Bechoros Chapter 8, Mishnah 6. This Mishnah includes many different elements. Its first part essentially summarizes what we learned in the recent mishnayos - situations of doubt and of unclear status regarding the son; and from here on, the Mishnah moves to cases of certainty and the monetary nature of the obligation of pidyon haben.
First case - doubtful offspring of two men:
"Achas bicherah v'achas shelo bicherah shel shnei anashim" - two women married to two different men: for one of them this is her first child, and for the other it is not her first child. They both gave birth together in a dark cave, the babies were mixed up, and in the morning the children were found without it being possible to know who their mother is and who their father is. There are two cases before us:
"V'yaldu shnei zecharim" - we do not know which son belongs to which mother and which father, but we know clearly that the woman who had never given birth before gave birth to a son, and whichever of the two sons is hers requires redemption. Therefore, "zeh shelo bicherah ishto nosen chamesh sela'im lakohen" - the husband married to the woman who has not given birth previously is obligated in the redemption of his son, whichever one of them it is.
"Zachar unekevah" - if one male and one female were found in the cave, the halachah is "ein kan lakohen klum" - there is nothing here for the kohen. The husband whose wife did not give birth previously claims that it is possible that the daughter is her child, and there is no obligation here, and the burden of proof is on the one seeking to exact payment. And the second husband claims that even if the son is his, it is not his wife's first child and there is no opening of the womb here.
The son died - cases of certainty:
In the Babylonian Talmud, a new mishnah and a new topic begin here: we leave the situations of doubt and uncertainty, and move to cases of certainty in pidyon haben.
"Mes haben besoch shloshim yom" - if the son died within thirty days, "af al pi shenasan lakohen, yachazir lo chamesh sela'im" - even though he gave it to the kohen, he must return five sela'im to him. Even if the father gave the kohen five sela'im early - for example, because the kohen was present before him and he did not know when they would meet again, and with the intention that on the thirty-first day the son would be redeemed with these coins - the son did not reach the thirty-first day, and the kohen has no right to this money. The obligation of pidyon haben never took effect, as it only comes into force after a full month, on the thirty-first day.
"L'achar shloshim yom" - after thirty days, "af al pi shelo nasan, yiten" - even though he has not given it, he must give it. If the son died when he was thirty-one days old or older, and the father has not yet redeemed him, the father is obligated to give the five sela'im to the kohen even after the son's death.
From here it emerges that the mitzvah of pidyon haben has two facets. On the one hand, the primary mitzvah is incumbent upon the person himself, upon the son; the father precedes and takes care of this initially, just as he takes care of bris milah and Torah study, and if the father did not do so, the son redeems himself. On the other hand, there is also an element of monetary obligation here: once the firstborn reaches the age of thirty-one days, the father owes five sela'im to the kohen.
This is similar, in a general sense, to a person who did not separate Terumah from his crop and ate everything: the debt to the kohen exists even though the crop is no more. So too here - the son is no more, but the debt to the kohen remains in place, and therefore the father is obligated to give the five sela'im. This is practical halachah, and a berachah must even be recited on the pidyon haben, except that according to the Rema, we do not recite Shehecheyanu when the son is no longer alive.
The son died on the thirtieth day:
Is this day considered a complete obligation? For the obligation states "from a month old", and the question is whether the thirtieth day is included. The Mishnah states: "Yom shloshim kelifnei chen" - like the law of the twenty-ninth day. Therefore, if the son died on the thirtieth day, even if the father paid early, he gets his money back from the kohen, as there is no obligation of redemption until the thirty-first day. And this is the halachah.
Rabbi Akiva is in doubt about the law of the thirtieth day, and since it is a doubt: if the father already gave the money to the kohen, he cannot extract it from his hand, as the burden of proof is on the one seeking to exact payment, and he cannot prove his entitlement to a refund as long as the halachic doubt is unresolved. And if he has not yet given it, "lo yiten" - he should not give it, as the kohen cannot compel him, for it is a doubt whether he is obligated, and again the burden of proof is on the one seeking to exact payment.
Rabbi Akiva's doubt is a technical one, and much more complex than it seems. It is rooted in the fact that the expression "and upward" appears in two contexts - one regarding the redemption of the firstborn in the desert and one in the portion of Arachin - and the question is whether they are considered "two verses that come as one," for which the rule is that they do not teach regarding other cases, and therefore we cannot derive further laws from them; under these circumstances, Rabbi Akiva is in doubt as to how to rule. One who wishes to expand on this should look at least at the Bartenura, and preferably in the Gemara itself. The main point: it is a technical doubt, based on the methodology of deriving laws from verses.
If the father died:
"Meis ha'av besoch shloshim yom" - Meaning that he died before the obligation to redeem his son took effect. The law is "Bechezkas shelo nifdah" - The halachic presumption is that the son was never redeemed. When he reaches the age of obligation and a kohen comes to demand five selaim from him, he cannot claim that perhaps his father redeemed him; it is possible that he did, but it is unlikely, and the presumption is that he did not, and therefore the son must be redeemed. "Ad sheyavi re'ayah shenifdah" - He is not exempt from the obligation except with absolute proof, such as two witnesses testifying that the father gave the money to the kohen within thirty days.
What happens if the father died after the son passed the thirtieth day, at a time when the obligation of redemption had already taken effect, and it is unknown whether he fulfilled it or not? There are two sides to consider: on the one hand, there is a presumption that a person does not pay his debt before its time - and for this reason it was established in the first case that he is presumed unredeemed; on the other hand, people are eager to fulfill mitzvos and obligations.
