Eruvin, Chapter 6, Mishnah 1. From here on the mishnayos turn to the laws of eruvei chatzeiros (courtyard eruvin) and shitufei mevo'os (partnership of alleyways): when several houses open onto a single courtyard, their owners must make an eruv chatzeiros; and when several courtyards open onto an alleyway, a shituf must be made - a partnership among the courtyards.
The reason for the enactment, as we have mentioned in the past: even though there are partitions and the courtyard is a private domain according to Torah law, there is a certain resemblance between carrying out from the private domain of the house into the shared courtyard and carrying out from a private domain into a public domain, and a person is liable to err and think that it is permitted to carry out from a private domain into a public domain. The Sages therefore enacted that an eruv must be made, and through it the various domains and ownerships become like one domain, since everyone pools their resources together.
One with whom an eruv cannot be made:
Our mishnah opens with a discussion of one with whom it is impossible to make an eruv - the non-Jew. When a non-Jew lives in the courtyard, his participation in the eruv is not enough; rather, one must rent his domain from him ('sechiras reshus').
The reason for this, as the Gemara explains: the Sages did not want Jews living together with non-Jews and coming to assimilate among them. The calculation was that the non-Jew would not want to rent out his domain to a Jew, since the people of those days were steeped in superstitions, and the non-Jew was afraid that the Jew might work some sort of sorcery on him by means of the rental - and this fear kept him from renting. And if he nevertheless agreed to rent, the rental is effective.
The words of the Mishnah:
"Hadar im hanochri bechatzer" - one who lives with a non-Jew in a courtyard.
"O im mi she'eino modeh be'eruv" - one who does not believe in the very idea of an eruv, referring to the Kusim, whose status was that of half Jews and half non-Jews.
"Harei zeh oser alav" - they render the courtyard forbidden to him, and he may not carry in it, unless he performed sechiras reshus and rented the domain from them.
"Divrei Rabbi Meir" - this is the opinion of Rabbi Meir, and the main point of his ruling is that the law applies even to a single Jew, and there is no need for more than one Jew.
Rabbi Eliezer ben Yaakov disagrees and says: "Le'olam eino oser ad sheyihyu shnei Yisrael osrin zeh al zeh" - a single non-Jew does not render the courtyard forbidden to a single Jew, and no sechiras reshus is needed. Only when there are two Jews in the courtyard, who in any case render it forbidden to one another, is sechiras reshus from the non-Jew also required.
The root of the dispute:
Both Tanna'im agree on the fundamental point: in itself, the non-Jew does not create any prohibition, and the entire enactment was meant to prevent Jews and non-Jews from living together. They disagree over whether it is common for a single Jew to live with a single non-Jew:
Rabbi Eliezer ben Yaakov: this is a milsa delo shechicha, something uncommon. We learned in a mishnah in Avodah Zarah that Jews were afraid to live with non-Jews, and in practice it was forbidden, because a lone Jew was liable, Heaven forbid, to be murdered by the non-Jew of those days. Since this is not common, the Sages did not decree that he would have to rent the non-Jew's share in the ownership of the courtyard.
Rabbi Meir: at times, for various reasons, it does happen that a single Jew lives with a single non-Jew, and therefore the law applies that he may not live with him or use the courtyard unless he rents from him his share in the ownership of the courtyard.
In summary: in this mishnah we began the laws of eruvei chatzeiros and shitufei mevo'os and the reason for the enactment, and we learned that with a non-Jew one does not make an eruv but rather rents his domain from him - an enactment meant to prevent shared living and assimilation. Rabbi Meir and Rabbi Eliezer ben Yaakov disagree over whether the enactment applies even to a single Jew living with a single non-Jew, and it all depends on whether this situation is common or uncommon.