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According to this answer to a related question, the g'mara on Bava Kamma 82a requires reading torah at least every three days because we should never go longer than that without words of torah.

But at minimum we say the sh'ma, a torah text, twice a day.

Why does that not satisfy the requirement?
Is the g'mara talking specifically about public reading? (If so, why does that make a difference?)

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Your question is asked by no less than the P'ri M'gadim (OH Eshel Avraham: 135)!

  • According to the Amora Sh'muel, as quoted by R. Yehudah, in Berakhot (21a), the recitation of Sh'ma is merely rabbinic. Accordingly, we could suggest that the enactment to read the Torah on Monday and Thursday preceded the enactment to read the Sh'ma daily. This would be especially likely, since the enactment to read the Torah thrice weekly is very old; perhaps as old as Moshe (cf. Bava Kamma 82a, Hilkhot Tefillah 12:1).

However, some claim that even according to Sh'muel, there is still a Biblical obligation to study Torah each day; just no set formula. (cf. Talmidei Rabbenu Yonah to Rif Berakhot 12b). If that were the case, or if the recitation of Sh'ma were actually Biblical, then another answer would be needed.

  • We could suggest that the point of having Torah every three days isn't just that the individual should experience Torah periodically, for which any Torah should suffice, but rather that the Torah itself must be reviewed periodically so that it not be forgotten.

This is implied by the Paneah Razza (14th cent.) who writes (Deut 10:10):

לא יהיו לעולם ג' ימים בלא תורה ולא תשתכח

And that they never go three days without Torah, and it would not be forgotten.

  • The P'ri M'gaddim himself gives two answers. Either that one needs to lean Torah besides for Sh'ma (he does not clarify the nature of this need; indeed it seems to be an ad hoc solution). Alternatively, he suggests that there is a need to not exceed three days in Torah study from a written text in particular. (Why there would be such a need, he doesn't say).
  • R. Betsalel Stern provides an additional reason (fifth, for anyone counting): that the recitation of Sh'ma does not count as Torah study since it is meant specifically to fulfill its own obligation. (B'tsel HaHokhmah vol. I:1).

[Note that his assumption about the recitation of Sh'ma not fulfilling the obligation of Torah study is dubious. Cf. Nedarim 8a, and Menahot 99b).]

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Rava says that Shema does satisfy the technical requirement to learn Torah each day (a mitzva md'oraysa for men). So that takana must have been trying to accomplish more, probably to have a public reading, perhaps also to learn something new every week. The public reading has its own birchas haTorah on it, so its clearly quite significant. (Some even say its birchas haTorah is md'oraysa.) There can be different reasons for its significance. It is a Kiddush Hashem b'rabim, and perhaps its public nature is a recreation of Matan Torah.

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    Who says the brachot on an aliyah are deoraita?
    – Double AA ♦
    Sep 5, 2012 at 5:41
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Because it is not done through a way of learning, rather a way of praying and declaring belief etc.

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    But then birchas kohanim and Ezehu M'koman and the b'raysa of Rabi Yoshmael (all of which are said each morning) should count toward the "no three days without Tora" requirement, since they are study. (They count as study, according to many, toward the requirement of studying Tora each day.) Seemingly the "no three days without Tora" requirement doesn't hinge (only) on whether something is prayer.
    – msh210 ♦
    Dec 14, 2011 at 20:52
  • You said "according to many". However, according to others it doesn't count as learning. That's why in Siddur Od Yosef Hai they give a list of a few pesukim, mishnayot, and gemarot "latzet lekol hadeot." I guess my explanation only fits according to those who hold it doesn't count as learning
    – Hacham Gabriel
    Dec 14, 2011 at 21:02
  • But what if you recite those added passages? Do you not need to hear a public reading during the week, or even on Shabbath?
    – Seth J
    Jan 9, 2012 at 0:16
  • No, because we are not hayesh lemiuta- making gezerot for the minority.
    – Hacham Gabriel
    Jan 9, 2012 at 0:25
  • But the Talmud Nedarim 8a and Menahot 99b state that reciting the Sh'ma does fulfill the requirement to study Torah! Furthermore, who says that the Gemara is even dealing with the technical obligation to learn Torah?
    – mevaqesh
    Nov 30, 2016 at 0:34

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