Solomonoff induction is a specific probability distribution. It isn’t making “decisions” per se. It can’t notice that it’s existence implies that there is a halting oracle, and that it therefore can predict one. This is because, in general, Solomonoff induction is not embedded.
If there was a physical process for a halting oracle, that would be pretty sick because then we could just run Solomonoff induction. As shown in my post, we don’t need to worry that there might be an even better strategy in such a universe; the hypotheses of Solomonoff induction can take advantage of the halting oracle just as well as we can!
As shown in my post, we don’t need to worry that there might be an even better strategy in such a universe; the hypotheses of Solomonoff induction can take advantage of the halting oracle just as well as we can!
You do mention that the methods of reasoning have to be computable for this to work, and there I’m quite a bit more skeptical of that condition holding.
Solomonoff induction is a specific probability distribution. It isn’t making “decisions” per se. It can’t notice that it’s existence implies that there is a halting oracle, and that it therefore can predict one. This is because, in general, Solomonoff induction is not embedded.
If there was a physical process for a halting oracle, that would be pretty sick because then we could just run Solomonoff induction. As shown in my post, we don’t need to worry that there might be an even better strategy in such a universe; the hypotheses of Solomonoff induction can take advantage of the halting oracle just as well as we can!
You do mention that the methods of reasoning have to be computable for this to work, and there I’m quite a bit more skeptical of that condition holding.