We now begin Tractate Peah, chapter 6, mishnah 1. The mishnah opens with a dispute between Beis Shammai and Beis Hillel that does not bear directly on the tithe for the poor, and it is brought here because further disputes between Beis Shammai and Beis Hillel regarding the laws of forgotten sheaves follow. This dispute too deals with giving to the poor, and its subject is the law of hefker, declaring something ownerless.
The dispute between Beis Shammai and Beis Hillel concerning declaring property ownerless for the poor:
"Beis Shammai omrim: hefker la'aniyim hefker" - a person wishes to renounce ownership of his property and render it ownerless, but in a limited way: only the poor may acquire it, and not the wealthy. In the opinion of Beis Shammai this is a full-fledged declaration of ownerlessness.
"U'Beis Hillel omrim: eino hefker ad she'yufkar af la'ashirim ki'shemitah" - it is not considered ownerless until it is made available to everyone, so that the wealthy too may acquire it. This follows the model of the Shemitah year, in which the produce is ownerless to all, the wealthy included.
The practical difference between the two views concerns tithes: if the declaration takes effect, the produce is exempt from tithes, since ownerless produce is exempt from tithing.
The sources of the dispute:
The view of Beis Shammai - is derived from the verse "for the poor and for the stranger you shall leave them." Seemingly it would have been enough to say that they should belong to the poor and the stranger, so why does the verse add "you shall leave them"? Rather, the verse comes to teach about an additional form of leaving, namely hefker, which resembles those gifts that go to the poor and the stranger through the tithe for the poor, peah and gleanings. Just as these are given to the poor alone, so too this "leaving," which is hefker, may be for the poor alone.
The view of Beis Hillel - is derived from the verse stated regarding Shemitah: "and in the seventh year you shall release it and abandon it." The word "and abandon it" teaches about an additional type of abandonment, whose law follows that of Shemitah. And just as Shemitah produce is ownerless to every person, so too this abandonment, which is hefker, must extend to the wealthy as well.
The law of a large sheaf regarding forgotten sheaves:
From here the mishnah moves to a special law in the area of forgotten sheaves: "Kol omrei ha'sadeh shel kav kav, ve'echad shel arba'as kabin, u'shecheicho" - all the sheaves in the field are the size of a kav (one sixth of a se'ah), while one of them is four times the size of the others and holds four kabin, and that is the one he forgot.
"Beis Shammai omrim: eino shichechah" - the reason will be explained below in mishnah 5, that in the opinion of Beis Shammai, if a person forgot four sheaves in the field it is not considered forgotten, since something that substantial he is bound to remember. The same applies to one large sheaf whose size equals four sheaves: we view it as though it were divided, and just as four sheaves are not considered forgotten, so too a single sheaf of that measure.
"U'Beis Hillel omrim: shichechah" - Beis Hillel do not view the sheaf as divided. Even though four separate sheaves in the field would certainly not be considered forgotten, here we are dealing with only one sheaf, and although its size equals four sheaves we do not view it as separate, and therefore it is forgotten.
The Rambam, however, writes that in a case where the sheaf is larger than four kabin, even Beis Hillel agree that its size prevents it from being considered forgotten.
In summary: in this mishnah we learned two disputes between Beis Shammai and Beis Hillel. The first concerns property declared ownerless for the poor alone: according to Beis Shammai this is a valid declaration, while according to Beis Hillel it is not until it is made ownerless to the wealthy as well, as in Shemitah, and each view rests on its own verse. The second concerns a sheaf of four kabin forgotten among sheaves of one kav: according to Beis Shammai it is not forgotten, while according to Beis Hillel it is, and according to the Rambam, when it is larger than four kabin even Beis Hillel agree that it is not forgotten.