Anyway, since you keep taking the time to thoroughly reply in good faith, I’ll do my best to clarify and address some of the rest of what you’ve said. However, thanks to the discussion we’ve had so far, a more formal presentation of my ideas is crystallizing in my mind; I prefer to save that for another proper post, since I anticipate it will involve rejigging the terminology again, and I don’t want to muddy the waters further!
Looks like I forgot about this discussion! Did you post a more formal treatment?
I don’t know how you so misread what I said; I explicitly wrote that aliefs constitute the larger logic, so that beliefs are contained in aliefs (which I’m pretty sure is what you were going for!) and not vice versa. Maybe you got confused because I put beliefs first in this description, or because I described the smaller of the two logics as the “reasoning engine” (for the reason I subsequently provided)? What you said almost convinced me that our definitions actually align, until I reached the point where you said that that beliefs could be “more complicated” than aliefs, which made me unsure.
Sorry for the confusion here! I haven’t re-oriented myself to the whole context, but it sounds like I did invent a big disagreement that didn’t exist. This has to do with my continued confusion about your approach. But in retrospect I do think your early accusation that I was insisting on some rigid assumptions holds water; I needed to go a bit further afield to try and interpret what you were getting at.
Whether or not I manage to convince you that the Löbstacle doesn’t exist (because it’s founded on an untenable definition of trust), you have to acknowledge that the argument as presented there doesn’t address the following second problem.
Again, I haven’t yet understood your approach or even re-read the whole conversation here, but it now seems to me that I was doing something wrong and silly by insisting on a definition of trust that forces the Löbstacle. The original paper is careful to only state that Löb naively seems to present an obstacle, not that it really truly does so. It looks to me like I was repeatedly stubborn on this point in an unproductive way.
Looks like I forgot about this discussion! Did you post a more formal treatment?
Sorry for the confusion here! I haven’t re-oriented myself to the whole context, but it sounds like I did invent a big disagreement that didn’t exist. This has to do with my continued confusion about your approach. But in retrospect I do think your early accusation that I was insisting on some rigid assumptions holds water; I needed to go a bit further afield to try and interpret what you were getting at.
Again, I haven’t yet understood your approach or even re-read the whole conversation here, but it now seems to me that I was doing something wrong and silly by insisting on a definition of trust that forces the Löbstacle. The original paper is careful to only state that Löb naively seems to present an obstacle, not that it really truly does so. It looks to me like I was repeatedly stubborn on this point in an unproductive way.