You can logically conclude that Halachally-jewish people will not consider themselves half-breeds. The Halachally-jewish people exlude the paternally jewish people - I know because I've experienced it.
By the way this whole thing is a non-issue, because in the days of the Patriachs, it didn't matter what the mother was. And the whole mother-determining jewishness rule was a rabbinical innovation of the middle ages.
For instance if there really was maternal transmission of jewishness solely, there would be a tribe named after Jacob's daughter Dinah.
>For instance if there really was maternal transmission of jewishness solely, there would be a tribe named after Jacob's daughter Dinah.
Excellent! I missed this earlier.