Bechoros, chapter two, Mishnah nine. In this Mishnah, the last in the chapter, we will deal with the definition of a bechor: what is required for an offspring to be considered a bechor. The verse states: "Kadesh li chol bechor peter kol rechem bivnei Yisrael, ba'adam uvabehemah li hu" - "Sanctify to Me every firstborn that opens every womb among the Children of Israel, among man and among animal, it is Mine".
The two conditions in the verse:
"Chol bechor" - the first offspring in age, the oldest newborn.
"Peter kol rechem" - the one that opened the womb, the first to emerge from the womb.
The question is therefore: Is one of these two conditions sufficient, meaning either the oldest offspring or the one that opened the womb, or are both required together? And according to the second side, if the offspring is not both the oldest offspring and the first to emerge from the womb in a regular birth, it is not a bechor. The halachah follows the latter opinion, and this is the familiar concept, but nonetheless, the Tannaim debated it.
The case in the Mishnah: "Yotzei dofen vehaba acharav" - the mother, a cow, goat, or sheep, gave birth to male twins. The first emerged from the side ("yotzei dofen" literally: emerged from the flank, meaning a birth by Cesarean section), and the second, which came after it, emerged in the regular manner.
We find that each of the two animals has only one of the two qualities:
The first: It is the oldest in age, but it is not a peter rechem, as it was not the one to open the womb.
The second: It is a peter rechem, but it is not the oldest in age.
The dispute between Rabbi Tarfon and Rabbi Akiva:
Rabbi Tarfon says: "Sheneihem yir'u ad sheyista'avu veye'achlu bemumim labe'alim" - the matter is in doubt, and therefore both must be treated as a doubtful bechor: both should graze until they develop a permanent blemish, and then they may be eaten by the owners according to the law of a doubtful bechor.
Rabbi Akiva says: "Sheneihem einam bechor" - there is no doubt here at all, and neither of them is a bechor. "Ha rishon", the older one that emerged via Cesarean section, is exempt "mishum shelo patar rechem", because it did not open its mother's womb. "Vehasheni mishum shekadmo acher", for it cannot be called a bechor, since it is not the oldest offspring but rather the second in age.
In conclusion: The root of the dispute lies in how to read the verse. According to Rabbi Tarfon, it is possible that one of the two conditions is sufficient, and therefore both are a doubtful bechor; whereas according to Rabbi Akiva, the condition of "peter rechem" comes to define and explain what a bechor is: the one that is both the oldest and the one that opened the womb. And the halachah follows Rabbi Akiva.