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There are three categories of people who are free from doing Mitzvas:

  1. Cheresh - a deaf-mute
  2. Shoteh - a mentally incompetent person
  3. Kattan - a child.

How do we know that they aren't liable for doing biblical mitzvos?

  • 1
    חרש שוטה וקטן shows up all over Mishna and Gemara. Are you looking for an early source (perhaps Mishna?) that validates the assumption that they are exempt from mitzvos, or are you looking for why (perhaps a drasha?) that teaches this? – Shokhet Jan 28 '15 at 5:35
  • @Shokhet the latter – Shmuel Brin Jan 28 '15 at 6:10
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This is a somewhat complex subject. For now, I can supply only a partial answer regarding the Cheresh (deaf - mute) from this interesting article.

The original discussion seems to emanate from the first mishnah in Tractate Beitza. However, the article claims that the Chatam Sofer on Even HaEzer 2:2 posits that it is a Halacha l’Moshe Misinai. I don't have access to this source to research further what he says.

I am assuming that since the Talmud equated cheresh with shoteh and katan, that these other 2 fall under the same category, but I may be wrong. If you read Rash"i's explanation in Beitzah, he explains why the deaf are equated with the minor and imbecile. The article that I linked to focuses more on how the status of "cheresh" has probably changed, so while interesting, the majority of it doesn't address your question. But the beginning, listing the sources, probably does.

  • Even though the answer seemed more like a comment, it actually asked a yet unasked question of mine, why isn't a Cheresh included in Shoteh. – Shmuel Brin Jan 28 '15 at 2:09
  • The Cheresh is the one you would most expect not to be exempt from certain mitzvot as they could have understanding. Dan's only son was one. Yet he went on to father a large tribe – CashCow Jan 28 '15 at 12:10
  • A shoteh doesn't have control over his decisions because he has an emotional disturbance. A cheireish is uneducable. (Which is why today's deaf mute is not considered a cheireish.) A qatan is both -- lacks emotional maturity AND knowlege. A pesi... R Hershel Schachter defines a pesi as someone who is intellectually handicapped. So, he is sane, but also can't learn. And thus of a kind with a cheireish, not a shoteh. – Micha Berger Sep 17 at 19:31
  • The case RHS dealt with was of a man who had a brain injurty and became mentally retarded after marriage. A cheireish may divorce, if he can gesture in ways that make it clear he knows what's going on and wants the divorce. A shoteh cannot divorce. By noting that a mentally retarded person is closer in cause to a cheireish than to a shoteh, it was possible for the man's wife to get a gett. – Micha Berger Sep 17 at 19:53
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here's a relevant source (chovos halevavos shaar bechina ch.5)

It is through the understanding that we realize the Creator's wisdom, power and mercy, of which the universe provides clear evidence. It is the understanding which shows us that we ought to serve Him, because service is rightly due to Him, and because of His beneficence, bestowed upon all universally and on each one specifically. Through the understanding we are confirmed in our faith in the truth of the Book of G-d's Law given to Moses, His prophet, peace be upon him. Because of a human being's faculty of reason and perception, he is an accountable creature whom his Creator will hold to a strict reckoning. A person who has lost his understanding, loses all the excellencies of a human being and is exempt from the mitzvot (precepts), and reward and punishment.

the cheresh, shoteh, and katan are below the requisite amount of understanding to be liable for mitzvot as the talmud says in Chagiga 2b "just as the shoteh and katan lack understanding, so Cheresh [means] one that lacks understanding".

hence this is derived from reason.

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