Mr. Hen, As I understand your notation, B(B(X)) would mean “I believe that I believe X”. Lemmon’s fourth axiom for doxastic modal logic is B(X) implies B(B(X)). This is sometimes called the positive introspection axiom. I’m pretty sure it applies in any reasonable theory of “rationality”
But this is apparently not what the post says that “Belief in belief” is. In this thread, “Belief in belief” seems to be something like “I ought to believe X, therefore I want to believe X, therefore I will myself to believe X, and I believe that I have succeeded, therefore I believe that I believe X (even though an objective observer can see that I don’t really believe X deep down)” This kind of belief in belief is irrational.
I believe that I believe that such a notable philosopher as Dennett has not completely messed up the meaning of the word “belief” in his zeal to deprecate the continued existence of non-atheists.
Mr. Hen, As I understand your notation, B(B(X)) would mean “I believe that I believe X”. Lemmon’s fourth axiom for doxastic modal logic is B(X) implies B(B(X)). This is sometimes called the positive introspection axiom. I’m pretty sure it applies in any reasonable theory of “rationality”
But this is apparently not what the post says that “Belief in belief” is. In this thread, “Belief in belief” seems to be something like “I ought to believe X, therefore I want to believe X, therefore I will myself to believe X, and I believe that I have succeeded, therefore I believe that I believe X (even though an objective observer can see that I don’t really believe X deep down)” This kind of belief in belief is irrational.
I believe that I believe that such a notable philosopher as Dennett has not completely messed up the meaning of the word “belief” in his zeal to deprecate the continued existence of non-atheists.