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Maseches Demai opens up by addressing the "leniencies of Demai." As the Bartenura there explains, these lenient items are those which are essentially garbage - foods that people typically wouldn't eat and therefore throw away, but are sometimes eaten anyway. Since there is a chazakah that it's from hefker, we can be lenient. Furthermore, one can be lenient from a sefeik sefeika: it's a safek whether it was hefker or not, and it's a safek whether it was tevel or chulin.

Why does one need both a chazakah and a sefeik sefeikah? Are one of them not enough alone?

Granted that I could see the Bartenura being read as "because there is this chazakah, there is a sefeik sefeikah," the fact still remains that there is a chazakah, which should be enough to make the Demai patur.

Demai 1:1

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This mishnah is according to the pirush mishnajot of the Rambam: As i understand this mishnah, this is not a normal chazaka, but a statement that most of these fruits or vegetables come from hefker.

Because of this fact we have two sfekot.

For the other sorts of fruits and vegetables we wouldn't even have a safek that it came from hefker because we bought it from a person.

The rambam in hilchot maaser chapter 12 halacha 1 says that even the am haaretz did say that he did not measer these sort types of vegetables it is patur from maasrot because cheskatan from hefker. This implies that the Rambam changed his mind there. Look at the Radbaz there and at the rabi Akiva eger on the mishnah.

  • Then why does he call it a chazakah? He should call it something that many people do that makes it a valid safek. – DonielF Mar 16 '17 at 17:23
  • Because we are speaking about the fruit and not the people. – David Michael Gang Mar 16 '17 at 18:54
  • But if it's a chazakah, then that's all he needs to say. He doesn't need to get into sefeik sefeikah. According to the way you're reading the Bartenura, he should say that they're things people typically through out, not things we assume were thrown out. – DonielF Mar 16 '17 at 18:57
  • one safek appearently is not enough because we have also a rov that most ame haaretz are measrim and i don't rely on this. The only question is why he does write sfek sfeka and not two rovs, but one rov is not enough here – David Michael Gang Mar 16 '17 at 18:59
  • Of course one safek isn't enough. You need two sefeikos to be meikel. That's an interesting point about rov, but it doesn't address the chazakah question whatsoever. He can still give a sefeik sefeikah without calling it a chazakah, and if he wants to call it a chazakah, the sefeik sefeikah is completely unnecessary. – DonielF Mar 16 '17 at 19:19
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I. The concept of Demai. Mishna Maaser Sheni 5, 15:

Yochanan the High Priest and in his day, no one had to ask about Demai

The Bartenura in his comment wrote (this is a summary of the comment of Rambam):

Yochanan High Priest refreesh to his generation the knowledge that Teruma Maaser is punishable by death as Teruma Gedola. {there was people who take Teruma Gedola only from the grain, because they were aware of the severity of its consumption}. He introduced a procedure to avoid this doubt. Scrupulous people who buy fruits from Am Haarets need to take Terumat Maaser.

II. The degree of doubt

But this doubt is not truly a doubt according to Tora criterion, because a Majority of Ame Haarets still take maaser Rishon, which contains the Terumat Maaser (Bartenura Berachot 7, 1). Thus, from the Tora Point of view, fruit from Am Haarets are allowed because of the Rule of Majority. But Rabbis decided to be stringent and made a special procedure to be sure that Terumat Maaser was taken.

Since this is not a "true doubt", there are several circumstantial leniencies (see chapter 3, Mishna 1).

The first Mishna of the Tractate Demai taught us one of those leniencies. It is known that fruit coming from an abandoned field are exempt from trumot and maasrot. If the majority of one specie of fruits come from abandoned fields, following the Rule of Majority, one can consume, without Teruma or Maaser. Rabbi Yochanan (Yerushalmi Demai 1, 1) says that the majority of the fruits listed in the Mishna come from fruits that belongs to no one.

As Yochanan High Priest is stringent with Demai despite the majority. It is logical to expect that he is stringent to take Teruma and Maaser for fruit that generally come from abandoned places.

III. Conjunction of two majorities

But here the conjunction of both majorities generates a leniency. One majority alone is not good derabanan, but two are: If it is hefker, it is exempt, if not hefker, majority says that maaser was taken. So we need two sfekot, Sfek sfeka is not relevant here because according to the Din Derabanan there is no safek, Mideorayta there is no din safek but din Chezkat Heyter.

In the first edition of this answer I tried to explain the Bartenura and Rambam according to the explanation of the Bavli for the opinion of Rabbi Yochanan, to explain a couple of Kashiot, but I skipped it.

  • You still didn't address why both are needed. – DonielF Mar 31 '17 at 3:12
  • @DonielF yes I do! thr second safek is needed to stop the chumra of demai – kouty Mar 31 '17 at 8:53
  • Why is that chazakah not enough? – DonielF Mar 31 '17 at 14:24
  • as rov is not enough by stringency, chazaka similarly is not enough alone. e.g. (safek hefker safek tevel) + (hazkat hefker) is not enough. sh safek dmai + chezkat hefker is enough. @DonielF – kouty Mar 31 '17 at 15:18
  • But once you have the sefeik sefeikah the chazakah isn't necessary. So, again, why do we need the chazakah to begin with? – DonielF Mar 31 '17 at 15:30

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