Yes I agree, there is only a rough isomorphism between the mathematics of binary logic and the real world; binary logic seems to describe a limit that reality approaches but never reaches.

We should consider that the mathematics of binary logic are the limiting case of probability theory; it is probability theory where the probabilities may only take the values of 0 or 1. Probability theory can do everything that logic can but it can also handle those real world cases where the probability of knowing something is something other than 0 or 1, as is the usual case with scientific knowledge.