 One thing this tells us is that the right way to read \(p(B\mid A)\) is not as the probability of some sentence, \(B\mid A\), but instead as a two-place function. The syntax \(p(B\mid A)\) is misleading, and might be more clearly written \(p(B,A)\), the standard notation for a two-place function like \(f(x,y)=x^2+y^2\).