1) "ANAN SAHADEI" ABOUT WHAT A PERSON HAS IN HIS MIND
QUESTION: The Gemara searches for a source for Rava's ruling that "Devarim sheb'Lev Einam Devarim" -- intentions in a person's heart (that he has not expressed verbally) are not binding.
The Gemara cites a Mishnah which teaches that when a person makes a vow to bring a Korban and he fails to fulfill his vow, Beis Din "forces him until he says, 'I want to bring it!'" Although in his heart he does not want to bring the Korban, his verbal statement overrides any unspoken intent he might have. This Mishnah proves that "Devarim sheb'Lev Einam Devarim." The Gemara refutes the proof and says that in the case of the Mishnah there, it is assumed that even in his heart he wants to bring the Korban, because everyone wants atonement (Kaparah) and the Korban will achieve atonement for him.
TOSFOS (49b, DH Devarim) cites a number of proofs from various sources that in cases of "Anan Sahadei" no verbal expression of the person's intent is necessary, and the intent in his heart is binding. ("Anan Sahadei" literally means "we are witnesses" and refers to a situation in which his intention is as clear to us as if he had explicitly stated it.) Accordingly, when the Gemara here asks that "in his heart he does not want [to bring the Korban]," it means that it is evident to all that he is bringing the Korban against his will. Even if the Halachah is "Devarim sheb'Lev Einam Devarim," his intentions in the case are evident to all ("Anan Sahadei") and thus the Korban should not be valid. Why does "Anan Sahadei" not apply in this case?
ANSWER: The TOSFOS HA'ROSH explains how the principle of "Anan Sahadei" functions. When the person's intentions are so evident, he is considered as though he actually verbalized them. This reasoning does not apply in the case of the Korban, however. Since the person explicitly stated that he will bring the Korban willingly, his verbal statement stands in direct conflict with his assumed intentions, and thus his intentions cannot be considered to have been spoken explicitly. This situation poses a dilemma of an "Anan Sahadei" (his intentions were evident to all) which conflicts with what he said explicitly. In such a situation, the "Anan Sahadei" does not have the power to override an explicit, verbal statement.
2) "FORCED" TO DO A MITZVAH
The Beraisa states that Beis Din may force a man to consent to give a Get to his wife or a Shtar Shichrur to his Eved. The Gemara attempts to prove from the Beraisa that "Devarim sheb'Lev" are not "Devarim," and that is why the man's intention in his heart is meaningless. The Gemara refutes this proof by saying that this case is different because it is a "Mitzvah to listen to the words of the Chachamim."
The RAMBAM presents a unique explanation for this Gemara (Hilchos Gerushin 2:20). His explanation is based on a profound understanding of the nature of the Jew.
The Gemara initially views the man as being coerced by Beis Din to do an act which he does not want to do. When the Gemara explains, "It is a Mitzvah to listen to the words of the Chachamim," it does not mean merely that a person changes his mind as a result of judiciary coercion (which seems to be the explanation of RASHI). Rather, the Gemara alters its understanding of the forces which cause the man to act against his will.
The Rambam maintains that every Jew has an essential, natural desire to fulfill the will of Hash-m. If a Jew does not acting properly, it is because he is being coerced by external forces (namely, the Yetzer ha'Ra) to act contrary to his natural tendency. When Beis Din involves itself in the Jew's decision-making process to ensure that he fulfills Mitzvos in the proper manner, Beis Din does not force him to act against his will. On the contrary, Beis Din frees him from the influence of the Yetzer ha'Ra which impels him to act against his own, essential desire to fulfill Hash-m's will. (See Insights to Eruvin 19:1 and Chagigah 27:3.)

50b----------------------------------------50b

3) A DOUBT ABOUT THE PURPOSE OF A GIFT
QUESTION: The Gemara discusses a case in which a man sent gifts to a woman and there is a doubt whether he intended to be Mekadesh her. Rav Papa rules that in a place where the common practice is to be Mekadesh a woman and then send gifts of "Sivlonos" to her, we must be concerned that the man sent these gifts to the woman with intention to be Mekadesh her. The Gemara asks that this is obvious, and it concludes that Rav Papa's ruling is necessary in a place where there is a Rov (majority) of men who are Mekadesh first and then send Sivlonos, and a Mi'ut (minority) of men who send Sivlonos first. Rav Papa teaches that the Mi'ut is not taken into consideration.
Throughout all of Shas, the principle of "Rov" is decisive in resolving doubts, both when it resolves the doubt stringently and when it resolves the doubt leniently. Here, the Rov dictates that the Sivlonos were sent for the sake of Kidushin, while the Mi'ut states that they were sent merely as a gift. Why is Rav Papa's ruling necessary to teach that the Mi'ut is not taken into consideration at all (particularly in this case, in which the Mi'ut is a leniency in that it would permit the woman to marry someone else without first receiving a Get from the first man)?
ANSWERS:
(a) The TOSFOS HA'ROSH explains that since the man made no mention of Kidushin when he sent the Sivlonos, he presumably did not intend to give the Sivlonos for the sake of Kidushin, but merely for a gift. One might have thought that since there is both a Mi'ut and a logical reason to assume that the Sivlonos were merely a gift, the Rov is disregarded in this case.
(b) The RITVA has a different Girsa in the text of the Gemara. According to his Girsa, the Gemara refers to a place where the majority of men send Sivlonos first and then perform Kidushin, and a minority of men perform Kidushin first and then send Sivlonos. One might have thought that the Mi'ut is not taken into consideration because of the Rov. Rav Papa teaches that the Mi'ut is taken into consideration; even though only a Mi'ut of men perform Kidushin first and then send Sivlonos, there is still a concern that Kidushin took place.
The Ritva asks why, though, does Rav Papa rule that the Mi'ut is taken into consideration, when normally there is never a concern for a Mi'ut (even l'Chumra)?
The Ritva answers by differentiating between a "Rov b'Metzi'us" and a "Rov b'Minhag." A "Rov b'Metzi'us" (a majority based on reality) states that a certain event likely occurred because that is what usually, naturally occurs (such as the Rov that most animals are not Tereifos). A "Rov b'Minhag" (a majority based on practice) states that a certain event likely occurred because that is what most people do or how most people act.
When the doubt about what occurred involves a "Rov b'Minhag," since the event in question was subject to a person's conduct there is a concern for the Mi'ut (and Kidushin may have taken place), because a person might choose not to act like most other people and instead do whatever he wishes. (A person's conduct and how he chooses to act is not subject to what usually, naturally occurs.)