Taharos, Chapter 6, Mishnah 5. This chapter turns on a single distinction: a safek tumah that arises in a reshus harabbim leaves a person tahor, while the same safek in a reshus hayachid renders him tamei. Our Mishnah brings a case that looks straightforward, and it becomes the testing ground for a dispute about what kind of doubt actually triggers that rule.
The Case
"Nichnas labik'ah biyemos hageshamim": a man walks into the bik'ah, the valley. This valley makes appearances throughout Shas. It is not a single field but an area containing a number of fields belonging to different owners. The Mishnah specifies biyemos hageshamim, the rainy season, and that detail is the key to the whole case: in the winter months there is little planting or farming going on, so few people are passing through. With the crowds absent, the valley carries the status of a reshus hayachid.
The Mishnah then locates the impurity: "Vehatumah bisdei plonis", somewhere in a certain field there is tumah. The man's own testimony follows. He says "halachti lamakom halaz", that he made his way over toward that spot, and then he adds that he has no idea whether he set foot in the very field where the tumah was lying or only in one of the adjoining fields, which had no tumah in them at all: "eini yodei'a im nichnasti l'osah hasadeh im lo nichnasti."
So we have a safek tumah in a reshus hayachid, which would ordinarily mean tamei. But notice the shape of the doubt. This is not a safek maga, a doubt about whether he came into contact with the tumah. It is a safek bi'ah, a doubt about whether he was ever in that place at all.
The Machlokes
"Rebbi Elazar metaher, vachachamim mitam'in." Rebbi Elazar rules that the man is tahor; the Chachamim rule that he is tamei.
To appreciate Rebbi Elazar's position, one has to know where the entire law of reshuyos comes from. The whole framework, that a safek is treated strictly in a private place and leniently in a public place, is derived from the sotah. A sotah is a woman suspected of adultery. If her infidelity were established she would not be a sotah at all, she would be an adulteress; her case is defined precisely by the doubt. She is known to have secluded herself in a private space, and what happened there is unknown. The Torah treats her as tmei'ah until her status is resolved, and that is our model for a safek tumah in a reshus hayachid.
Now look carefully at the sotah. There is no uncertainty about whether she entered the room; she was unquestionably there. The only uncertainty concerns what happened once she was inside. Rebbi Elazar therefore maintains that only a doubt of that type carries over into hilchos tumah: safek maga, a doubt about contact, is a genuine safek tumah in a reshus hayachid and yields tumah, but safek bi'ah, a doubt over whether the person ever entered the place, has no parallel in the sotah and leaves him tahor. Our man in the valley does not even know which field he walked into, so by Rebbi Elazar's standard he is tahor.
The Chachamim do not draw that line. For them a safek is a safek: whether the uncertainty concerns entering the place or touching the tumah once inside, a doubt in a reshus hayachid is resolved toward tumah, and the man is tamei.
The halachah follows the Chachamim. Still, Rebbi Elazar earns our admiration for the consistency of his approach: he stakes out the distinction between safek bi'ah and safek maga and then applies it faithfully, exactly as he said he would, even in this case where he stands alone.