The general rule, of course, is "safeik d'rabanan l'kula" -- In a situation where one may or not be running afoul of a rabbinic prohibition, the halacha is that one is not running afoul of the prohibition. I tried to state that carefully, because "safeik d'rabanan l'kula" does not mean that you can assume there is no problem. It is the situation that has the s'feikos/doubts, not the halacha. That can mean that sometimes s'feik safeik d'rabanan l'kula can lead to a chumra/stringency. For example, we add "al ha'nisim"/for the miracles to bentching and shmone esrei during Chanuka and Purim. If one is in doubt if he said them, then he is not obligated to repeat with the insertion. Once he is not obligated, then he now not allowed to repeat, because the (now) unnecessary insertion becomes a forbidden interruption.
The interesting thing about "safeik d'rabanan l'kula" is all of the exceptions. Consider the siman 325 -- concerning a non-Jew who does a malacha on Shabbos for a Jew's benefit. The basic rule is that a Jew is not allowed to benefit from a malacha that was done for him on Shabbos by a non-Jew; even though the non-Jew was asking on his own volition. It is rabbinic enactment to forestall a Jew from asking a non-Jew to do something for him; since he can't benefit, he won't ask. Suppose you aren't sure if he did a malacha for you. For example: A non-Jew brings fresh fruit to you on Shabbos. If the fruit was brought from outside the t'chum/shabbos boundaries, then that fruit cannot be eaten by any Jew till after Shabbos sometime, and it is muktza for the one (and his family) for whom it was brought. So far, so good.
The interesting thing about "safeik d'rabanan l'kula" is all of the exceptions. Consider the siman 325 -- concerning a non-Jew who does a malacha on Shabbos for a Jew's benefit. The basic rule is that a Jew is not allowed to benefit from a malacha that was done for him on Shabbos by a non-Jew; even though the non-Jew was asking on his own volition. It is rabbinic enactment to forestall a Jew from asking a non-Jew to do something for him; since he can't benefit, he won't ask. Suppose you aren't sure if he did a malacha for you. For example: A non-Jew brings fresh fruit to you on Shabbos. If the fruit was brought from outside the t'chum/shabbos boundaries, then that fruit cannot be eaten by any Jew till after Shabbos sometime, and it is muktza for the one (and his family) for whom it was brought. So far, so good.
What if he only might have brought it from outside the t'chum? You would think "safeik d'rabanan l'kula", so we should be able to eat it, right? Nope. There is another rule that kicks in: "davar sh'yeish li materin"/the fruit will become permissible in just a few hours, so in that case the rabbis didn't permit it even in the case of safeik.
Unless the non-Jew has two houses -- one inside the t'chum and one outside the t'chum. In that case you are allowed to assume that he brought the fruit from his house that is inside the t'chum. That's a rule known as "kahn nimtza, kahn hayu"/it's here now, so we can assume it was here before.
What if has two houses outside the t'chum? The biur halacha on syef 9 (d.h. shnei batim) brings the Ta"z who invokes the rule of "karov v'rov, rov adif"/when the safeik is about whether he came from the closest area or the area where he has the majority of his residences, the majority takes precedence. The biur halacha takes issue with that, though, because we can apply the rule of "kahn nimtza, kahn hayu" to the non-Jew himself, which he feels probably overrides the "karov v'rov, rov adif" rule in this case.
One thing about which there is no doubt at all... this is so much fun!
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