The first perek of Eduyot lists a number of debates between Beit Shamai and Beit Hillel, where Beit Hillel ultimately concedes. The Rambam in his introduction to the masechet notes the significance of these Mishnayot as they demonstrate that the Tanaim were motivated by a pursuit for truth rather than any other motives.
One of these debates (1:13) was also studied this week as part of Daf Yomi (Erchin 2a). The debate is regarding how to deal with a half eved (servant) half ben churin (free person). This case can occur if two people jointly purchased an eved and then one of the parties frees his share. Beit Hillel maintained that the eved would serve the remaining master one day, and then look after his own needs on the next. Beit Shammai however argued that while that solution satisfied the financial interest of the remaining party, the eved's needs were being neglected – the eved would not be able to marry. Considering his half-half status, he would not be able to marry a maidservant or a Jewess. Leaving him in that state is not a solution since "the world was created for procreation". They cite the following pasuk to support that claim: "lo tohu vera'ah, lashevet yetzarah" - "… He did not create it for emptiness; He fashioned it to be inhabited" (Yeshayahu 45:18). Beit Shammai therefore argued that the remaining master is forced to free the eved. A loan contract for half the eved's value is also written, obligating the eved to pay the second master. This solution satisfies both the needs of the half eved and the remaining master. Beit Hillel ultimately agreed that this is the correct solution.
The Tosfot (Gittin 42b, s.v. lo tohu) ask why Beit Shammai cited the pasuk from Yeshayau rather than the more obvious choice of "pru u'rvu" (be fruitful and multiply) from Bereishit. The Tosfot provide two answers. The first is that if the half-eved could have fulfilled the mitzvah of lo tohu by marrying a shifcha, despite not being able not fulfil the mitzvah of pru u'rvu1, Beit Shammai would not have forced the master to free him.
Based on this first answer, the Ketav Sofer explains that the inability to fulfil the mitzvah of pru u'rvu alone would not be enough, since it would be defined as ones – beyond his control – and he would therefore be exempt. The Ketav Sofer continues that lo tohu compels use to free the slave, not because of it is a personal mitzvah (like pru u'rvu) but rather because it is expresses the will of Hashem that "he fashioned [the world] to be inhabited". The Ketav Sofer uses this explanation to rationalise why the solution is referred to as being "mipnei tikkun olam" – in order to improve the world. It is motivated by a broader interest, instead of the eved's specific needs.
The second answer is that the Mishnah is teaching us that lo tohu is a "mitzvah raba" – a great mitzvah. The Tosfot cite the Gemara (Megila 27a) that lists two exceptional circumstances in which one can sell a sefer Torah. The first is to fund the study of Torah and the second is to fund a marriage. When justifying the latter, the Gemara cites this pasuk, lo tohu, to stress the importance of the mitzvah.
Finally, the Tosfot cites the Rivam, who explains that the reason why lo tohu was chosen is because it applies equally to an eved and ben churin – both halves of this individual. This unlike the mitzvah of pru u'rvu that only applies to a ben churin.
Based on the Ketav Sofer above, we can perhaps suggest the difference between the three answers of why the Mishnah did not cite "pru u'rvu" as the motivation. According to the first answer we see the motivation to free the eved is not for him to fulfil any mitzvah, but to heed to Hashem's desire of lo tohu. According to the second answer, the mitzvah of lo tohu itself is exceptional which alone is enough to free the eved. According to the Rivan however, the driving force to free this half-eved was to enable him to fulfil a mitzah that applied to him completely in his current state.1
1 See the Chatam Sofer (41b, s.v. she'neemar) that provides a different explanation for the difference between these three answers that has a practical implication on which circumstance one can sell a sefer Torah to fund a marraige.
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