If someone warned his wife but she secluded herself, even if he hears of it from a little bird he must divorce her and give her her ketubah; this is the opinion of Rabbi Eli'ezer. Rabbi Yehoshu'a says: not until it is discussed by those who spin in the moonlight.
1:
The chapter that we begin to study now is the last chapter of this tractate that deals directly with the main topic, the Sotah. (It will be followed by three more chapters which deal with several very interesting topics, but which are sparked only in a very indirect way by the topic of the Sotah.) The topic of our present chapter is that of the nature of the testimony that must be available in the case of the Sotah.
2:
At the very start of our study of this tractate we learned that if a man suspects his wife of infidelity he must warn her not to seclude herself alone with a man whom he must identify by name. This warning is called by our tractate by a special term derived from three Hebrew letters Qof, Nun and Alef [קנא]. On the significance of this root in this context see what we wrote in the fifth paragraph on Sotah 1:1. But it is not sufficient for the husband to identify the suspected paramour by name and to demand that his wife never more seclude herself with him: he must issue this warning in the presence of two competent witnesses.
3:
We have explained on numerous occasions that the test of the 'cursing waters' is only to be applied in cases where there is no proof that the woman is guilty of infidelity, but also where there is not sufficient testimony to accuse her of adultery. Where there is some testimony, but it is insufficient to warrant a charge of adultery, the husband must divorce his wife. Our present mishnah is concerned with a situation in which a husband, in the presence of two competent witnesses, formally charged his wife not to consort privately with a certain named man and he subsequently hears a rumour to the effect that she was still consorting with this man.
4:
The very first mishnah of our present tractate presented a 'maĥloket' [difference of opinion] between two sages (both of them students of Rabban Yoĥanan ben-Zakkai and both of them, to a greater or lesser extent teachers of Rabbi Akiva). What was clear in that first mishnah of the tractate was that Rabbi Eli'ezer was much the less strict regarding the acceptability of testimony in these matters and that Rabbi Yeshoshu'a was much the more strict. This is also reflected in our present mishnah: while Rabbi Eli'ezer is of the opinion that a husband is required to divorce his wife if, after having warned her, he hears a mere rumour that she had consorted with the previously identified man. Rabbi Yehoshu'a requires much more than a rumour whose origin know one knows; he requires the woman's behaviour to be the persistent subject of gossip among the local women (who continue their spinning after dark, so engrossed are they in this gossip).
5:
At first glance this would seem to be against the general pattern that we associate with these two sages. We would, perhaps, have expected Rabbi Yehoshu'a to take the lenient view, that mere rumour is sufficient, and we would have expected Rabbi Eli'ezer to take the stricter view. However, deeper consideration shows that both sages are following their habitual trend. What is at the heart of their consideration in this matter is not the quality of the testimony but the quality of the rumour which will require the husband to divorce his wife. Rabbi Eli'ezer is so strict in the matter of the 'purity' of the marriage bond that mere groundless rumour is sufficient to require this union to be disbanded; Rabbi Yehoshu'a is much more lenient: only persistent gossip among the women who know should require the husband to divorce his wife.
6:
Rabbi Eli'ezer was a "shammuti", a follower of the school of Shammai, a school of opinion known to be generally more stringent than the majority school of Hillel, to which Rabbi Yehoshu'a subscribed. Rabbi Eli'ezer Finkelstein z"l may be right in assuming that social and economic factors also distinguish the views of these two schools of halakhic thought. Certainly, the more 'bourgeois' school of Shammai had more stringent demands of their womenfolk while the more 'proletarian' school of Hillel were more generous. When votes were taken in the Sanhedrin to determine halakhah, the school of Hillel was almost invariably in the majority. (One terrible exception was the bloody day some time during the 50's when an artificial Shammuti majority was obtained at sword point in order to pass 18 pieces of anti-Roman legislation. In the 60's the Shammutis were on the side of the nationalists whereas the Hillelites supported the peace-camp.)
7:
In his commentary on our present mishnah Rambam states that, as usual, in this matter too halakhah follows the lenient view of Bet Hillel (Rabbi Eli'ezer) and not the stricter view of Bet Shammai (Rabbi Eli'ezer).