The bottom line is that the Mishnah rules that we assume the son was redeemed, since it is a mitzvah, but it is a weak presumption and there is no need for absolute proof to contradict it. The text of the Mishnah: "Bechezkas shenifdah" - We assume that the father took care of his halachic obligations before he died. Further on, instead of the common text found in many Mishnayos, "until he brings proof," it seems the correct reading is "Ad sheyomru lo shelo nifdah", and this is also reflected in halachah. The meaning of this: if anyone testifies, even a servant in the house, that before his passing the father said to him, "I must redeem my son" or "I have not redeemed my son" - that is sufficient as proof that the son has not yet been redeemed.
There is no need for absolute proof of two witnesses testifying that the father swore to them that he never redeemed him, and the like. And so is the halachah: once a person says that the son was not redeemed, he is believed; and without this, we assume that the son was redeemed and that the father made sure to fulfill his halachic obligation.
"Hu lifdos uvno lifdos":
A new case: Reuven - let us call him Yitzchak - whose father Avraham never redeemed him, has a son named Yaakov who requires redemption. It turns out that two redemptions are incumbent upon him, his own and his son's, while he has only five selaim in his possession. Whom should he redeem first? The Mishnah states: "Hu kodem livno" - Yitzchak takes precedence over his son Yaakov, because it is his own mitzvah.
The reason, as mentioned above: the primary mitzvah rests upon the person himself, and therefore Yitzchak is obligated to redeem himself. Although he is also obligated to take care of his son's obligation, when an obligation upon oneself and an obligation concerning care for another face each other - the obligation upon oneself takes precedence. Therefore, he should spend the five selaim on his own redemption, and the son will redeem himself once he grows up.
The opinion of Rabbi Yehudah:
The last line of the Mishnah is slightly misleading: it seems that Rabbi Yehudah argues with the ruling, but things are not as they seem. Rabbi Yehudah is speaking of a specific and limited case, where Avraham, Yitzchak's father, never redeemed his son, and upon his death bequeathed him real estate worth five selaim or more.
Rabbi Yehudah holds - as was mentioned in passing in the previous Mishnayos - that the obligation of redeeming a firstborn has the status of a loan, and since the Torah wrote it explicitly, it is considered a "loan written in a contract," like a loan documented in a deed, and the Torah is the deed. A loan written in a contract places a lien on the borrower's real estate. It turns out that when Avraham died and bequeathed his property to his son, a lien of five selaim rested upon it in favor of the kohen, for the purpose of Yitzchak's redemption.
Therefore, if Yitzchak sold the property before his son Yaakov reached thirty days of age, the buyer purchased an encumbered property. In this scenario, Rabbi Yehudah says: Since Yitzchak only has five selaim, he should use them to redeem his son Yaakov, while for his own redemption he should go to the buyer of the property and collect from him. This is because this property, which belonged to his father, was encumbered for his redemption, and has the status of a loan recorded in a document. In this way, Yitzchak will obtain money for his own redemption as well.
The language of the Mishnah: "Rabbi Yehudah omer, beno kodmo" - with the only five selaim in his possession he should redeem his son. This is in the specific case described, where this money is all he has, but he had previously inherited property from his father and sold it before his son was born. According to Rabbi Yehudah, this property is encumbered and can be collected from. "Shemitzvaso al aviv" - since the mitzvah to redeem him was incumbent upon his father Avraham, this encumbered the property he inherited and sold, and from there he can collect the money for his own redemption. "Umitzvas beno alav" - and he has a separate obligation to redeem his son.
It turns out that if he first redeems his son with the five selaim in his possession, he will be able to collect an additional five selaim for his own redemption. However, if he spends the five selaim on his own redemption, he will not be able to collect from the encumbered properties for the purpose of redeeming his son Yaakov, because there is no lien on them for Yaakov's redemption. This is the opinion of Rabbi Yehudah.
The Opinion of the Sages and the Halachah:
The Sages disagree and maintain that a person's obligation to pay the kohen for the redemption of his son is not considered to be written in a document. Even though the Torah stated it, this does not give it the status of a written document. It remains like a verbal loan which does not encumber properties. Therefore, Yitzchak has no way to go back to the properties he inherited from his father Avraham and collect from them the money for his own redemption. Because of this, the Sages say that in any case, one who only has five selaim redeems himself first and not his son, as this is his own obligation, and the son will redeem himself when the time comes.
The halachah does not follow Rabbi Yehudah, but rather the Tanna Kamma: A person always redeems himself before his son when he must decide between them. In practice, there is no lien on properties here at all. If someone did not redeem his son, there is no obligation resting upon his estate, and one who buys his properties buys them clear of any lien for the payment of the son's redemption.
In summary: In this Mishnah we learned the conclusion of the cases of doubt - two wives of two men who gave birth together, and their laws regarding two males, or a male and a female. From here we moved to cases of certainty: If the son died within thirty days - the kohen returns the money, and after thirty days - the father must give the money even after the death, since there is a monetary obligation here and not just a mitzvah. If he died on the thirtieth day - it is treated like before then, and Rabbi Akiva is in doubt, so we follow the rule that the burden of proof rests on the one trying to extract money from his fellow. If the father died within thirty days - the son is presumed to be unredeemed until he brings proof, and after thirty days - he is presumed to be redeemed until he is told he was not redeemed. And finally, the law of precedence in redemption when the father only has five selaim - he precedes his son, and the dispute between Rabbi Yehudah and the Sages regarding the issue of a loan recorded in a document and the encumbrance of properties.