Mikvaos, Chapter 2, Mishnah 1. With this mishnah we enter a new subject: the halachos of safeik, doubt. The mishnayos that follow deal with a very particular kind of doubt. The person's tumah is not in question at all; we know for certain that he was tamei. What is in question is the tevilah that was supposed to remove that tumah: did it actually work?
Three Cases of Doubt
The mishnah presents three situations, all built on the same foundation.
The first: "Hatamei sheyarad litbol, safeik taval safeik lo taval." A tamei person stepped down into a mikveh in order to be toveil, and when he comes out he cannot say for sure that the immersion counted. It may be that a limb or some other area stayed above the waterline and never made contact with the water at all, so that his whole body was never submerged at once.
The second: "Afilu taval" - even in a case where he knows beyond any question that all of him went beneath the surface. Here the uncertainty has shifted away from the man and onto the mikveh itself. The mishnah's wording sets one possibility against the other, "safeik yesh bo arbaim se'ah", and its opposite: perhaps the pool held the required forty se'ah when he immersed, and perhaps its water came up short of the shiur. Either way, whether the tevilah accomplished anything is left unsettled.
The third: "Shnei mikvaos, echad yesh bo arbaim se'ah v'echad she'ein bo." Two mikvaos stood in front of him. About the first we have definite knowledge that it holds the forty se'ah, and about the second we know just as definitely that it does not. He was toveil in one of the pair, "taval b'echad meihen", but which of the two he entered he is no longer able to say.
The Ruling and Its Reasoning
In all three cases the mishnah rules: "sfeiko tamei." The man retains his status of tumah.
The principle behind this is chazakah d'me'ikara, the strength of an established prior status. Before the tevilah, this person's condition was clear and settled: he was tamei. The doubt did not arise until afterwards, and a doubt that arises later has no power to uproot what was already firmly established. Since we cannot say with confidence that a valid tevilah took place, we leave him exactly where he was, and he is treated as tamei.