whose third-degree impurity came from contact with an item of second-degree impurity, in which case the item with the second-degree impurity is itself forbidden, i.e. impure, even if it is non-sacred food, isn’t it logical to infer that it should be able to impart fourth-degree impurity upon sacrificial food?

And if you would say that the reason Rabbi Yosei did not employ this a fortiori inference is because it can be refuted as follows: What is unique about one who immersed that day is that prior to his immersion he was a primary source of impurity, this cannot be, as Rabbi Yosei brought proof for the existence of a fourth degree of impurity from the case of one who has not yet brought an atonement offering, who was also a primary source of impurity prior to his immersion, and Rabbi Yosei clearly did not refute the proof due to this factor. Therefore, the reason Rabbi Yosei did not employ an a fortiori inference from the case of food that contracted impurity from one who immersed that day is clearly that he disagrees with the opinion of Abba Shaul. Consequently, Rabbi Yoḥanan concluded that he cannot understand Rabbi Yosei’s reasoning.

§ Rabbi Asi said that Rav said, and some say Rabba ben Isi said that Rav said: Rabbi Meir, and Rabbi Yosei, and Rabbi Yehoshua, and Rabbi Elazar, and Rabbi Eliezer all hold that an item of second-degree ritual impurity status cannot impart third-degree ritual impurity status to non-sacred items. Rav proceeds to prove this by attributing support from the rulings of each of these tanna’im.

Rabbi Meir is of this opinion, as we learned in a mishna (Para 11:5): Anything that requires immersion in water by rabbinic law renders sacrificial food impure upon contact, with second-degree impurity, and disqualifies teruma, meaning that it renders the teruma itself impure, but not to the extent that the teruma can render other teruma impure. And anything that requires immersion in water by rabbinic law is permitted for non-sacred food and for the second tithe, i.e., it does not render these items impure. This is the statement of Rabbi Meir. But the Rabbis prohibit one who has this degree of impurity from partaking of the second tithe. From the fact that Rabbi Meir permits him to partake of the second tithe, it is inferred that he maintains that an item of second-degree impurity cannot impart third-degree impurity upon non-sacred items.

It is evident that Rabbi Yosei is of this opinion from that which we have stated above, that he derives that sacrificial food can contract fourth-degree impurity, because if he holds that non-sacred items can contract third-degree impurity, he should have derived through his a fortiori inference that there is fourth-degree impurity vis-à-vis teruma and fifth-degree impurity vis-à-vis sacrificial food, since each of these categories has a unique level of impurity.

Rabbi Yehoshua is of this opinion, as we learned in a mishna (Teharot 2:2): Rabbi Eliezer says: One who eats food with first-degree impurity assumes first-degree impurity. One who eats food with second-degree impurity assumes second-degree impurity. One who eats food with third-degree impurity assumes third-degree impurity. Rabbi Yehoshua says: One who eats food with first-degree impurity or food with second-degree impurity assumes second-degree impurity. One who eats food with third-degree impurity assumes second-degree impurity vis-à-vis sacrificial food, and he does not assume second-degree impurity vis-à-vis teruma.

Eating an item with third-degree impurity is possible only in the case of non-sacred items, as eating impure teruma or sacrificial food is prohibited. However, generic non-sacred food cannot contract third-degree impurity at all. Therefore, the case of one who eats food with third-degree impurity refers specifically to non-sacred food items that were prepared as if their level of purity were on the level of the purity of teruma. By means of a vow, one can establish the purity status of non-sacred food items to be treated on the level of purity necessary for teruma.

The Gemara infers from Rabbi Yehoshua’s statement that yes, one is able to prepare items as if their level of purity were on the level of the purity of teruma; but one is not able to prepare items as if their level of purity were on the level of the purity of sacrificial food, and such items would not contract third-degree impurity.

The Gemara concludes: Apparently, Rabbi Yehoshua holds that an item of second-degree impurity cannot impart third-degree impurity upon ordinary non-sacred items that were not prepared on the level of the purity of teruma.

Rabbi Elazar is of this opinion, as it is taught in a mishna (Teharot 2:7): Rabbi Elazar says: The three of these are equal in their ability to impart ritual impurity to other items: An item of first-degree impurity, whether it is an item of sacrificial food, or of non-sacred food, or of teruma.

With regard to sacrificial food, such an item renders impure two additional levels of contact, enabling the items that contracted ritual impurity from it to transfer that impurity to items that they in turn touch afterward. And it disqualifies one level afterward, imparting upon the food fourth-degree impurity, which cannot impart impurity to a fifth item.

With regard to teruma, an item of first-degree impurity renders impure one additional level of contact, i.e., it imparts second-level impurity to teruma food with which it comes into contact, and that item in turn disqualifies one additional level afterward, as that teruma food imparts third-degree impurity upon teruma.

And with regard to non-sacred food, an item of first-degree impurity merely disqualifies one additional level of non-sacred food. Evidently, non-sacred items cannot go beyond a second-degree impurity.

Rabbi Eliezer also agrees with this principle, as we learned in a mishna (Ḥalla 2:8): Rabbi Eliezer says: Ḥalla can be taken from ritually pure dough on behalf of ritually impure dough. How so? If there are two batches of dough, one of which is pure and one of which is impure, one takes the required amount of dough for separating ḥalla for both of the batches from the pure dough when its ḥalla has not yet been separated for itself, and then places less than an egg-bulk of dough, which is not susceptible to becoming ritually impure due to its size, in the middle, between the impure dough and the pure dough set aside for being used as the separated ḥalla. This joins all of the dough together, so that one can fulfill the requirement to take dough for separating ḥalla from dough that is situated near the dough it comes to exempt.