We come now to Mishnah 7 in the fifth chapter of Maseches Terumos, which presents a fascinating case. What is the law regarding a se'ah of Terumah that fell into a hundred se'ah of chullin? The law is straightforward: one lifts out a single se'ah from the mixture, and the rest is permitted. And what will the law be if afterward another se'ah of Terumah falls in? Here too, seemingly, he lifts out another se'ah and everything is set right again. And so it goes each and every time.
The parameters of nullification at each stage:
The reason for this is that at every single stage both required conditions are met: on the rabbinic level a ratio of one in a hundred is needed, and it exists; on the Torah level a simple majority suffices, and that exists as well. Seemingly, then, everything is in order.
But on the Torah level we must not delude ourselves. Each time additional Terumah falls in and one se'ah is lifted out of the mixture, the ratio between the Terumah and the chullin moves steadily closer to the point at which the Terumah becomes the majority. At the outset we had a hundred se'ah of chullin before us. Once a se'ah of Terumah fell in, the mixture became one part Terumah out of a hundred and one. When one se'ah is lifted out of the mixture, we are left with slightly more than ninety-nine parts chullin and slightly less than one part Terumah - for from this point on a certain quantity of Terumah is also present in the mixture. After all, the se'ah that was lifted out, assuming the mixture is uniform, contained one part Terumah out of a hundred and one, along with a hundred parts of chullin. And so, the next time we will approach a ratio of ninety-eight to two, and after that ninety-seven to three, and so on.
The question, then, is how many times this process can be repeated before the mixture becomes forbidden. The answer is that on the Torah level this is the point at which the majority of the mixture becomes Terumah - and in fact, even if the ratio is exactly half and half, the mixture is forbidden, since there is no longer a majority of permitted material to nullify the prohibition. At each and every stage the matter is permitted as far as the rabbinic laws are concerned, but at a certain stage the Torah prohibition enters the picture and declares: there is no majority of permitted material here. At that point the prohibition reawakens, and this is what is called "chozer v'ni'or". We cannot tell ourselves that there is no Terumah here at all; the Terumah accumulates, and at a certain stage the Torah prohibition returns and reawakens. This is the case of our Mishnah.
The language of the Mishnah:
"Se'ah Terumah shenaflah l'meah" - one se'ah of Terumah that fell into a hundred se'ah of chullin.
"Higbihah" - he lifts out one se'ah from the mixture, and we are back to a hundred se'ah. Their status is that of permitted produce, even though in terms of their content Terumah is mixed into them.
"V'naflah acheres" - a second se'ah of Terumah fell in and slightly raised the proportion of Terumah in the mixture, and he again lifts out a se'ah, and so too a third time and the times that follow.
"Muteres" - the mixture continues to be permitted to eat.
"Ad shetirbeh Terumah al hachullin" - until the point at which the Terumah becomes the majority of the mixture.
How many times? The views of the Rishonim:
The Mishnah does not spell out how to perform the calculation, and on this the Rishonim disagree:
The view of the Bartenura: the calculation must be based on the worst-case scenario, according to which the process can be repeated up to fifty times. The worst case is that each time, what is lifted out of the mixture of a hundred and one se'ah is pure chullin alone. It emerges that the first time we go down to ninety-nine se'ah of chullin, the second time to ninety-eight, the third time to ninety-seven, and so on. After fifty times, fifty se'ah of chullin have been lifted out and fifty remain, and when the fifty-first se'ah of Terumah falls in, the mixture becomes forbidden.
The view of the Rambam: what is lifted out each time is not pure chullin, and therefore the count rises to a hundred times. For each time additional Terumah falls in and a se'ah is lifted out of the mixture, the chullin becomes progressively more diluted, and when a se'ah is lifted out of the mixture it contains more and more Terumah - so that less and less chullin is lost. According to this reckoning, after a hundred times we have before us two hundred se'ah: a hundred of chullin and a hundred of Terumah, and here the line is crossed.
It is worth noting that a precise calculation of the numbers - assuming that with each fall the Terumah mixes uniformly and evenly throughout all the chullin, an assumption that in itself is not simple - yields the number seventy. On the seventieth time that Terumah falls in, the scale will tip toward a mixture that is mostly Terumah. Whether the Rambam would have ruled stringently at seventy had he been aware of this is not clear.
In summary: in this Mishnah we learned the principle of "chozer v'ni'or": even though at every single stage the nullification is valid both rabbinically and on the Torah level, the Terumah accumulates in the mixture, and once it becomes the majority (or even half and half), the Torah prohibition returns and reawakens. We examined the language of the Mishnah - "Se'ah Terumah shenaflah l'meah... higbihah v'naflah acheres... ad shetirbeh Terumah al hachullin" - and the dispute among the Rishonim regarding the calculation of the number of times: fifty according to the Bartenura, a hundred according to the Rambam, and seventy according to the precise reckoning. This is the calculation that emerges from the Mishnah, though the practical halachah requires further clarification.