In Rashi's second explanation (Bereishit 4:24 שבעים ושבעה) of what Lemech said to his wives, he explains that Lemech didn't kill anyone, but Ada and Tzila were worried because they knew the flood would come and kill all of Kayin's descendants, so they didn't want to have any more children. Lemech argued that he hadn't killed anyone, so if Kayin was given 7 generations, he would be given 77. Rashi says this is a קל וחמר של שטות.

For something so foolish, it was amazingly accurate. Based on the following Rashi, this happened in the year 129, around a year before Sheit was born. Based on Rashi at the beginning of the perek, Kayin and (maybe) Hevel were born before Adam and Chava were thrown out of Gan Eden. Kayin could have killed Hevel as early as the summer of year 1.

Since 7 generations from Kayin ended in 129, 77 generations from Lemech would have ended no later than 129 + (129-1)*11 = 1537. This is 1 year after Hashem decreed the flood (120 years before it happened, 1536).

(Maybe you could play around with the numbers and lose another year. I don't expect to be able to identify all the steps needed to make numbers come out exact unless I'm the Gr"a, which I'm not.)

I made some assumptions of when Kayin killed Hevel, but 1537 is an upper limit on when the 77 generations could have ended. Lemech really did get 77 generations before the decree, and even more before his descendents were actually killed.

Where's the שטות?

  • I think it would be fitting to edit your question to include rashi's reasoning as to why it was foolish and then point out how amazingly accurate the math worked out. That would preclude answers such as the one given. Also you can point to the kal vichomer by Miriams tzaraas and David's honoring Achitophel in Avos 6 3 to prove that Torah and chazzal make this kind of kal vichomer. But anyways, +1. Very nice. Did the hunch for this equation just pop into your head? – user6591 Oct 27 '16 at 22:43

Although your calculations are very interesting and thought provoking (I am sure they contain a lesson about Hashem listening to Lamech's claim etc.), the "shtus" or foolishness was not due to a wrong calculation.

Rather, the reason why it is foolish has been given by Rashi. "If so, then Hashem could never collect His due and keep his word."

A kal vachomer is a logical argument, recognized by Hashem as a Torah true method of deduction. However, it has limits. One limit is that a logical proof cannot cause a reality that will nullify a specific Torah truth elsewhere.

Hashem had already decreed that a flood would wipe out Kayin etc. Hashem already was aware of Lamech's potential reasoning when He made that decree. He decided to make the decree anyway. This is possibly because the decree's importance outweighed and overrides Lamech's (or anyone's) potential claim. Perhaps Hashem would recognize Lamech's complaint and grant him something else to make up for his good behavior (Olam HaBah, or as you hint to, being granted 77 "Kayin length" generations?)

If there had been no specific Torah decree, then Lamech's logic would apply in the face of no opposition.

But, once a decree is made, then logical proofs elsewhere have no force simply by virtue of logic. That is why the kal vachomer is foolish, even if the supplicant is granted what he wants. He may have been granted the claim through mercy working within the decree, but not by virtue of logical demand.

A second reason may be the "Dayo" ("enough") principle as explained in chapter two of the Gemara Bava Kama. A K"V is limited to grant only the conclusion of the first case, but no more than that.

If his painting is worth $1,000.00, then mine is certainly worth $1,000,000.00!

This is a foolish K"V, because the conclusion is limited to the result of the first case and no more.

If his painting is worth $1,000.00, then mine is certainly worth $1,000.00.

This is a correct K"V, because my painting is logically worth just as much as his (not more). More cannot be proven using a logical comparison. So, Lamech could have reached for 7 generations for himself by logical comparison, but not 8; and certainly not 77.

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