1) A MAN WHO DIVORCES HIS WIFE BASED ON UNFOUNDED RUMORS
OPINIONS: The Mishnah (45b) states that when a man divorces his wife because of her "bad name" (i.e. because of rumors that she was unfaithful, or because of rumors that she makes oaths, and he is not interested in living with a woman who makes oaths), he is not permitted to remarry her. RASHI (DH Lo Yachzir) explains that even if the rumors are later found to be untrue, or that her oaths were annulled by a Chacham, he still may not take her back.
The Gemara quotes Rav Yosef bar Minyomi who says that the man is prohibited from remarrying his wife only if he had told her at the time of the divorce that he was divorcing her because of her "bad name" or because of the oaths. The Gemara explains that Rav Yosef understands that the ruling of the Mishnah is based on the reasoning of "Kilkula" ("corruption"). What exactly is the reasoning of "Kilkula"?
(a) RASHI (DH Taima) explains that if Beis Din does not make it clear to the man that his divorce is final, he might spread rumors that the divorce was not legitimate in the first place: he will reveal that he found out that the rumors (on which the divorced was based) were false, and he then will claim that had he known that the rumors were false or that her oaths were able to be annulled, he never would have divorced her. He would support his claim by reminding Beis Din that he had clearly stated at the time of the divorce that the rumors about her disloyalty, or about her oaths, were the basis for the divorce, and now that those rumors have been proven to be unfounded the divorce should be annulled. (Rav Yosef clearly understands that had the man not stated the reason at the time of divorce, he would have no claim at all.)
The husband's claim that his divorce was based on a mistaken assumption means that the Get he gave was meaningless because it was given only on condition that his wife was unfaithful. Consequently, if she married another man after she received the Get from her first husband, she would be guilty of transgressing the Isur of "Eshes Ish," a married woman who lives in sin with another man, and her children from the second man would have the status of Mamzerim. Therefore, Beis Din warns the husband that if he divorces his wife for this reason he will never be able to take her back. He will not be believed to say that he divorced her only because of the rumors; had he genuinely wanted to remain married to her, he would have investigated whether the rumors were true before he divorced her. The fact that he divorced her without investigating the rumors shows that he wanted the divorce to be unconditionally final.
The Rishonim ask two questions on Rashi's explanation:
1. TOSFOS (DH Iy) argues that even if the husband would claim that he divorced his wife only because of the unfounded rumors, Rav Yosef would not rule that the Get is nullified and the children from the second marriage are Mamzerim. This is because the husband did not say at the time of the divorce that he was divorcing her "on condition" ("Al Menas") that the rumors were true. Although a mere "Giluy Da'as" (indication of one's intent without a verbal declaration thereof) often suffices to make a person's intention a key component of a transaction (see Kesuvos 79a) even without an explicit statement of "Al Menas," nevertheless in this case it is clear that a "Giluy Da'as" does not suffice. The Gemara later (46b) discusses a similar case and explains that according to Rebbi Meir a "Tenai Kaful" -- "an explicit double condition" -- is required. Although the Gemara here is not expressing the view of Rebbi Meir, it is clear that even those who disagree with Rebbi Meir and do not require a "Tenai Kaful" maintain that at least a "single" condition must be stated and a "Giluy Da'as" does not suffice. In the case of the divorce, no condition was stated, and a mere "Giluy Da'as" does not suffice. (See the MAHARSHA's explanation of the words of Tosfos.)
The RITVA (45b) answers that Rebbi Meir requires a "Tenai Kaful" (46b) only because he does not agree with the principle of "Michlal Hen Atah Shome'a Lav" -- "from the [explicitly-stated] positive you hear the negative." This means that when we know the reason why someone does a certain act, we may infer that he would not do that act without that reason. Since Rebbi Meir does not consider a person's intent unless he makes a formal statement to express that intent, it follows that Rebbi Meir also maintains that a person always must make a "Tenai Kaful," even in a case in which the person's intent is clear. (However, the Ritva points out that Rebbi Meir would not require other laws of conditions to be fulfilled when there is absolute certainty about the person's intent.) This is why the Gemara later says that according to Rebbi Meir one needs a "Tenai Kaful." However, according to those who argue with Rebbi Meir, even a single condition is not needed in this case because those opinions agree with the principle of "Michlal Hen Atah Shome'a Lav." This explains why Rashi writes that once we know the husband's reason for divorce, we also understand that if the reason would not apply he would never have divorced his wife.
2. The RASHBA questions Rashi's reasoning for why the husband is told that he may not remarry the woman. Rashi explains that had he truly loved her and did not want the divorce to be final, he would have investigated the truthfulness of the rumors before he divorced her. Although the Rashba concedes that this explanation is also stated by the Yerushalmi, he questions its logic. For how long is the husband expected to research the rumors that his wife was unfaithful? It is possible that he divorced her now because he did not want to live with a woman rumored to be unfaithful, and he was unable to find evidence that the rumors were false. He divorced her after he investigated the matter to the best of his ability.
(b) TOSFOS writes that the Gemara's concern about "Kilkula" is that the husband will spread rumors that the Get he gave was invalid in order to persuade the second husband to give her a Get.
Tosfos addresses the obvious question on this explanation. What does the first husband stand to gain from such a tactic? The Torah clearly states that when a man divorces his wife who then marries another man who divorces her, her first husband is not allowed to remarry her. What, then, does the first husband stand to gain from spreading such rumors? Tosfos explains that the first husband will think that the second marriage was not binding but rather was mere promiscuity (as his divorce was not a real divorce), and he therefore will have no hesitation about remarrying his first wife. (D. Bloom)

46b----------------------------------------46b

2) THE DIFFERENCE BETWEEN ONE WHO DIVORCES HIS WIFE BASED ON RUMORS AND ONE WHO DIVORCES HIS WIFE BECAUSE SHE IS FOUND TO BE AN "AYLONIS"
QUESTIONS: In the Mishnah, Rebbi Yehudah states that when a man divorces his wife because she is found to be an Aylonis (a woman incapable of bearing children; see Yevamos 80b), he is never allowed to remarry her. RASHI (DH Mishum) writes that when he married her he did not know that she was an Aylonis.
