Earlier quoted context omitted.
Everything is a bitstring, and Solomonoff is optimal for predicting bitstrings. Probabilistic induction, if it is computable, cannot do better than that. Halting oracles require fewer program bits to generate longer bitstrings, so they make compressible bitstrings more likely than Turing machines. Applying bayesian reasoning, the existence of compressible bitstrings implies the existence of halting oracles. Or, even…
Solomonoff induction is optimal for, given an initial portion of a computable bitstring, predicting the rest of (or the next portion of) the bitstring. Logical induction (my apologies for referring to “probabilistic induction”; I was speaking unclearly when I did so. What I meant to communicate by that phrase was “if you attempt to do Bayesian updating on math statements in a naive ‘just apply Bayes’ rule’ way”, as a…
Re: Can Computers Prove Theorems?
#61Yes I'll continue over email. Good discussion! You are surprisingly open minded on the issue.