Commentary for Kiddushin 130:15

The Talmud now assumes that in this mishnah there were witnesses, but only witnesses that they were secluded, not that they had intercourse, which would constitute betrothal. Bet Shammai says that this is not sufficient to create an assumption of sex and betrothal and therefore she does not require a divorce. Bet Hillel says it is sufficient.
However, they both agree that if the couple had not previously had intercourse because they were never married, then she does not require a get. In such a circumstance, we cannot assume that they had sex at the inn.

Without two witnesses, there is no betrothal.

Whoever this great court is, they do not believe that kiddushin performed in front of one witness is valid.

A twisted scenario indeed. Both men have to give her a get, which means we must have some degree of certainty that they are married to her. But if either has two witnesses, then how could she claim, “These are my slaves.” Thus it must be that there is one witness. This is sufficient to create the suspicion of kiddushin. And thus this is a difficulty against those who say that with one witness, we disregard her kiddushin.

A twisted scenario indeed. Both men have to give her a get, which means we must have some degree of certainty that they are married to her. But if either has two witnesses, then how could she claim, “These are my slaves.” Thus it must be that there is one witness. This is sufficient to create the suspicion of kiddushin. And thus this is a difficulty against those who say that with one witness, we disregard her kiddushin.

One witness might have, at certain times, some level of believability. But not when this witness is contradicted by the woman herself.
Rather, the men do not give her a divorce in order to free her to marry someone else. She is free to marry someone else even without a divorce from either of them. They give her a divorce in order for her to collect the ketubah, which according to R. Meir, can be collected from movable property.

One witness might have, at certain times, some level of believability. But not when this witness is contradicted by the woman herself.
Rather, the men do not give her a divorce in order to free her to marry someone else. She is free to marry someone else even without a divorce from either of them. They give her a divorce in order for her to collect the ketubah, which according to R. Meir, can be collected from movable property.

R. Kahana and R. Papa argue over whether we are concerned for kiddushin done in front of one witness in a case where the man and woman agree that there was kiddushin. R. Kahana says that such kiddushin are not valid. But R. Ashi argues with him. Perhaps R. Kahana is thinking that just as the word “davar” stated in reference to monetary matters (Deuteronomy 19:15) means that we require two witnesses, so too the word stated in reference to sexual matters (Deuteronomy 24:1) implies that we need two witnesses. The problem with this analogy is that in monetary matters, a person who admits he is liable is liable. But R. Kahana is arguing that even if the couple says they were betrothed, without two witnesses, the betrothal is invalid.
R. Kahana responds by noting the difference between the two situations. In the case of monetary matters, if a person admits he owes money, he is not causing others to be obligated. But here, the couple’s admission impacts each other’s relatives, who will not be able to marry them. Therefore, it is invalid.

R. Kahana and R. Papa argue over whether we are concerned for kiddushin done in front of one witness in a case where the man and woman agree that there was kiddushin. R. Kahana says that such kiddushin are not valid. But R. Ashi argues with him. Perhaps R. Kahana is thinking that just as the word “davar” stated in reference to monetary matters (Deuteronomy 19:15) means that we require two witnesses, so too the word stated in reference to sexual matters (Deuteronomy 24:1) implies that we need two witnesses. The problem with this analogy is that in monetary matters, a person who admits he is liable is liable. But R. Kahana is arguing that even if the couple says they were betrothed, without two witnesses, the betrothal is invalid.
R. Kahana responds by noting the difference between the two situations. In the case of monetary matters, if a person admits he owes money, he is not causing others to be obligated. But here, the couple’s admission impacts each other’s relatives, who will not be able to marry them. Therefore, it is invalid.

Mar Zutra and R. Ada want their division of property to be finalized without the need for witnesses. So they ask R. Ashi whether witnesses are there just to prevent people from changing their mind and therefore, if they waive the need for witnesses, the contract can exist without witnesses. He agrees that it can.

Mar Zutra and R. Ada want their division of property to be finalized without the need for witnesses. So they ask R. Ashi whether witnesses are there just to prevent people from changing their mind and therefore, if they waive the need for witnesses, the contract can exist without witnesses. He agrees that it can.

One witness is believed to make the other person liable for bringing a sacrifice for accidentally eating forbidden fat, as long as the other person does not disagree. But if the other person protests, one witness would not be sufficient.

This is the same tradition but about purity instead of being about eating forbidden food.

Again, this is the same law. One witness is sufficient to lend a certain amount of credibility to the idea that bestiality had been committed with the ox. The result of this is that the ox will not be able to be sacrificed. Had there been two witnesses, the ox would be stoned.