Reddit reviews The Law of Non-Contradiction

Well, to answer the question "is it logical that both can be correct?" Sure! There are logics that allows contradictions to be designated, so it's "logical" in that it's perfectly acceptable within the rules of at least one logic that "p ^ ~p" is true.

As far as the applicability of those logics to reality, which might be another aspect to the question rather than a new question, the Liar Sentence and phenomena in the boundary area of vague predicates have been put forth as examples of things that actually are contradictory, and so would be accurately modeled by logics that tolerate contradictions.

http://www.amazon.com/The-Law-Non-Contradiction-Graham-Priest/dp/0199204195

That book there is highly relevant.