Demai, Chapter Four, Mishnah Three
As we explained in the introduction to Demai, in the third and sixth years of a sabbatical cycle, a person separates poor mans tithe from his produce and gives it to the poor. In our mishnah, there is a debate over whether one has to separate poor mans tithe from demai.
1) Rabbi Eliezer says: a man need not designate the poor mans tithe of demai.
2) But the sages say: he must designate it, but he need not separate.
Section one: According to Rabbi Eliezer, the am haaretz does separate poor mans tithe from his produce, and therefore, one need not do so again.
Section two: The sages disagree with Rabbi Eliezer and hold that it is unclear whether an am haaretz separates poor mans tithe from his produce, just as it is unclear whether he separates the other tithes. Therefore, the person who wants to eat demai must first separate the poor mans tithe. However, he does not have to actually give it to the poor person because the poor person cannot prove that the am haaretz did not separate the poor mans tithe. Demai is only doubtfully untithed produce. Since the poor cannot prove that this produce belongs to them, the person who separates the poor mans tithe from the demai can keep it for himself.