Our Gemara quotes a Mishna whose source is in Massekhet Yevamot (23b) where we find a most unusual case. What happens if a man marries one of two sisters, but does not know which one he married? The Mishna teaches that in such a case the man must divorce each of them, since he cannot marry two sisters. Even after he divorces one he cannot marry the other, since she may be the sister of his divorced wife, which is also forbidden by the Torah.
The suggestion raised in our Gemara is that the confusion in our story stemmed from the fact that the marriage somehow was done without clarity from the very beginning – perhaps a situation where both sisters appointed a single individual to act as their agent to accept marriage proposals on their behalf. Someone approached the agent and offered him kesef kiddushin to effect the marriage and said, “With this money I am marrying one of the sisters,” without clarifying which one he intended.
The Ritva suggests that if we assume yesh bereira – that we can ascertain someone’s intent retroactively, once they make a decision later on – then such a marriage may work. Still, he argues, the case might be where a person leaves the decision to someone else (e.g. “I will marry whichever woman my father decides”) and then that person disappears and cannot make the decision.
Our Gemara brings this case in order to support Abaye’s position that we learned on yesterday’s daf – that kiddushin she-lo nimseru le-biah is still considered marriage – after all we require divorces to undo them.
This proof is rejected because the case could be a situation where a marriage took place with one of the women, and afterwards there was a dispute about what happened, to the extent that no one was sure who was truly married. In this case, it is clear that a marriage took place between two people; we just cannot determine which two people they were.