The Brandenburger-Keisler paradox runs as follows.
1) Suppose that A believes that B assumes that A believes that B's assumption is wrong
2) Ask whether A believes that B's assumption is wrong
3.1) If A believes that B's assumption is wrong, then in A's view B's assumption is right. But then A believes that B's assumption is right. Contradiction.
3.2) If A believes that B's assumption is right, then in A's view B's assumption is wrong. But then A believes that B's assumption is wrong. Contradiction.
Now, there is something I cannot clear about all this.
a) As it stands, it runs as well if we replace 2) with Ask whether A believes that B's assumption is right, doesn't it?
b) Suppose that A believes that B's assumption is wrong/right. Then, shouldn't B's assumption be, so to say, objectively right/wrong, not only in A's view?
c) Be it as it may, why should we conclude from A believing that B's assumption is wrong/right, and from B's assumption being right/wrong, that A also believes that B's assumption is right/wrong? I mean, A believes that B's assumption is wrong/right, and depending on that B's assumption will be right/wrong respectively, but why such a belief should then be ascribed to A?
d) Couldn't we say: suppose that A believes that B's assumption is wrong. Then A believes that A believes that B's assumption is right. We assume that A believes that A believes that p is tantamount to A believes that p, and then we get that A believes that B's assumption is right.
Brandenburger-Keisler Paradox:
a) Yes.
b) No, beliefs are not equivalent to objective truths. In fact, I suppose the only thing "objective" used in deriving a contradiction from this paradox is the law of excluded middle.
c) You're right and this is the point that allows us to conclude that the BK-paradox is a paradox. Another point of view: We want to know if the BK-paradox is consistent, i.e. we are trying to see if anyone, taking the place of $A$, can hold the belief of the BK-paradox without running into a contradiction.