The Gemara rejects this: No, the mishna is referring to a case of documents of stipulation that record the amounts that parents agree to provide to their son or daughter, and this is in accordance with the opinion of Rav Giddel. לָא בִּשְׁטָרֵי פְסִיקָתָא וְכִדְרַב גִּידֵּל
As Rav Giddel said that Rav said: When two families negotiate the terms of marriage for their respective children, one side says to the other: How much do you give your son? And the second side answers: Such and such amount. How much do you give your daughter? And the first side responds: Such and such amount. Then, if the son and daughter arose and performed the betrothal, all of these obligations are acquired and therefore binding. These are among the things that are acquired through words alone, without the need for an additional act of acquisition. The mishna is referring to a document that records such an agreement. דְּאָמַר רַב גִּידֵּל אָמַר רַב כַּמָּה אַתָּה נוֹתֵן לְבִנְךָ כָּךְ וְכָךְ וְכַמָּה אַתָּה נוֹתֵן לְבִתְּךָ כָּךְ וְכָךְ עָמְדוּ וְקִידְּשׁוּ קָנוּ הֵן הֵן הַדְּבָרִים הַנִּקְנִין בַּאֲמִירָה
Come and hear another challenge to the opinion of Reish Lakish, based upon the following mishna (Bekhorot 51a): If he wrote to a priest with whom he wants to perform the redemption of his firstborn son: I am obligated to pay you five sela, then he is obligated to give him five sela and his son is not redeemed even once he pays the money. This baraita apparently supports the opinion of Rabbi Yoḥanan. תָּא שְׁמַע כָּתַב לְכֹהֵן שֶׁאֲנִי חַיָּיב לְךָ חָמֵשׁ סְלָעִים חַיָּיב לִיתֵּן לוֹ חָמֵשׁ סְלָעִים וּבְנוֹ אֵינוֹ פָּדוּי
The Gemara answers: It is different there, because he is obligated to give the five sela to him by Torah law in order to fulfill his obligation of redeeming his firstborn son, even without writing a contract. The Gemara asks: If that is so, why did he write the contract at all? The Gemara answers: In order to select for himself a specific priest with whom to perform the redemption of his son. שָׁאנֵי הָתָם דִּמְשׁוּעְבַּד לֵיהּ מִדְּאוֹרָיְיתָא אִי הָכִי אַמַּאי כָּתַב כְּדֵי לְבָרֵר לוֹ כֹּהֵן
The Gemara asks: If that is so, why is his son not redeemed once he pays the money? The Gemara answers: This is in accordance with the opinion of Ulla. As Ulla said, by Torah law a son is redeemed when the father gives the money. And for what reason did the Sages say: His son is not redeemed? It is a rabbinic decree that was enacted lest people say that one can redeem a firstborn son with documents, i.e., by giving a document allowing the priest to collect a debt from a third party. This is not effective, since the Torah requires that one redeem his son with actual money. אִי הָכִי בְּנוֹ אַמַּאי אֵינוֹ פָּדוּי כִּדְעוּלָּא דְּאָמַר עוּלָּא דְּבַר תּוֹרָה פָּדוּי לִכְשֶׁיִּתֵּן וּמַאי טַעְמָא אָמְרוּ בְּנוֹ אֵינוֹ פָּדוּי גְּזֵירָה שֶׁמָּא יֹאמְרוּ פּוֹדִין בִּשְׁטָרוֹת

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Rava said: The dispute between Rabbi Yoḥanan and Reish Lakish is like a dispute between tanna’im over the same matter in the following mishna (Bava Batra 175b): In a case where a guarantor appears after the signatures in contracts, i.e., someone wrote that he is a guarantor for a loan after the contract was signed, the creditor collects only from the unsold property of the guarantor. Since the guarantee is not viewed as though it were written in the document, it is like a loan by oral agreement, which is collected only from unsold property. אָמַר רָבָא כְּתַנָּאֵי עָרֵב הַיּוֹצֵא אַחַר חִיתּוּם שְׁטָרוֹת גּוֹבֶה מִנְּכָסִים בְּנֵי חוֹרִין
An incident came before Rabbi Yishmael, and he said: The creditor collects from unsold property. Ben Nannas said to him: He does not collect from the guarantor at all; not from unsold property, nor from liened property that was sold, since what the guarantor wrote has no legal standing whatsoever. מַעֲשֶׂה בָּא לִפְנֵי רַבִּי יִשְׁמָעֵאל וְאָמַר גּוֹבֶה מִנְּכָסִים בְּנֵי חוֹרִין אָמַר לוֹ בֶּן נַנָּס אֵינוֹ גּוֹבֶה לֹא מִנְּכָסִים בְּנֵי חוֹרִין וְלֹא מִנְּכָסִים מְשׁוּעְבָּדִים
Rabbi Yishmael said to him: Why? Ben Nannas said to him: If someone was strangling another in the marketplace and demanding money that is owed to him, and a friend of the victim found him and said to the strangler: Leave him alone and I will give you what you are demanding from him, the friend of the victim is exempt from having to make any payment. This is because the creditor did not lend the money based on his trust in the friend of the victim, as the friend promised to repay the loan only after the money had been loaned. The same should apply in the case of the guarantor who comes after the contracts were already signed. אָמַר לוֹ לָמָּה אָמַר לוֹ הֲרֵי שֶׁהָיָה חוֹנֵק אֶת חֲבֵירוֹ בַּשּׁוּק וּמְצָא[וֹ] חֲבֵירוֹ וְאָמַר לוֹ הַנַּח לוֹ וַאֲנִי אֶתֵּן לָךְ פָּטוּר שֶׁלֹּא עַל אֱמוּנָתוֹ הִלְוָהוּ
Rava concludes: Let us say that Rabbi Yoḥanan stated his ruling in accordance with the opinion of Rabbi Yishmael, that the obligation that one accepts upon himself is binding, and Reish Lakish stated his ruling in accordance with the opinion of ben Nannas. לֵימָא רַבִּי יוֹחָנָן דְּאָמַר כְּרַבִּי יִשְׁמָעֵאל וְרֵישׁ לָקִישׁ דְּאָמַר כְּבֶן נַנָּס
The Gemara responds: According to the opinion of ben Nannas, everyone agrees that if he wrote in a contract: I owe you one hundred dinars, he is not obligated to pay. אַלִּיבָּא דְּבֶן נַנָּס כּוּלֵּי עָלְמָא לָא פְּלִיגִי