Given one, we can infer the other either necessarily or by making a minimal assumption of consistency.
No. A belief can be wrong, right? I can believe in the existence of a unicorn even if the world does not actually contain unicorns. Belief does not, therefore, necessarily imply existence. Likewise, something can be true, but not believed by me (e.g., my wife is having an affair, but I do not believe that to be the case). Thus, belief does not necessarily follow from truth.
If all you are saying is that truth conditionally implies belief, and vice versa, I of course agree; I think most of our beliefs do correspond with true facts about the world. Many do not, however, and your theory has a difficult time accomodating that.
Also: what do you mean by a “minimal assumption of consistency?” It is hard for me to understand how this can be of use to you, if it means anything other than, “I assume that beliefs are never wrong.” And you can’t assume that, because that is what you were trying to show.
Given one, we can infer the other either necessarily or by making a minimal assumption of consistency.
No. A belief can be wrong, right? I can believe in the existence of a unicorn even if the world does not actually contain unicorns. Belief does not, therefore, necessarily imply existence. Likewise, something can be true, but not believed by me (e.g., my wife is having an affair, but I do not believe that to be the case). Thus, belief does not necessarily follow from truth.
If all you are saying is that truth conditionally implies belief, and vice versa, I of course agree; I think most of our beliefs do correspond with true facts about the world. Many do not, however, and your theory has a difficult time accomodating that.
Also: what do you mean by a “minimal assumption of consistency?” It is hard for me to understand how this can be of use to you, if it means anything other than, “I assume that beliefs are never wrong.” And you can’t assume that, because that is what you were trying to show.