1) PRIVILEGES FOR TORAH SCHOLARS
QUESTION: The Gemara relates that Rav Dimi of Neharde'a came to town with merchandise of dried figs to sell. The Reish Galusa asked Rava to determine whether or not Rav Dimi was a Talmid Chacham. If he was a Talmid Chacham, then he would be granted the right to sell his figs in the city before anyone else could sell figs there.
Rav Dimi was examined with a difficult question regarding the Halachos of Tum'ah and Taharah. He did not answer the question adequately and was not granted the monopoly on figs.
RAV ELCHANAN WASSERMAN Hy'd in KOVETZ SHI'URIM (#73) quotes the ROSH (1:26) who writes that when the Gemara earlier says that Talmidei Chachamim are exempt from paying taxes, that exemption applies only to Talmidei Chachamim "whose sole occupation is Torah study." Rav Elchanan Wasserman adds that even if a Talmid Chacham has a trade or business from which he earns his livelihood, he still is entitled to the exemption from taxes on two conditions: that he uses all of his extra time to learn Torah and to review his studies, and that his business provides him only with his basic necessities and does not make him wealthy. Since he ceases his Torah study only to earn the minimum amount of money needed to live, such a person is considered a "Talmid Chacham" with regard to the tax exemption.
According to the Rosh's ruling as explained by the Kovetz Shi'urim, the definition of a Talmid Chacham is a person who spends every possible moment engaged in Torah study. The status of Talmid Chacham does not depend on a person's ability to resolve difficult questions. Why, then, was it necessary to test Rav Dimi with a difficult question? Rav Dimi surely used every spare moment to learn Torah, and even though he was not an expert in every aspect of the Torah, he still should have qualified for the monopoly on figs.
ANSWER: The KOVETZ SHI'URIM distinguishes between the level of scholarship necessary to receive a tax exemption and the level necessary to obtain a monopoly on trade. A person must have a higher, more advanced level of knowledge in order to obtain exclusive rights to market his merchandise. When one merchant is given a monopoly on the sale of a certain item, all of the other merchants experience a financial loss because they cannot sell their merchandise in the market. When a person receives an exemption from taxes, on the other hand, his exemption has no negative effect on others, and thus he is entitled to an exemption even if his level of scholarship is lower.
However, this distinction is questionable. A Talmid Chacham's exemption from the obligation to pay taxes also causes a financial loss to others, because it places an additional burden on the rest of the community who will have to compensate for what the Talmid Chacham does not pay. Why, then, is a Talmid Chacham exempt from taxes on the grounds that others will not suffer financially on his account?
The answer to this question lies in the statement of the Gemara earlier (8a), "Misfortune comes to the world only because of the unlearned." Accordingly, had all of the members of the community been Talmidei Chachamim, the king would not have imposed the tax on the public in the first place. Thus, it is not the Talmid Chacham's exemption from the tax that causes an additional burden on the rest of the people; rather, it is their own lack of the merit of Torah study.
Accordingly, any Talmid Chacham who spends all of his spare time learning is granted an exemption from taxes, since the very act of learning prevents misfortune from coming to the world. A person does not have to be an expert in all parts of Torah in order to be exempt from taxes. In contrast, a Talmid Chacham merits a trade monopoly only when he has attained a mastery of the entire Torah. (Y. Marcus)

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2) ACTIVITIES WHICH ARE PROHIBITED EVEN IN ONE'S OWN DOMAIN BECAUSE OF DAMAGE THEY CAUSE ELSEWHERE
QUESTION: The Mishnah teaches that when a person's dovecote is situated adjacent to his neighbor's property, and the neighbor wants to lean a ladder near the dovecote, he must distance the ladder at least four Amos from the dovecote. This is required so that an animal (such as a marten) will not be able to climb the ladder, jump into the dovecote, and prey on the doves.
The Gemara initially assumes that the Mishnah's ruling is unlike the view of Rebbi Yosi, who maintains that a person is permitted to do an act in his own domain that might later cause damage to his neighbor's property. The Gemara rejects this assumption and concludes that the Mishnah is also consistent with the view of Rebbi Yosi, because Rebbi Yosi agrees that one is prohibited to "fire arrows from one's house into a neighbor's domain" ("Girei Didei") -- that is, a person may not do an act in his own domain that directly causes damage to his neighbor's property. In the case of the Mishnah, a marten might jump from the ladder into the dovecote at the exact moment at which the neighbor places his ladder next to the dovecote; such an occurrence would be considered "Girei Didei." RASHI stresses that the concern is that the marten will jump into the dovecote while the neighbor is holding the ladder, and it will be considered as though he fired arrows and damaged his neighbor's property.
The CHAZON ISH (Bava Basra 10:1, DH v'Ha) asks why, in this case, would it be considered "Girei Didei"? After all, the neighbor did not throw the marten into the dovecote; he simply happened to be holding the ladder at the moment that the marten jumped on it. Why should that case differ from a case in which the marten jumped from the ladder after it was placed on the ground?
ANSWER: The CHAZON ISH suggests three answers to his question. In his third answer, he suggests that in the case of the Gemara, the marten jumps onto the ladder while the neighbor is holding it, and the neighbor then places the ladder next to the dovecote. When he does so, he actively brings the marten closer to the dovecote. Only in such a case does Rebbi Yosi agree that the action is prohibited because of "Girei Didei," because the neighbor actively brings the damaging object closer to the object being damaged. Therefore, even though the neighbor's action is confined to his own domain, everyone agrees that it is prohibited, because it is considered as though he shot arrows from his own house into his neighbor's property. (Y. Marcus)