Eduyos chapter 3, mishnayos 3 through 7. From here on we turn to four disputes between Rabbi Yehoshua and the Sages. It appears that the order of the mishnayos roughly follows the ages of the Tannaim, from the older to the younger, whether or not that is actually the case. All four of Rabbi Yehoshua's points of dispute revolve around matters of tumah and taharah, and in every one of them Rabbi Yehoshua is stringent and rules that the item is tamei, while the Sages rule that it is tahor.
The Basic Rule in Cases of Doubtful Tumah:
The thread connecting all four cases (and in fact there are really only two pairs) is the rule that governs a situation of doubt regarding the spread of tumah:
A doubt about tumah in a public domain - the doubt is ruled tahor. "Public domain" in the context of these halachos means a place where at least three people are found, and there we treat the doubt as tahor.
A doubt about tumah in a private domain - the doubt is ruled tamei. "Private domain" is a private place where two people or fewer are found, and there we rule that the item is tamei.
The Tumah of a Metzora:
The four cases before us are a kind of borderline case, and two of them concern a metzora. A metzora, whose skin has been afflicted with tzaraas, is a very severe source of tumah, and he transmits tumah in a variety of ways: through touch, through carrying and through moving. Whether the person touched the metzora or the metzora touched him, whether the person moved him or he moved the person, whether he bore his weight or was borne by him - tumah is transmitted from the metzora to the person or to the vessel.
Unique to the metzora is that he transmits tumah even through entry, that is, by coming into a room. This law is very similar to the tumah of an ohel, though it is not identical to it: until now we have dealt with being under one roof with a corpse or a significant part of it, and here the resemblance exists, but this is not the place to spell out the differences. The point is that when a stationary metzora is under one roof with something capable of receiving tumah, the tumah spreads through entry, and everything under that roof becomes tamei.
Here Rabbi Yehoshua and the Sages disagree: according to the Sages, even though the general rule is that a doubt about tumah in a private domain is ruled tamei, that rule does not apply to a metzora, for reasons beyond the scope of our discussion. Tzaraas is somewhat different, and we are not stringent about it on the strength of that rule. Therefore questions that arise about the transmission of tumah from a metzora through entry will be decided leniently according to the Sages, even in a private domain. This is the essence of the first half, and also most of the second half.
The Language of the Mishnah:
"Arba sefeikos Rabbi Yehoshua metamei vachachamim metaharin" - four questions may arise regarding the spread of tumah, and in all of them Rabbi Yehoshua says that the tumah was transmitted and rules the item tamei, while the Sages say that we treat the item as tahor. How so? These are the cases:
"Hatamei omeid vehatahor oveir" - a tamei person, and in particular a metzora, is standing in place under an ohel, whether it is a tree, a roof or a building, and the tahor person passes by, and it is not known whether he passed under the ohel or not, or perhaps he touched the metzora and bumped into him. The question is whether the metzora transmitted his tumah, and this is even in a private domain. In a public domain all agree that it is tahor, and the dispute is in a private domain.
"Hatahor omeid vehatamei oveir" - the tahor person or object is stationary under a roof, and the metzora passes by him, and we do not know whether, when he passed under the overhang, he remained there long enough to transmit tumah. For example, he stopped to tie his shoe, and it is not known whether he stopped while still under the overhang or past it. These are the first two cases, which deal with a metzora in a private domain.
"Tumah birshus hayachid vetaharah birshus harabim" - the source of tumah is lying in a private domain. For example, a dead mouse is at the entrance of a store that borders on a public domain, and the store is a private place where only one person is found, the storekeeper. A person is walking down the street, and we do not know whether, as he passed, his foot touched the dead mouse lying on the boundary line, inside the private place but very close to the public domain. The tahor receiver is in the public domain, in full public view.
"Taharah birshus hayachid vetumah birshus harabim" - the potential receiver is inside the store, such as a tahor vessel resting on the floor, while the tumah is in the public domain: a zav or a niddah passed by it, and we do not know whether they touched it or not.
In the last two cases the source of tumah is in one halachic domain, the public domain, and the receiver is in the opposite domain. The question is whether we treat this as a doubtful tumah in a public domain and rule leniently, or as a doubtful tumah in a private domain and rule stringently, and that is the dispute.
And in all of those cases, in the language of the Mishnah: "safek naga safek lo naga, safek he'ehil safek lo he'ehil, safek hesit safek lo hesit":
"Safek naga" - perhaps there was contact between the source and the recipient and perhaps there was not.
"Safek he'ehil" - in a place where there is tumas ohel, such as a piece of corpse tumah inside a house, and also with regard to a metzora who passes by, since his overshadowing is like entering.
"Safek hesit" - perhaps he moved it and perhaps he did not, like a zav who shifts objects and transmits tumah even without direct contact.
In all of those cases, when we are not certain whether the tumah was transmitted or not, "Rabbi Yehoshua metamei" - Rabbi Yehoshua rules that it is tamei and takes the stringent position, "vachachamim metaharin" - and the Sages rule that it is tahor.
Let us review and summarize the cases: in the first two, we do not know whether the source, the metzora, and the recipient were under one roof at one and the same time, when the metzora was stationary, whether it was the metzora who was in motion or the recipient who was in motion. There the Sages say that the rule of a doubtful tumah in a private domain does not apply at all, and therefore the recipient is tahor. In the last two, the question is one of a divider: the tumah is in one domain and the recipient on the other side of it, and the question is whether we view this as an event of the public or as an event of an individual. Here too the Sages rule leniently, treating both sides as an event of the public domain and ruling tahor; whereas Rabbi Yehoshua sees it as an event of an individual and rules tamei because of the doubt.
The halachah:
The halachah in all of these cases follows the opinion of the Sages. According to the Rambam's approach, however, matters are a bit more involved: if the source of tumah is lying in a private domain and there is a doubt whether the pure person touched it - in this simple case, which is roughly the case described in the Mishnah - the Rambam rules that the doubtful case is tamei, since the doubt arose regarding something that took place in a private domain, and this is a doubtful tumah in a private domain. Matters become somewhat more complicated when several items are standing there, some of tumah and some of taharah, one in a private domain and one in a public domain, and it is not known which of them he touched: here there is no certainty that the event took place in the public domain, and therefore the doubtful tumah is decided leniently. It turns out that the halachah is a bit more involved than what emerges from the Mishnah alone, but this is how it was ruled.