all K not in J
By construction, this hypothesis must be compatible with the known input-output pairs, since it is indistinguishable from your f_4 given the observations in J. S_I must therefore contain f iff it contains f_4. Your S_I does not satisfy this, so it is not a counterexample.
I think you're right. You may have unravelled my counterexample. Tentative congratulations!
I now get to eat a piece of chocolate, as a reward for being proven wrong.
Suggestion: treat yourself to a second piece of chocolate and add an ETA at the top of the post - the parent comment is buried too deeply in the thread, for informational purposes.