Rambam - 1 Chapter a Day

I.e., we consider it as if he had six sons, not five, and give two portions to the firstborn.

The Ramah (Choshen Mishpat 277:3) states that if the son is born while his father is dying (goseis), the son is not given the right of the firstborn. This ruling requires a somewhat forced interpretation of the second clause of this halachah. See Sefer Me’irat Einayim 277:7.

I.e., the father must at least have the possibility of recognizing his son “on the day when the inheritance is transferred” - i.e., the day of the father’s death.

There is a question among the Rabbis whether the baby’s entire forehead must emerge in his father’s lifetime, or merely the majority of his forehead (Bedek Habayit 277).

And thus his sex could not be determined. Such a person is called a tumtum in Talmudic terminology. See Hilchot Ishut 2:5.

Instead, the estate is divided equally among them.

See the illustration of this concept in the following halachah.

I.e., their manhood must be apparent.

Our translation is based on the gloss of Sefer Me’irat Einayim 277:11. This interpretation saves the two clauses from being redundant.
The share of the inheritance due the son who died is divided equally among his brothers, for they are his heirs. Nevertheless, the fact that he is theoretically given a share reduces the share of the firstborn. For example, if there is a firstborn, two brothers and the brother that died, the firstborn receives a fifth of the estate as the firstborn’s share rather than a fourth.

From Deuteronomy 21:15: “And she will bear him sons,” our Rabbis derived that the sons must be born in the father’s lifetime. In both the instances described in this halachah, the firstborn’s share is determined first and then, the remainder of the inheritance is divided in the ordinary manner.

A person had two wives who both gave birth at approximately the same time. At the time of birth, it was known which baby was born first. Afterwards, however, the babies became intermingled, and it was impossible to differentiate one from the other.

Since it was originally known which of the sons was the firstborn, an extra portion of the estate is allocated for that son. Nevertheless, since it is not known which of the sons is in fact the firstborn, he cannot be given his portion. If, however, both (all) of the sons whose identities were confused give each other power of attorney, the extra share will be given to them to share.

Where it was dark and thus it was never discerned which of the babies was in fact the firstborn.

Since the firstborn’s identity was never distinguished, the father never had the opportunity to “recognize” him. Hence he is not granted an extra share.

Bava Batra 117a states that this law represents the situation pertaining to the daughters of Tzelofchad. (See Numbers, Chapters 26, 27, 36.) Tzelofchad was the firstborn son of Chefer. Thus, Tzelofchad - and hence his daughters - deserved a double portion of Chefer’s share in Eretz Yisrael.
As stated in Chapter 3, Halachah 1, a firstborn receives a double share only of property in the deceased’s possession at the time of his death, but not of property that accrues to that estate after his death. Nevertheless, the estate of the firstborn is granted a double share even though the firstborn himself is no longer alive. Hence, in this instance, the son’s daughter receive her father’s firstborn share.

Since a firstborn does not receive a double portion of money that will accrue to the estate - i.e., money that the estate will acquire afterwards - we cannot say that we are speaking about a situation where a person died childless, but his brothers and father died before him, in which instance, his brother’s sons would be his heirs. For in this situation, there would be no firstborn’s (i.e., the firstborn among the deceased’s brothers) share. Even if that brother had been alive at the time of the deceased’s death, he would not have received a double share, because the inheritance was not part of his father’s estate at the time of his death.
Hence, we are speaking about a situation where a person died childless and his brothers died before him. His father inherited the estate and died afterwards. The sons of the deceased’s brothers inherit their grandfather’s estate. Hence, if one of the deceased brothers was a firstborn, his son would receive a double portion of the estate.
After explaining the Rambam’s words in this manner, the Maggid Mishneh questions why it was necessary to mention this situation. Seemingly, it would be self-apparent. He explains that perhaps the Rambam’s intent was to describe the situation with all of its details.

Bava Batra111b derives this concept from Deuteronomy 21:17: “To give him a double portion of everything that he possesses” - i.e., “that he possesses,” and not “that she possesses.”

Who is not necessarily regarded as the firstborn with regard to the mitzvah of redeeming the firstborn. See Halachot 9-10 and notes.

Who must be redeemed even though he is not necessarily the one who receives the firstborn’s share of his father’s estate - i.e., when the father had another wife whose son was his firstborn.

I.e., although this son did not have to be redeemed as the mother’s firstborn.

The term “stillborn” is not a totally appropriate translation, as reflected by the following clause. The intent is a child who was born prematurely, and it is obvious that from the outset the fetus was never viable.

Such a son would not be considered to be the firstborn with regard to the mitzvah of the redemption of the firstborn. Nevertheless, to be mentioned above, the two sets of laws operate on the basis of different sets of principles and are by no means analogous.

A firstborn must be “born” - i.e., emerge from the womb - as implied by the proof-text.

Even if the sons convert, the firstborn and his father are not considered to have any family ties. Nevertheless, since while he was a gentile, the firstborn was considered to be the convert’s son, even if the convert fathered children after he became Jewish, the first of those sons is not considered a firstborn.

See Chapter 1, Halachah 7.

Sefer Me’irat Einayim 277:17 offers two interpretations of this term: a) a woman with whom marriage involves a transgression, b) a woman whose marriage is not binding because of the transgression involved.
The Lechem Mishneh notes that the Talmudic source for this law, Yevamot 23a, cannot be accepted by the Rambam, for he does not acknowledge other concepts that are derived from the same exegetical reference. Kin’at Eliyahu explains that this reflects a pattern found several times within the Mishneh Torah. The Rambam will quote a concept stated in the Talmud, but ignore the method of exegesis stated in the source, and at times suggest an original method of his own.

When such a woman marries a priest, relations with her are forbidden by Scriptural Law or Rabbinic Law, respectively.

On the eighth day, even before the child is circumcised, the father takes the baby from the mother for the circumcision. From this time onward, he pays more attention to him. Hence, it is his word that is significant. See Sefer Me’irat Einayim 277:23; Kiddushin 74a.

This also appears to apply in a situation where the woman gave birth to twins.

Bava Batra127b derives this concept from Deuteronomy 21:17: “he shall recognize,” which is interpreted to mean that he shall cause others to recognize. The father must make known the identity of his firstborn son.

The father’s statement may cause his son to be considered illegitimate. For if we know that the son was borne by the man’s wife and we accept the father’s word, the only possible conclusion is that he was born out of adultery. Even when this is the outcome, the father’s word is accepted. If, however, the son has already married and has fathered children, the father’s word is no longer accepted with regard to his legitimacy (Hilchot Issurei Bi’ah 15:15-16). Nevertheless, even after the son has fathered children, his father has the potential to disqualify him from receiving a share of the inheritance, as the Rambam states in Chapter 4, Halachah 2.
If, however, the father once declared a son to be his firstborn, he can no longer retract his statements [Ramban, Rashba, as quoted by the Maggid Mishneh; Tur and Ramah (Choshen Mishpat 277:12)]. See Chapter 4, which describes several examples of a father’s identifying a person as his heir, or alternatively, stating that a person assumed to be a heir is not.

See Hilchot Gerushin 2:16. That source explains that a bill of divorce must be given by a man while he is mentally sound, and when a man loses his ability to speak there is room for suspicion that he is no longer of sound mind. Hence, he is asked several questions, requiring both positive and negative answers. If the manner in which he answers demonstrates that he is of sound mind, he is able to initiate the divorce. Similarly, in the present instance, if through his gestures he indicates that he is of sound mind, his word is accepted and the person is accepted as his son.

And hence, had to be redeemed.