Why may he not remarry her? Rashi (DH Rebbi Yehudah) gives a lengthy explanation for this prohibition. His premise is that there is a concern that after the man divorces his wife, she will marry another man and bear children with him. The first husband might then claim that had he known that she was capable of bearing children, he never would have divorced her. His claim would render the Get invalid retroactively, and the children from the second marriage would be Mamzerim. In order to insure that the husband will never make such a claim, Beis Din informs him before the divorce that one who divorces his wife because she is an Aylonis is never allowed to take her back.
The Mishnah earlier (45b) discusses a similar case in which a man divorces his wife only because of rumors about her infidelity, which later are found to be untrue. The Tana Kama rules that the husband is informed at the time of the divorce that he may not remarry this woman.
Rashi there, however, explains the husband's claim in that case differently from the way he explains it in the case of the Gemara here.
1. Rashi earlier (46a, DH Ta'ama) writes merely that the husband said at the time of the divorce that he was divorcing his wife because of her bad name. Rashi there does not write that the husband said at the time of the divorce that if the rumors are found to be untrue that he does not want the divorce to take effect. This is contrast to Rashi's explanation in the case of the Aylonis, where Rashi writes that the husband mentioned both the positive and negative sides of the conditional divorce. He stated, "I divorce you with the intent that if you should develop Simanim (which show that you are not an Aylonis), I will take you back," and he stated, "If I would have known that you would not return, I would not have divorced you."
2. Another difference is that Rashi earlier (46a, DH Ta'ama) writes that since the man knew that if he divorced his wife he would never be able to remarry her, the fact that he went ahead with the divorce shows that his real reason for divorcing her was simply that he did not like her. Rashi does not mention this reasoning in the case of the Aylonis.
What is the reason for these differences in Rashi's explanation of the two Sugyos?
ANSWERS:
(a) The AVNEI MILU'IM (10:1) quotes the MISHNEH L'MELECH (Hilchos Ishus 6:1) who suggests a novel proposal to the application of the requirement of "Tenai Kaful." Perhaps a "Tenai Kaful" is necessary only when the stated condition is to be fulfilled at a later date, similar to the prototypical condition which Moshe Rabeinu stipulated with the tribes of Gad and Reuven. In contrast, when the condition involves merely a clarification of an event which has already transpired, a "Tenai Kaful" is not necessary. (The Avnei Milu'im asserts that this actually is the opinion of the RAN.)
What is the difference between the two cases? The Mishneh l'Melech explains that when the condition involves a future event, the transaction is considered as though it has taken effect but can be overturned later by the failure to fulfill the condition. Overturning a transaction requires a strong condition, a proper "Tenai Kaful." In contrast, when the condition is a clarification of the outcome of a past event, the condition determines whether or not the transaction actually takes effect in the first place. Accordingly, even an ordinary condition (without a "Tenai Kaful") suffices to enable the transaction to take effect (or to prevent it from taking effect).
The Avnei Milu'im applies this distinction to the Gemara here in order to explain why Rashi writes only with regard to the case of the Aylonis that the man stated both sides of the condition. In the case of the Aylonis, the man not only states that he is divorcing his wife because she has been found to be an Aylonis, but he also states that the divorce is on condition that his wife will not be cured from her condition of Aylonis after the divorce. Since the husband makes a condition based on a future event, a "Tenai Kaful" is necessary to cause the Get to be annulled retroactively. If the husband would not make a "Tenai Kaful," his condition would not be valid. In contrast, in the case of the woman rumored to be unfaithful, the man attempts to make the Get contingent on what has already happened (his wife's unfaithfulness). In such a case, even an ordinary condition suffices to prevent the Get from taking effect in the first place.
This approach answers the second question as well. Since the condition in the case of a Get given because of rumors about her unfaithfulness is based on events that have already happened, it makes sense to say that if he really liked her he would not have divorced her based solely on rumors. This logical argument against the intent of his condition, combined with the fact that he did not state a "Tenai Kaful," renders his condition ineffective. In the case of the Aylonis, however, the man made a strong condition, a "Tenai Kaful." The logic that he would not have divorced his wife merely because she was an Aylonis is not enough to ruin an explicit "Tenai Kaful." This is why he must be told at the time of the divorce that his condition is not valid.
(b) Another answer may be suggested for the second question. In the case of the divorce given because of rumors, it is logical to assume that the man divorced his wife because he simply did not like her because, otherwise, he would have waited to clarify whether or not the rumors were true. However, in the case of the Aylonis, the man intends to reserve the right to cancel the divorce retroactively in the event that she is later healed of her condition. Beis Din cannot tell him later that "had you truly loved your wife you would have endeavored to ascertain whether or not she was an Aylonis," because she was an Aylonis as far as anyone could tell at the time of divorce. The husband's stipulation at the time of the divorce was that although she clearly seems to be an Aylonis now, he does not want the divorce to be effective if she ever becomes cured from that condition. This condition, if it would be valid, obviously would stand as a tremendous obstacle to her ability to marry anyone else, because if she would ever become cured she would find herself married to her first husband while living in sin with the second man. This is why Beis Din tells the man, in response to his stipulation, that if he follows through with the divorce his condition will not take effect and she will be divorced unconditionally. (D. Bloom, Y. Montrose)