In terms of what we call semicha today, does one have to be Jewish to receive or hold it? Is it simply an indicator of learning (like an academic degree) which could be reached by anyone?
Knowing that many semicha conferring programs won't accept a non-Jew, I suggest the following hypothetical:
Someone raised a religious ("Orthodox") Jew studies for and is granted semicha. He writes, learns, answers practical questions based on his learning and "is" a rabbi. Ten years later, after some digging by members of his family, he discovers that his maternal great-grandmother was not Jewish. Therefore, he was never Jewish.
During the time that he practiced as a rabbi, was he one? The learning was the same as was his personal piety (if that matters). If someone asked him for an answer on a situation and was bound (at the time) by his answer as we do not shop for answers, is that person still bound after the heritage is discovered?
[I wonder if I asked a local smart Jewish person a question and he gave me an answer, whether I would be bound by his words even without semicha as I chose him as my generic expert...separate question]