I appreciate the links. I haven’t read Gaifman’s paper before, so I’ll go ahead and read that.
Anyhow, I won’t cotton to any method of assigning a logical probability that takes longer than just brute-forcing the right answer. For this particular problem I think a bottom-up approach is what you want to use.
I see the sentiment there, and that too is a valid approach. That said, after trying to use the bottom-up approach many times and failing, and after seeing others fail using bottom-up approaches, I think that if we can at least build a nonconstructive top-down theory, that would be a starting point. After all, Solomonoff Induction is completely top down, yet it’s a very powerful theoretical tool.
I am a long time LessWronger (under an anonymous pseudonym), but recently I’ve decided that it is finally time to bite the bullet, abandon my few thousand karma, and just move over to my real name already.
Back in the day, when I joined LessWrong for the first time, I followed my general policy of anonymity on the Internet. Now, I’m involved with the Less Wrong community enough that I find this anonymity holding me back. Thus the new account.
Edit: For my first post on this new account, I posted a few of my thoughts on logical uncertainty.