As we have seen (section 3), people fulfill an important Torah commandment with every child they are privileged to have. Nevertheless, the Torah established an obligation for every Jewish man to have one son and one daughter. The Sages (Yevamot 62b) added a rabbinic obligation to have even more children for two reasons: a) the tremendous value of life, and b) to ensure fulfillment of the Torah commandment. Let us now expand upon these.
The first reason is the tremendous value of life, revealed within each and every soul. The Torah states many times that an increased number of children is both a mitzva and a blessing: “God blessed [Adam and Ḥava] and God said to them, ‘Be fruitful and multiply, fill the earth and conquer it’” (Bereishit 1:28); “God blessed Noaḥ and his sons and said to them, ‘Be fruitful and multiply and fill the earth’” (Bereishit 9:1); “Be fruitful and multiply, abound on the earth and multiply on it” (ibid., v. 7). Later, God told Avraham, “I will bestow My blessing upon you and make your descendants as numerous as the stars of heaven and the sands on the seashore” (ibid., 22:17). God said to Yitzḥak, “I will make your descendants as numerous as the stars of heaven” (ibid., 26:4). God promised Yaakov, “Your descendants shall be as the dust of the earth” (ibid., 28:14). One of the blessings promised to the Jewish people if they obey God is, “I will look with favor upon you, and make you fertile and multiply you” (Vayikra 26:9). Likewise, in the blessing Moshe bestowed upon them he said, “May the Lord, the God of your fathers, increase your numbers a thousandfold” (Devarim 1:11). Finally, the blessing will be fulfilled at the time of the redemption: “They will be fruitful and multiply” (Yirmiyahu 23:3), “I will multiply men and beasts upon you, and they will multiply and be fruitful” (Yeḥezkel 36:11), and “I will multiply their people like sheep” (ibid., v. 37).
This is what Rambam means when he writes:
Although a man has fulfilled the mitzva of procreation (by having a son and daughter), he is rabbinically commanded not to neglect procreating as long as he has the strength, for anyone who adds a soul to the Jewish people is considered to have built a world. (MT, Laws of Marriage 15:16)
The second reason is to ensure the fulfillment of the Torah commandment. Even one who has a son and daughter cannot be sure that he will take part in the general objective of the mitzva, namely, that his son and daughter will continue his family line. Perhaps one of them will die, or will turn out to be infertile. This concern is what led R. Yehoshua to advise:
If one had children in his youth, he should also have children in his old age, as it states (Kohelet 11:6), “Sow your seed in the morning, and don’t hold back your hand in the evening, since you don’t know which is going to succeed, the one or the other, or if both are equally good.” R. Matna says, “The halakha accords with R. Yehoshua.” (Yevamot 62b)
The same applies to keeping the set times of ona. One who has not fulfilled the Torah obligation to procreate must keep all the times of ona when his wife can get pregnant; however, when it comes to the rabbinic obligation, if his wife agrees, they may forgo some onot (Birkei Yosef, EH 1:2; Pitḥei Teshuva ad loc. 1; AHS ad loc. 10; Rav Kook, Mitzvat Re’aya, EH §1). However, according to Beit Shmuel 1:1 and Taz 1:1 (in the first answer), a man must keep all the onot even to fulfill the rabbinic obligation.
The second reason we mentioned for having many children is based on the objective of the mitzva to procreate. If one of a man’s children is infertile or predeceases him, he does not fulfill his obligation. In contrast, if someone’s children never marry (which is more common), he still fulfills his individual obligation. However, what is not fulfilled is the objective of the general mitzva, which is for one’s line to endure through his son and daughter. Netziv writes in Ha’mek She’ala 165:3-4 that according to She’iltot, since a son or daughter might die, there is a Torah obligation to have an additional son and daughter. However, Rambam maintains that we do not make the assumption that a child will predecease his parents. Therefore he wrote that the mitzva to have more children is due to the inherent value of each and every child.
Rashi interprets the phrase from Kohelet, “You don’t know which is going to succeed, the one or the other,” to mean you don’t know which child will turn out to be upstanding and God-fearing nor which child will survive. We find an example in the story of Boaz. Our Sages identify him with Ivtzan, one of the judges, who had numerous wives and fathered thirty sons and thirty daughters (Shoftim 12:9), all of whom he successfully married off. Toward the end of his life, when he was close to eighty years old, his wife died. Because of his devotion to the mitzva, he did not decide that he already had enough children and grandchildren. Instead, when the opportunity came his way to continue fulfilling this mitzva, he married Ruth the Moabite. This union ultimately led to the birth of King David and the start of the Davidic dynasty (Ruth 4:18-22). We are also told that all sixty of Boaz’s earlier children predeceased him, while only Oved, the son who was born to him in his old age, outlived him. Generally, we would not advise an eighty-year-old to marry a woman of child-bearing age, since he would not be able to raise the children. Nevertheless, in the case of Ruth, his marrying her was an act of special kindness. It was a kindness to her, since she was a foreigner whom no one else was likely to marry, and it was a kindness to the family of Elimelekh and Naomi, who now had someone to carry on for them. Additionally, since Boaz was part of a large and wealthy family, the child born from Ruth would be well provided for even if he were to be orphaned. In any case, this is an example of a youngest child bringing enormous blessing. Being aware of this encourages the optimal fulfillment of the mitzva.