I think Diffractor’s post shows that logical induction does hit a certain barrier, which isn’t quite diagonalization, but seems to me about as troublesome:
As the trader goes through all sentences, its best-case value will be unbounded, as it buys up larger and larger piles of sentences with lower and lower prices. This behavior is forbidden by the logical induction criterion… This doesn’t seem like much, but it gets extremely weird when you consider that the limit of a logical inductor, P_inf, is a constant distribution, and by this result, isn’t a logical inductor! If you skip to the end and use the final, perfected probabilities of the limit, there’s a trader that could rack up unboundedly high value!
I think Diffractor’s post shows that logical induction does hit a certain barrier, which isn’t quite diagonalization, but seems to me about as troublesome: