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How do we know that a person is not obligated in Mitzvos before the age of 13, and is obligated from that point forward?

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See also judaism.stackexchange.com/questions/8631. (The question there could serve as an answer here.) – Monica Cellio Oct 10 '12 at 13:02
related: judaism.stackexchange.com/questions/7349/… – Michoel Oct 10 '12 at 13:22

The Gemora (Sukka 5b) says that all measurements are halocha lemoshe misinai; received orally by Moshe Rabeinu on Har Sinai. Many Rishonim say that the age of 13 as Bar Mitzvah is included in this (Sheilos V'Teshuvos HaRosh Klal 16 Siman 1, Sheilos V'Teshuvos Maharil Siman 51, Rashi to Avos 5:21).

However there are hints from the Torah. The most famous is by Shimon and Levi when they killed the city of Shechem, the Torah (Bereshis 34:25) calls them "Ish" - men, when Levi was exactly 13 (See Tosfos Yom Tov to Avos 5:21 for a calculation). This is the youngest person we find described as a man (Rashi to Nazir 29b "V'rebi Yossi b'Rebi Yehuda"). There is a Posuk elsewhere in the Torah (Bamidbar 5:6) which implies that one who is an Ish, an adult, is held accountable for his transgressions.

This article (found through this answer) provides more sources.

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How do you know Levi was 13, let alone exactly? – Double AA Oct 10 '12 at 12:52
Ok how does the Midrash know it (and if you say tradition then your argument is circular)? – Double AA Oct 10 '12 at 13:03
Also I don't see it in Rashi 34:25 – Double AA Oct 10 '12 at 13:03

Nitei Gavriel Bar Mitzva introduction mentions Pasuk Braishis 21:8 ויגדל הילד ויגמל. Medrash Raba Vayeira 23:14 - note 25 says that this was when Yitzchok was 13 years old.

In addition Medrash Raba Toldos Parsha 63:14 says that at 13 is when Eisav and Yaakov parted ways. Until then they were both going to Yeshiva. Rabbi Elozor says until 13 one has to raise his child, at 13 he says Boruch Shepatranu.

Zohar Part 2 Page 98:1 וז״ל כד מטא לתליסר שנין חכה בההוא יומא דעאל לארביסר, כדין כתיב (תהלים ב׳ זי) ה' אמר אלי בני אתה אני היום ילדתיך, ושם(ק״א א׳) כד סליק אינש(לא רק דוד, אלא כל אדם) לי״ג שנין מה כתיב הי אמר אלי בני אתה אני היום ילדתיך, היינו שביום הבר מצוה נולד מחדש, ויום זה הוא גמר ועיקר כניסת נפש הקדושה באדם בי׳׳ג שנה ויום א׳ לזכר, שלכן נתחייב אז במצוות התורה.

Avos 5:21 Ben Shalosh Esrei L'Mitzvos

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Does that mean there is no obligation to learn Gemara until 15? Or perhaps that "Mishna" (quotes because it isn't in the Rambam's nussach) in Avos is aggadic and not halachik? – Double AA Oct 10 '12 at 13:12
I want to upvote and downvote at the same time! – Seth J Oct 10 '12 at 15:44

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