Almost this entire daf is dedicated to a painfully detailed analysis of a tool for logic and textual interpretation that we have seen countless times already in our Daf Yomi study: the kal vachomer (literally, “lenient and strict”) argument, also called an a fortiori inference.
What exactly is a kal vachomer? In essence, if a serious matter has a particular leniency to it, then a matter that is less serious will also have that leniency. The reverse is true too: If a less serious matter includes a particular stricture, a more serious matter will also include that stricture. As an example, in Exodus 6:12, Moses argues against returning to Egypt by noting that if the lowly Israelites don’t listen to him, why would a high-powered Pharoah? This is one of ten times that a kal vachomer argument appears in the Bible. There are over 1,000 examples in the Talmud.
Kal vachomer arguments often go hand in hand with the principle of dayyo, meaning “it is sufficient.” In essence, a kal vachomer argument can only go so far. For example, touching a corpse renders a person unclean for seven days. Using kal vachomer, we can conclude that the more serious transgression of moving a corpse renders a person unclean for at least seven days. While we might speculate that there are more severe consequences — say, 14 days of uncleanness — for moving a corpse, the principle of dayyo precludes us from going beyond what we know from the information at hand.
The mishnah that began on yesterday’s daf discusses a kal vachomer argument regarding damage caused by an ox, which is how we got on this topic in the first place. But the Gemara on today’s daf discusses an example of this logic from the Torah itself. Moses’ sister Miriam has been gossiping about Moses’ wife, becomes afflicted with a skin disease and is banished from the camp for seven days.
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“And the Lord said to Moses: If her father had but spit in her face, should she not hide in shame seven days? Let her be shut up seven days outside the camp, and after that she shall be brought in again.”
Using an a fortiori inference, if the Divine Presence (reprimanded her, it should be) 14 days. Rather, it is sufficient for the conclusion that emerged from the a fortiori inference to be like the source.
There’s a lot to unpack here. For starters, what’s the deal with the 14-day banishment? One commentator suggests that because God is a partner in creating each human being and is therefore equal to the two human parents combined, if a single parent’s shame is worth seven days of banishment, God’s shame should result in 14 days.
But Miriam isn’t punished for 14 days. Why? Because even though a kal vachomer argument could be made that she should be, the principle of dayyo limits us. If shaming from a parent leads to seven days of banishment, we can reason through kal vachomer that shaming from God can’t be less than seven days, but we can’t necessarily say that it’s more than seven days. The rabbis invoke the kal vachomer argument here, but they are limited in how far they can take it by the principle of dayyo.
Dayyo too has its limits, and the Gemara records a dispute between Rabbi Tarfon and the other rabbis about the extent of it:
When does (Rabbi Tarfon) does not accept the principle of dayyo? When it refutes kal vachomer. But where it does not refute kal vachomer, he accepts it.
In the case of Miriam, kal vachomer tells us the punishment must be at least seven days, but dayyo tells us it can’t be more than seven. Because dayyo limits the number of days but doesn’t refute it — i.e. cancel them out entirely — Rabbi Tarfon seems fine with it. But in cases where this isn’t true, Rabbi Tarfon is not fine with it (and would impose higher penalties) while the rabbis would not.
Kal vachomer is an incredibly powerful tool and one of the most commonly invoked in the Talmud. That said, there are limits to how far it can go, and dayyo is one of the principles that can keep it in check.
Read all of Bava Kamma 24 on Sefaria.
This piece originally appeared in a My Jewish Learning Daf Yomi email newsletter sent on November 25th, 2023. If you are interested in receiving the newsletter, sign up here.
