Before us is Mishnah 9 in the third chapter of Maseches Kiddushin, which deals with a man who betrothed one of his daughters without specifying which one. The Mishnah clarifies the scope of the doubt that arises, and at its center stands the dispute between Rabbi Meir and Rabbi Yosi regarding the fundamental question: does a person allow himself to enter into a situation of doubt or not?
The case with which the Mishnah deals:
"Mi sheyesh lo shtei kitei banos mishtei nashim" - a man who has two groups of daughters from two wives, at least two daughters from the first wife and at least two daughters from the second wife. The daughters from the first wife are the older ones, while the daughters from the second wife are the younger ones.
"Kidashti es biti hagedolah":
The father says: "Kidashti es biti hagedolah, v'eini yodea" - I betrothed my older daughter, and I do not know which of them I betrothed. The doubt extends over three possibilities:
"Gedolah shebagedolos" - the oldest of the older group.
"Gedolah shebaketanos" - the oldest of the younger group, who is also called "older" relative to her sisters.
"Ketanah shebagedolos, shehi gedolah min hagedolah shebaketanos" - the youngest of the older group, for she is older than the oldest of the younger group, and therefore she too may be considered "older."
The opinion of Rabbi Meir: "Kulan asuros chutz min haketanah shebaketanos" - all the daughters are forbidden, except for the very youngest of the younger group, for only regarding her is it known with certainty that she is not included in the betrothal. Rabbi Meir holds that a person does allow himself to enter into a situation of doubt, and therefore it is possible that his intention was to any daughter who could be called "older" in some manner.
The opinion of Rabbi Yosi: "Kulan mutaros chutz min hagedolah shebagedolos" - all the daughters are permitted, except for the oldest of the older group. Rabbi Yosi holds that a person does not allow himself to enter into a situation of doubt, and therefore when he said "the older one" we must assume that he intended that daughter who is definitively the oldest.
"Kidashti es biti haketanah":
And so too in the reverse case, where the father said: "Kidashti es biti haketanah, v'eini yodea". Here as well the doubt extends over three possibilities:
"Ketanah shebaketanos" - the very youngest of the younger group.
"Ketanah shebagedolos" - the youngest of the older group.
"Gedolah shebaketanos, shehi ketanah min haketanah shebagedolos" - the oldest of the younger group, for she is younger even than the youngest of the older group, and therefore she too may be considered "younger."
The opinion of Rabbi Meir: "Kulan asuros chutz min hagedolah shebagedolos" - all the daughters are forbidden, except for the oldest of the older group, since regarding her there is no way at all to call her by the name "younger." This follows his approach, that a person permits himself to enter into a situation of doubt.
The opinion of Rabbi Yosi: "Kulan mutaros chutz min haketanah shebaketanos" - all the daughters are permitted, except for the youngest of the younger group, who is the absolute youngest. When he said "the younger one" he intended the one who is definitively the youngest, for a person does not allow himself to enter into a situation of doubt.
Why were both cases necessary?
The Gemara explains the need for the two different cases. According to Rabbi Meir, who broadens the doubt and includes more daughters within it, one might have thought that he stated his ruling only where the father said "my older daughter," since a person is willing to apply the description "older" to any of his daughters and would therefore broaden the doubt; but where he said "younger" - which is not a description a person wishes to say about his daughter - it is possible that Rabbi Meir would not have ruled this way. Therefore the second case was also necessary.
And according to Rabbi Yosi the need is the reverse: the case of "older" was necessary, to teach us that even there the father does not include the rest of the daughters, but only that daughter who is definitively the oldest.
In summary: In this Mishnah we learned the law of one who has two groups of daughters from two wives, who betrothed "his older daughter" or "his younger daughter" and does not know whom he intended. According to Rabbi Meir - a person does allow himself to enter into a situation of doubt, and therefore all the daughters are forbidden except for the one to whom there is no way whatsoever to apply the term he used. According to Rabbi Yosi - a person does not allow himself to enter into a situation of doubt, and therefore all are permitted except for that daughter whom the description fits with certainty. The Gemara explained why both cases, the older and the younger, were necessary according to the approach of each of the Tannaim.