The Talmud (Pesachim 10a, Tahahrot 5:5) teaches the case of the “two paths”, one of which is pure and the other impure. An individual walks along one of the two paths, and not knowing if he is pure or impure, inquires as to his status. He is told that he can consider himself pure; that is a function of the rule of “safek tumah b’reshut harabbim tahor”, which allows one to assume purity in an indeterminate situation in a public setting. If, afterwards, another individual takes the other route, he receives the same ruling (According to R. Yehudah, against R. Yose). This is true even though we know in actuality they cannot both be pure. Nonetheless, the rule addressing a “safek” is one of practice (hanhagah) rather then one meant to determine the reality (birur). Thus, there is no inconsistency in allowing a lenient practice in both cases, even though it is impossible in reality that both paths are pure.

If, however, the two individuals come together, each having taken one of the paths, and inquire at the same time, the ruling is different, resulting in impurity for both. In truth, it would seem that the above logic should still apply, and a paradox could still be tolerated. If they can both be treated as pure when they come separately, the same should hold true when they come together. In line with that, Tosafot (Pesachim 10a, s.v. b’vat achat) assumes that the distinction must only be true on a rabbinical level; on a biblical level, even the second case would receive rulings of purity.

It might be suggested that there is a fundamental distinction between the two cases, in that the nature of the question posed is different. The first two individuals, who come separately, are each asking, in essence, “am I pure or impure?”. Thus, each is entitled to the ruling of safek indicating purity. When they come together, however, the question is an altogether different one: “Which one of us is impure?”. In that case, the “safek” principle cannot be used because neither possibility is “lenient”, or, in this case, “pure”.

This notion may be relevant as well to an issue dealt with by the Ran (to Pesachim 108). The Talmud notes that only two of the four cups of wine require “heseibah” (leaning), but does not identify whether it is the first two or the last two. The Ran discusses the fact that we require heseibah for all four, and do not utilize “safek d’rabanan l’kula” (indeterminate situations of rabbinical law are resolved leniently). While the Ran gives possible explanations for this, it can also be observed that the fundamental question here is not “does this cup require heseibah”, which would allow for a lenient answer, but rather “which of the two sets require heseibah”, a question with two possible answers, neither being more lenient than the others.

The model of “two paths” is also cited by the Meiri (in the fourth perek of Masekhet Berakhot) to illustrate the inappropriateness of davening both minchah and ma’ariv between plag ha-minchah a sh’kiyah. That time period is subject to a dispute in the Talmud as to whether it is the end of the minchah time zone or the beginning of that of ma’ariv. As the Steipler Gaon (Kehilot Yaakov, Berakhot, 1) explains, this model (in contrast with that of the Rosh, Berakhot I, 1) would allow using that time period for different prayers from one day to the next, in accordance with “safek d’rabanan l’kula”. However, to use the period for both prayers on the same day would be comparable to the second situation in the case of the “two paths”, where the two individuals ask about their status together, and thus cannot be declared pure.