Sotah, Chapter Five, Mishnah Two
The remaining four mishnayoth all contain midrashim which were stated on that day. According to the Babylonian Talmud Berakhot 28a, this refers to the day that the rabbis deposed Rabban Gamaliel and appointed Rabbi Elazar ben Azarya in his place. According to the story, when Rabban Gamaliel was head of the Sanhedrin, he limited access to the study sessions. When R. Elazar ben Azarya took over, he opened the doors and that day became a day of great Torah learning. Regardless of whether this story is historically accurate, it seems to touch on a profound truthtrue wisdom comes from intellectual exchange with fellow students and not from isolated speculation or from the gathering of the elite. When people study together they can question each other, pointing out the weaknesses in each others arguments. In such a manner, which one could deem as being both rabbinic and Socratic, the truth is best revealed. Rabban Gamaliel should not have excluded people from the bet midrash for we can never know who will help arrive at the truth.
The reason that this chapter brings these midrashim is that the first three were stated by Rabbi Akiva, the author of the midrash which began yesterdays mishnah.
As a note, I translate darash as expounded. This is the root of the word midrash, a word which I use to mean the expounding of a word or phrase from a Biblical text.
1) On that day, Rabbi Akiva expounded, And every earthen vessel, into which any of them falls, everything in it shall be unclean (Leviticus 11:33), it does not state tame (is unclean) but yitma, (shall make unclean). This teaches that a loaf which is unclean in the second degree, makes unclean [food and liquids which come into contact with it] in the third degree.
2) Rabbi Joshua said: who will remove the dust from your eyes, Rabban Yohanan ben Zakkai, since you used to say that in the future another generation will pronounce clean a loaf which is unclean in the third degree on the grounds that there is no text in the Torah according to which it is unclean! Has not Rabbi Akiva your student brought a text from the Torah according to which it is unclean, as it is said everything in it shall be unclean.
Section one: The verse in Leviticus states that anything that falls into an unclean earthen vessel becomes itself unclean. The verse uses the word yitma, which if vocalized differently could be read yetame, which means will make unclean. Rabbi Akiva uses this proposed alternative vocalization to conclude that something which falls into an unclean vessel makes other things unclean. The thing that falls into the vessel has second degree defilement, and that which it makes impure becomes defiled in the third degree, a lesser form of defilement. What defiled the vessel was a primary source of impurity, such as a creepy crawly thing, a menstruant, a zav, etc. The primary source of impurity made the vessel into a first degree defiler, which made the loaf into a second degree, which when it comes into contact with other things will give them third degree defilement.
Section two: Rabbi Joshua, one of Rabbi Akivas teachers, speaks wistfully to his own, deceased teacher, Rabban Yohanan ben Zakkai. He laments the fact that Rabban Yohanan ben Zakkai is no longer alive, for he would have been astounded at the brilliance of Rabbi Akivas midrash. Evidently, the issue of third degree defilement was one of some contention in Rabban Yohanan ben Zakkais time; he feared that eventually people would claim that there is no third degree defilement. The reason why they would forget this halakhah is that there is no clear proof for it from any biblical verse. In Rabban Yohanan ben Zakkais time it was only a tradition, not rooted in the Torah. Rabbi Akiva improved and solidified the status of this halakhah by tying into a biblical verse.