Before tackling the first assignment, read How to Read a Mitzva.
Listen to the Audio class:
[podcast]http://www.hinnuch.com/class-1/Class001.mp3[/podcast]
Mitzvah #1: Be fruitful and multiply
Our goal here is to find the four expected sections of this essay, as describes in the How to Read a Mitzva section, above, and to summarize each one.
1. The mitzva is to procreate. Its source is the blessing given by God to Adam and Eve in the first chapter of Genesis.
2. The root/reason for this mitzva is that God wants His world to be settled and inhabited, and it is the job of people to do that.
3. The details of the mitzva include at what age one should marry, how many children one needs to have in order to fulfill the mitzva. Discussion of these topics can be found in gemara Yevamot chapter 6 and gemara Brachot. (For the first section of Sefer haChinnuch, this section is a list of topics for further study and places in the halachic literature where you would find that discussion. Note that the references to mishna and gemara are by chapter; there was no standard pagination in the gemara when this book was written. If your text includes page references, they were added by the editor/translator.)
4. The mitzva applies to men, but not to women. It applies in all times and places, but only to men who have reached the requisite age. There is no precise punishment for not fulfilling this mitzva, but God is likely to take failure to fulfill this mitzva very seriously.
Notes:
This mitzva is very good at showing the structure the author will use for each of the following 612 essays. The content, however, is not very satisfying. More questions are left open than are answered. Don’t worry, the interest level of the essays will improve as the author hits his stride.
Meanwhile, note that nothing in this mitzva is specific to Jews. The blessing that is the source of this mitzva is addressed to all people, and our author’s interpretation applies equally to all people. Presumably, the mitzva only applies to Jews, although the author doesn’t actually say that.
There is a problem with using this verse as the source of this mitzva as it applies to Jews. In general, mitzvot only apply to the Jewish people if the mitzvot were given at Sinai or through Moses sometime after Sinai. We would normally expect our author to cite at least some parallel source from later in the Torah, a notion our author may be alluding to in mitzva #2.
Nor is there any discussion of why this mitzva does not apply to women.
The punishment section may feel a little vague. The author says there is no punishment imposed by a human court for failure to fulfill this mitzva, but he does not say why. We also need to be a little patient with the author on the topic of understanding the punishments. We will accumulate more information about how punishments work little by little, as we get little tidbits in each mitzva, until the whole topic develops some clarity.
The author chooses to do a very limited job on the content of this mitzva; he wants, I think, to focus on showing the reader how the mitzva/essays will be structured. Therefore, I don’t want to go too much further than he does by way of filling in the content. There is an interesting essay in David Feldman’s book Birth Control and Abortion in Jewish Law, New York University Press 1968. (I believe there is a more recent edition with a slightly different title.)
As to the “topics for further study,” Feldman explains that there are various versions of the tanaitic source that defines the minimum number of children: 1 child of either gender, 1 of each gender, 2 boys, 2 of each gender. The accepted opinion is that of Hillel, who says one child of each gender. The later rabbis extend the mitzva in various ways. The theme seems to be that the children themselves survive and have children of their own, so to make sure that happens, one should have as many children as possible.
It is clear from the gemara that this mitzva does not apply to women, but the reason is not at all clear. Note, however, that the structure of Jewish law related to marriage and divorce would make it difficult to figure out how this would work if women were obligated in this mitzva. Picture a married woman who is not having children. Although a man may have more than one wife, a woman may not marry more than one husband. And the woman cannot obtain a divorce without the cooperation of her husband. So if she was obligated to procreate but was not fertile within her current marriage, there isn’t much she could do on her own to fulfill the obligation.

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