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Birkat HaMazon and its Sources
תָּנוּ רַבָּנַן: מִנַּיִן לְבִרְכַּת הַמָּזוֹן מִן הַתּוֹרָה? — שֶׁנֶּאֱמַר: ״וְאָכַלְתָּ וְשָׂבָעְתָּ וּבֵרַכְתָּ״ — זוֹ בִּרְכַּת ״הַזָּן״, ״אֶת ה׳ אֱלֹהֶיךָ״ — זוֹ בִּרְכַּת הַזִּמּוּן, ״עַל הָאָרֶץ״ — זוֹ בִּרְכַּת הָאָרֶץ, ״הַטּוֹבָה״ — זוֹ ״בּוֹנֵה יְרוּשָׁלַיִם״, וְכֵן הוּא אוֹמֵר ״הָהָר הַטּוֹב הַזֶּה וְהַלְּבָנוֹן״. ״אֲשֶׁר נָתַן לָךְ״ — זוֹ ״הַטּוֹב וְהַמֵּטִיב״. אֵין לִי אֶלָּא לְאַחֲרָיו, לְפָנָיו מִנַּיִן? — אָמְרַתְּ קַל וָחוֹמֶר: כְּשֶׁהוּא שָׂבֵעַ מְבָרֵךְ, כְּשֶׁהוּא רָעֵב — לֹא כׇּל שֶׁכֵּן.
The Sages taught in a Tosefta: From where is it derived that Grace after Meals is from the Torah? As it is stated: “And you shall eat and be satisfied, and you shall bless the Lord, your God, for the good land that He has given you” (Deuteronomy 8:10). The Gemara explains: And you shall bless, that is the blessing of: Who feeds all. The Lord, your God, that is the zimmun blessing in which God’s name is invoked. For the land, that is the blessing of the land; good, that is the blessing: Who builds Jerusalem, and it also says: “This good mountain and Lebanon” (Deuteronomy 3:25), which is interpreted homiletically as referring to Jerusalem and the Temple. That He gave you, that is: Who is good and does good. However, I only have a Torah source for blessings after eating, i.e., Grace after Meals. From where is it derived that one is obligated to recite blessings before eating? You said that it can be derived through an a fortiori inference: When one is satisfied, he is obligated to recite a blessing and thank God for food; when he is hungry, all the more so that he should recite a blessing to offer thanks for the food he will eat.
רַבִּי אוֹמֵר: [אֵינוֹ צָרִיךְ]: ״וְאָכַלְתָּ וְשָׂבָעְתָּ וּבֵרַכְתָּ״ — זוֹ בִּרְכַּת הַזָּן, אֲבָל בִּרְכַּת הַזִּמּוּן מִ״גַּדְּלוּ לַה׳ אִתִּי״ נָפְקָא. ״עַל הָאָרֶץ״ — זוֹ בִּרְכַּת הָאָרֶץ, ״הַטּוֹבָה״ — זוֹ ״בּוֹנֵה יְרוּשָׁלַיִם״, וְכֵן הוּא אוֹמֵר ״הָהָר הַטּוֹב הַזֶּה וְהַלְּבָנוֹן״. ״הַטּוֹב וְהַמֵּטִיב״ בְּיַבְנֶה תִּקְּנוּהָ. אֵין לִי אֶלָּא לְאַחֲרָיו, לְפָנָיו מִנַּיִן? תַּלְמוּד לוֹמַר: ״אֲשֶׁר נָתַן לָךְ״ — מִשֶּׁנָּתַן לָךְ.

Rabbi Yehuda HaNasi says: It is not necessary to interpret the verse this way; rather, it should be understood in a slightly different manner, as follows: “And you shall eat and be satisfied, and you shall bless,” that is the blessing of: Who feeds all; however, the zimmun blessing is derived from the verse: “Praise God with me and we will exalt His name together” (Psalms 34:3). He continues: For the land, that is the blessing of the land. Good, that is the blessing: Who builds Jerusalem, and it also says: This good mountain and Lebanon. They instituted the blessing: Who is good and does good, at Yavne and, as such, it has no biblical source. However, I only have a Torah source for blessings after eating, i.e., Grace after Meals. From where is it derived that one is obligated to recite blessings before eating? The verse states: That he gave you. A blessing must be recited over food from the moment that God gave it to you, not only afterward.

(י) וְאָכַלְתָּ֖ וְשָׂבָ֑עְתָּ וּבֵֽרַכְתָּ֙ אֶת־יְהוָ֣ה אֱלֹהֶ֔יךָ עַל־הָאָ֥רֶץ הַטֹּבָ֖ה אֲשֶׁ֥ר נָֽתַן־לָֽךְ׃
(10) When you have eaten your fill, give thanks to the LORD your God for the good land which He has given you.
(כה) אֶעְבְּרָה־נָּ֗א וְאֶרְאֶה֙ אֶת־הָאָ֣רֶץ הַטּוֹבָ֔ה אֲשֶׁ֖ר בְּעֵ֣בֶר הַיַּרְדֵּ֑ן הָהָ֥ר הַטּ֛וֹב הַזֶּ֖ה וְהַלְּבָנֽוֹן׃
(25) Let me, I pray, cross over and see the good land on the other side of the Jordan, that good hill country, and the Lebanon.”
(ג) בַּ֭יהוָה תִּתְהַלֵּ֣ל נַפְשִׁ֑י יִשְׁמְע֖וּ עֲנָוִ֣ים וְיִשְׂמָֽחוּ׃
(3) I glory in the LORD; let the lowly hear it and rejoice.
רַבִּי יִצְחָק אוֹמֵר: אֵינוֹ צָרִיךְ, הֲרֵי הוּא אוֹמֵר ״וּבֵרַךְ אֶת לַחְמְךָ וְאֶת מֵימֶיךָ״, אַל תִּקְרֵי ״וּבֵרַךְ״ אֶלָּא ״וּבָרֵךְ״, וְאֵימָתַי קָרוּי ״לֶחֶם״ — קוֹדֶם שֶׁיֹּאכְלֶנּוּ.
Rabbi Yitzḥak says: That source for the obligation to recite a blessing beforehand is not necessary, as it says: “And He will bless your bread and your water” (Exodus 23:25); do not read: And He will bless [uveirakh], rather: And you will bless [uvareikh]. And when is it called bread? Before it is eaten.
רַבִּי נָתָן אוֹמֵר: אֵינוֹ צָרִיךְ, הֲרֵי הוּא אוֹמֵר ״כְּבֹאֲכֶם הָעִיר כֵּן תִּמְצְאוּן אוֹתוֹ בְּטֶרֶם יַעֲלֶה הַבָּמָתָה לֶאֱכוֹל כִּי לֹא יֹאכַל הָעָם עַד בֹּאוֹ כִּי הוּא יְבָרֵךְ הַזֶּבַח אַחֲרֵי כֵן יֹאכְלוּ הַקְּרֻאִים״.
Rabbi Natan says: That source for the obligation to recite a blessing beforehand is not necessary, as it says when the maidens told Saul: “As soon you come into the city, find him right away, before he goes up to the high place to eat; for the people will not eat until he comes, because he will bless the sacrifice; and afterwards all those who are invited will eat; now go, for you shall find him at this time of day” (I Samuel 9:13). A blessing recited prior to eating is explicitly mentioned in that verse.