Our halachah: chapter 2, mishnah 9. This mishnah continues the ideas discussed in the previous mishnah, where we dealt with leaven of chullin and forbidden leaven that fell into a single dough.
The case before us:
As in the previous mishnah, "se'or shel chullin" - permitted leaven - fell into a permitted dough. Here, however, the dough had already been leavened by the power of the permitted leaven, meaning that it had already become chametz. Afterwards, "se'or shel Terumah" or "se'or shel kil'ei hakerem" fell in, leaven that also had enough to leaven the dough - but the leavening had already taken place beforehand.
The opinion of the Tanna Kamma - forbidden:
According to the Tanna Kamma the dough is forbidden. At first glance the forbidden leaven added nothing, since the dough had already become chametz; in practice, however, it did add something: a dough that has undergone a double leavening, with a double quantity of leaven, has greater power to leaven and to transmit leavening to other doughs that will come afterwards. Because of the two different types of leaven that fell into it, its ability to transmit leavening is greater and more effective.
The opinion of Rabbi Shimon - permitted:
Rabbi Shimon permits the dough, for two reasons:
The leavening was accomplished by something permitted: the dough had already become chametz through the power of the permitted leaven, and therefore when the forbidden leaven enters it has no effect upon it.
The additional leaven has a negative effect: if anything, the extra leaven is harmful - it makes the dough more leavened than it should be, and this is not a benefit but the opposite.
A dispute among the commentators:
The commentators disagree as to whether Rabbi Shimon, who permits here, also permits in the case of the previous mishnah. There the permitted leaven of chullin fell into the dough but had not yet produced chametz, and only afterwards did the forbidden leaven fall in. Some understood that there too Rabbi Shimon would say that the forbidden leaven has no effect, since ultimately its effect is negative: even though the leavening happens more quickly, the excess leaven works to the detriment of the dough, and therefore there too the dough would be permitted.
In summary: this mishnah discusses a case in which the dough was first leavened by the power of permitted leaven, and only afterwards leaven of Terumah or of kil'ei hakerem fell into it. The Tanna Kamma forbids it, because the double leavening increases the dough's power to leaven other doughs; Rabbi Shimon permits it, since the leavening was already accomplished by something permitted, and the additional leaven is even harmful. The commentators disagree as to whether this opinion of Rabbi Shimon applies to the case of the previous mishnah as well.