Bava Basra, Chapter 9, Mishnah 10 - the final Mishnah in the chapter and the last in the series on inheritance laws. Here too, the Mishnah deals with two people who died simultaneously, but this time it involves a mother and her son. Let us call the mother Leah and her son Reuven. Leah has no other children and no husband: she was married to Yaakov, but in the meantime Yaakov either passed away or divorced her. The question before us is who inherits Leah's property.
The two sides contesting the inheritance:
Lavan, Leah's father: If Reuven, her only son, died first, Leah has no heir from below, and her heir is her father.
Yosef, Reuven's half-brother: If Leah died first, her heir is her son Reuven. Since Reuven died after her, the property goes up to his father Yaakov, and since Yaakov is not alive, it goes down to his other son, Yosef (Yaakov's son from another wife).
Consequently, the ruling depends on who died first. Lavan claims that his grandson Reuven died first, meaning Leah died after him and Lavan is her heir. Yosef, on the other hand, claims that Leah died first, and through Reuven, the property rightfully goes to him.
The text of the Mishnah:
"Nafal habayis alav ve'al imo" - Leah and Reuven both died in the house, and it is unknown who died first. Regarding this, the Mishnah says: "Eilu ve'eilu modim sheyachaloku" - Beis Shammai and Beis Hillel both agree that Leah's property is divided equally between Lavan, her father, and Yosef, her son's half-brother.
It is worth noting that there is no familial connection between Lavan and Yosef, yet their claims carry equal weight: everything depends solely on the question of who died first, and neither side is in presumptive possession.
We must remember that in the previous Mishnah we dealt with tzon barzel property, melog property, and the kesubah; here these concepts do not apply at all, since Leah is not a married woman and simply owns an apartment. For this reason, they divide it: Lavan's claim to the apartment is exactly equal to Yosef's claim, and neither takes precedence. Even Beis Hillel, who in the previous Mishnah ruled that the property should remain with the one in presumptive possession, agree here, as there is no presumptive owner at all - the last person to definitively possess the property was Leah herself.
The view of Rabbi Akiva:
Rabbi Akiva employs a poetic phrasing here. Countering the Mishnah's phrase "both agree that they divide it", he says: "Modeh ani bazeh shehanechasim b'chezkasan" - what do I agree with? That Beis Hillel ruled to leave the property in the hands of the one with presumptive possession. In fact, he does not agree with the Mishnah at all but rather argues against it, yet he uses the language of agreement. This is a rhetorical expression that is difficult to translate precisely.
Rabbi Akiva's reasoning is that there is indeed a presumptive owner here. What is this comparable to? Leah belonged to her father's family - let us call them the Capulet family. When she married Yaakov she became part of the Montague family, but when he divorced her she returned and identified as part of her father's family, and no longer has any connection to her husband's family. She had married into that family, and has since been completely disconnected from them.
Thus, we have two competing families before us: Lavan her father, a member of the Capulet family, claiming her apartment, and opposite him Yosef, a member of the Montague family, who is like her stepson. Since on the eve of her death Leah belonged to her father's family, this family has presumptive possession of the property, and the members of the other family must bring proof to contradict this. Therefore, Rabbi Akiva maintains that even Beis Hillel would rule that the property passes to Lavan the father, and not to Yosef.
Ben Azzai's Response:
"Amar lo Ben Azzai: al hachalukim anu mitzta'arim" - we have enough distress from the instances where Beis Shammai and Beis Hillel disagree, where we are forced to rule according to Beis Hillel and reject the words of the sages of Beis Shammai. Even though we establish the halachah according to Beis Hillel, the very need to decide between them is distressing. "Ela shebata lachlok aleinu al hashavin" - yet you are making the situation even worse: in our Mishnah, we had an agreement that everything is divided equally, and you are seeking to stir up a new dispute between Beis Hillel and Beis Shammai even where their opinions are aligned. This is inappropriate, and even distressing.
Halachah: These words were spoken rhetorically, and the halachah follows the Tanna Kamma, namely, according to Beis Hillel who concede to Beis Shammai in this case: Leah's apartment is divided in half - half to her father Lavan, and half to Yosef, her stepson.