Taharos, Chapter 5, Mishnah 4. The subject of this chapter is safek tumah that comes up in a reshus harabbim, a public domain, where the halachah settles the doubt in the lenient direction and the person remains tahor. Our mishnah brings another such case, this time not with two paths but with two small creatures lying out in the open.
The opening words are "Hasheretz vehatzfardea bireshus harabbim." A sheretz, meaning one of the eight creeping creatures whose carcass carries tumah, is lying in a public place, and next to it lies a frog. Picture the sheretz as a lizard: it has the status of an av hatumah, and anyone who touches it becomes tamei. A frog, by contrast, conveys no tumah at all. Here is where the problem begins: to the eye, a lizard and a frog can resemble one another closely enough that a man who touched one of them may be unable to say which of the two it was.
The first touch
"Naga be'echad mehem ve'asah taharos vene'echlu." He made contact with one of the two, not knowing which. Afterward he prepared taharos, that is, foods of terumah, and they were served and consumed. Those foods no longer exist, so there is no ruling left to issue about them.
"Taval." He then went down to a mikveh and immersed. Where the tumah comes from a sheretz, nothing more than immersion and the arrival of night is needed.
The second touch
"Naga basheini ve'asah taharos." Later he touched the second creature, and here too he could not identify which one it was, and once again he prepared foods of terumah. Are those foods tahor or tamei?
"Harei eilu tehoros." The mishnah rules that they are tahor. The earlier batch was eaten and is past our reach, so the doubt is resolved by treating the second creature as the frog and the first contact as the one with the sheretz. The food that lies before us right now may be handled as tahor.
When the first batch is still on hand
"Im kayamos harishonos, eilu va'eilu teluyos." Should that first terumah still be in existence, both sets of food are placed in suspension. There is no way to establish which of the two contacts involved the sheretz, and each possibility yields the opposite verdict about the two batches. That leaves us stuck: burning is not an option for either batch, since it is entirely possible that the batch in question is fully tahor, and tahor terumah may not be destroyed. And so both are simply set aside, not eaten and not burned.
When he never immersed in between
"Im lo taval beintayim, harishonos teluyos vehasheniyos yisarefu." Now alter a single detail: no immersion took place between the two contacts. The first batch is still in suspension, because we cannot know whether that opening touch landed on the sheretz or on the frog. The second batch, however, is tamei beyond question. Once he had touched the second creature, he had made contact with both the sheretz and the frog, and whichever came first, he had contracted tumah and had done nothing to remove it. The terumah he handled at that point is definitely tamei, and it is burned.
Why the mishnah teaches the case twice
It is fair to ask what this mishnah adds, given that its rulings line up exactly with those taught in the previous mishnah about the two paths. The Rambam supplies an answer, and it turns on the three Tannaic opinions recorded in this chapter. First there is the position of the Chachamim, and this is the halachah we follow, that a doubt originating in a public domain leaves the person tahor. Second is Rebbi Akiva, who took a stricter line. Third is Rebbi Yose, who divided the material in his own way, setting the case of the paths apart from every other case and ruling stringently in the rest, the sheretz and the frog included. The Rambam explains that our mishnah is here to inform us that even Rebbi Yose, for all his stringency in the cases outside of the paths, accepts the lenient ruling in this situation, where a man touched one creature, immersed, and only then touched the other.