1) KIDUSHIN WITH STOLEN MONEY
QUESTION: The Beraisa states that a man may be Mekadesh a woman with an item he stole, or with a coin he snatched from her hand.
Why may a man be Mekadesh a woman with an item he stole? The Kidushin is valid only when a man gives a woman an item that belongs to him.
(The Beraisa is not referring to a case in which the original owner of the item gave up hope ("Ye'ush") of retrieving his item, in which case the thief can acquire the item by making some change ("Shinuy") in it. In such a case it is obvious that the Kidushin is valid (and the Beraisa would be teaching nothing new). The Beraisa must be referring even to a case in which the owner did not give up hope. This is also apparent from the incident the Gemara cites in which a man snatched a "Varshecha" from a woman.)
ANSWER: The RASHBA, RITVA, and ROSH explain that if the woman expresses interest in having the man betroth her with this item (such as in the Beraisa's case of "Shadich"), presumably she transferred ownership of the item to the man before he gave it back to her. Consequently, the man is Mekadesh her with an object that belongs to him.
These Rishonim point out that this seems to be the intention of the Rif, who writes that the Beraisa refers specifically to an object which the man stole from the woman and not from anyone else. Since he stole it from her, she is able to pardon him and give him ownership of it. If he stole the item from someone else, the Kidushin will not be valid.
2) BUYING A FIELD WITH LESS THAN A "PERUTAH"
QUESTION: The Gemara cites Rebbi Asi who teaches that just as a woman cannot become Mekudeshes with less than a Perutah, a field cannot be purchased with less than a Perutah.
Why would one have thought that a field may be purchased with less than a Perutah? Since a woman cannot become Mekudeshes with less than a Perutah, and the only source for Kinyan Kesef of a woman is the Kinyan Kesef of a field, it is obvious that a field cannot be purchased with less than a Perutah (as the Gemara on 4b states).
ANSWERS:
(a) TOSFOS answers that perhaps Rebbi Asi derives that Kinyan Kesef works for Kidushin from the verse, "v'Yatz'ah Chinam" (Shemos 21:11), and not from the Kinyan Kesef of a field.
(b) TOSFOS suggests further that the Gemara occasionally phrases its teaching as the inverse of the actual correlation (see RASHASH). That is, Rebbi Asi actually means to say that just as a field cannot be purchased with less than a Perutah, the Kidushin of a woman cannot be done with less than a Perutah. This is the logical correlation, since the Kinyan Kesef of a woman is derived from the Kinyan Kesef of a field.
(c) The TOSFOS HA'ROSH answers that according to the Girsa of Rashi (beginning of 3b), Kidushin depends not only on the laws derived from the purchase of a field, but also on the self-respect of a woman. A woman cannot become Mekudeshes with less than a Perutah because she considers it disrespectful and she does not fully consent to the Kidushin (see Insights there). Hence, even though Kidushin cannot be done with less than a Perutah, one might have thought that a field can be purchased with less than a Perutah. Therefore, Rebbi Asi teaches that a field cannot be purchased with less than a Perutah.
Tosfos does not accept this answer, presumably because he follows his opinion expressed earlier (3a), where he rejects Rashi's Girsa and writes that the amount of the Kesef used for Kidushin does not depend on the woman's self-respect.
In a similar vein, HE'OROS B'MASECHES KIDUSHIN writes that the RAMBAM in a number of places seems to differentiate between the Kesef used to purchase a field and the Kesef used to marry a woman. For example, a man may be Mekadesh a woman by lending her money (as long as he states his intention at the time he gives her the loan; see Insights to 6:1), but he cannot purchase a field in such a way. Also, a man cannot be Mekadesh a woman by giving her a "Matanah Al Menas l'Hachzir," a gift given on condition that it be returned to the giver, but he can acquire a field in such a way.
The reason for these differences is that the Kidushin of a woman takes effect through the Hana'ah (pleasure) the woman receives and not through the Kesef itself. (Since a woman has no quantifiable monetary value, Kesef itself cannot effect a transfer of domain as it can for a field, which has a quantifiable monetary value.) The Hana'ah she receives motivates her to allow herself to become Mekudeshes to the man (see AVNEI MILU'IM 29:2). Accordingly, one might have thought that a woman does not become Mekudeshes with less than a Perutah because that amount is not considered Hana'ah, while a field can be purchased with less than a Perutah because that amount is still considered Kesef, even though it does not constitute Hana'ah. Rebbi Asi teaches that not only is less than a Perutah not considered Hana'ah, it also is not considered money and cannot be used to buy a field.
(d) The RASHASH explains that Rebbi Asi means to say merely that although the Mishnah does not discuss how much money is needed for the purchase of a field (as it discusses how much money is needed for the Kidushin of a woman), the minimum purchase price of a field nevertheless is a Perutah.
Perhaps the Rishonim do not accept this answer because if this indeed is Rebbi Asi's intention, Rebbi Asi should clearly state the connection between these two Halachos. He should say, "The reason why a woman must be Mekudeshes with a Perutah (as the Mishnah says) is because a field must be purchased with at least a Perutah (and Kidushin performed with Kesef is derived from the way a field is purchased)."