Tevul Yom, Chapter 3, Mishnah 5. This mishnah continues the chapter's central concern: when a tevul yom touches one spot of a food, do we treat the whole thing as one connected unit, so that everything he touched becomes possul, or do we say that only the exact point of contact is affected? Our mishnah brings two separate cases, and in each one the answer depends on how we understand the mixture in front of us.
Take the first situation the mishnah presents. A batch of chullin dough has become bound up with terumah in one of two ways: terumah dough was mixed into it, which the mishnah calls "isa shenidme'ah," or it was made to rise, "o shenischamtzah," through a leavening agent of terumah, "bise'or shel terumah." Under the ordinary laws of terumah, a combination like this is treated stringently. Terumah forfeits its identity inside chullin only when the chullin exceeds it a hundredfold; with any smaller proportion of chullin, the entire batch carries the halachic status of terumah.
With regard to a tevul yom, however, the Tanna Kamma of our mishnah holds that we may be more lenient: "einah nifseles betevul yom." Even though for other purposes the mixture is treated as terumah, if a tevul yom touches this combined dough he does not render it invalid. The mishnah then records the dissenting view: "Rabbi Yose veRabbi Shimon poslin." Rabbi Yose and Rabbi Shimon maintain that the tevul yom does indeed render such dough possul by touching it.
The mishnah now turns to a second case: "Isa shehuchshira bemashkeh venilusha bemei peiros." To understand it, we need to recall how food becomes susceptible to tumah in the first place. Flour on its own is not yet susceptible; it becomes susceptible when it comes into contact with one of the seven liquids. Ordinarily, when flour of terumah is made into dough, the very water used for the kneading is one of those seven liquids, and that same water both renders the flour susceptible to tumah and turns it into dough.
In our case, though, the two steps were separated. The flour of terumah was first made susceptible to tumah, "shehuchshira bemashkeh," through contact with one of the seven liquids, and only afterward was it kneaded, "venilusha bemei peiros," with fruit juice, which is not one of the seven liquids. So what stands before us is a mass of terumah flour bound together by fruit juice. And that raises the question: is this simply dough of terumah with the ordinary halachos of dough, or is it really a collection of tiny flour particles held together by juice? In other words, is it a single chibbur, one connected mass, such that a tevul yom who touches one portion has invalidated all of it, or does his touch affect only the spot where his hand made contact?
What happens when such a mixture is touched? The mishnah records, "venaga bahen tevul yom," that a tevul yom came into contact with part of it, and it then preserves two conflicting traditions, each attributed to the very same authority. Rabbi Elazar ben Yehuda of Bartosa transmits from his teacher Rabbi Yehoshua the ruling "passal es kulah": the contact has spoiled the batch in its entirety, because the whole mass counts as joined together. Rabbi Akiva cites that identical teacher with the opposite conclusion, "lo passal ela mekom maga'o": nothing is disqualified beyond the precise area his hand reached, and all the remaining dough is still fit.
Two arguments, then, emerge from this mishnah. Where chullin dough has taken in terumah, whether by admixture or through terumah leaven, the anonymous opinion holds that a tevul yom's contact leaves it fit, while Rabbi Yose and Rabbi Shimon disqualify it. And where terumah flour was made susceptible by one of the seven liquids and only later bound into dough by fruit juice, Rabbi Yehoshua's position reaches us in two contradictory reports: Rabbi Elazar ben Yehuda of Bartosa has him invalidating the entire mass, while Rabbi Akiva has him limiting the loss to the spot that was touched.