Seeing Mulligan

Pat and Jimmy-Joe met and one said to the other, "Have ye seen Mulligan lately, Pat?" Pat said, "Well, I have and I haven't." His friend asked, "Shure, and what d'ye mean by that?" Pat said, "It's like this, y'see... I saw a chap who I thought was Mulligan, and he saw a chap that he thought was me. And when we got up to one another...it was neither of us."