I think we have all been fascinated by the question: What is peculiar about Talmudic logic? Is it the same as Western logic but presented differently? Does it have methodological procedures that violate what a Western logician (or a naïve modern student) would regard as normal or acceptable? Does it push forward where Western logic fears to tread, sometimes (maybe anticipating Gödel) pointing out the Achilles heel in Western (read: Aristotelian or Euclidian) logical assumptions?
Probably yes to all the above.
And finally (the real payoff in my opinion): Where does Talmudic logic lay the basis for Talmudic meta-ethics and ethics? What (in the Talmud) is the bottom-line criterion (or is there more than one) of determining right action?
A colleague of mine said that in teaching Talmud there were instances too numerous to count when a student would react in surprise or disbelief: How can you reason that way? The experienced student of Talmud has learned to take for granted the idiosyncratic methods of reasoning that are part of the fabric of Talmudic argument. By slowing down and recapturing the idiosyncratic and odd in Talmudic discourse, we can perhaps isolate and identify the core of Talmudic logic itself, and shed light on our initial questions—and lead also to additional questions that remain unarticulated at this point but are just as much part of the enterprise (rightly conceived) and worth pursuing.
Case #1: The Failure of Transitivity (A > B and B > C but (A not > C))
I start with one example that sticks in my mind from the time that I was studying Chapters 4 and 5 of Sanhedrin with some friends. I refer to the sugya that links Sanhedrin 35a-35b:
Said Resh Lakish to R. Johanan: Shouldn’t burial of a “met mitzvah” override Shabbat from kal-vahomer? Just as the Avodah overrides Shabbat, so burial of the dead should override Shabbat deriving from “ve-la’ahoto”, as it is taught (citing Numbers 6:7)...: What does this come to teach us? Even if [a Nazirite] was going to slaughter his Pesah or circumcise his son, and he heard that a relative of his had died, could it be that he should defile himself? You say, “he shall not defile himself.” Could it be that just as he should not defile himself for his sister, he should not defile himself for a “met mitzvah”? The text teaches, “ve-la’ahoto” —it is for his sister that he does not defile himself, but he defiles himself for a “met mitzvah.” Now, if Shabbat is overridden by the Avodah, does it not follow logically that burial of a “met mitzvah” should override it? (But of course it doesn’t.)
Explanation:
Met mitzvah: If one is traveling and finds an unattended dead corpse, one is duty-bound to set aside all other tasks and bury it.
Avodah: The Temple service.
Avodah overrides Shabbat: The daily sacrifices in the Temple must be offered on Shabbat, even though offering them entails certain actions (such as slaughtering) which ordinarily would be forbidden on Shabbat.
Met mitzvah overrides Avodah: A Nazirite, going to the Temple to offer his Pesah sacrifice, if he encounters a met mitzvah, must bury it, even though he thus defiles himself and disqualifies himself from offering the Pesah sacrifice.
Shabbat overrides met mitzvah: If one encounters a dead body on Shabbat, he should wait until after Shabbat before burying it.
Kal va-homer: If Case A is more severe than B, and particular "p" is true of B (B(p)), then particular "p" should be true of A also (A(p)). In this case, the particular is "overrides C." Thus, if B overrides C, and A is more severe than B (because A overrides B), then A should override C.
Attempted application of Kal va-homer in this case: If burial of the dead overrides the Temple service, and the Temple service overrides Shabbat, shouldn't burial of the dead override Shabbat? (But this is refuted: Shabbat overrides burial of the dead.)
Argument from ve-la'ahoto: A Nazirite is forbidden to defile himself, even for close relatives. But the rabbis interpreted the redundant vav in the word ve-la'ahoto to mean that he should defile himself for a met mitzvah.
Analysis:
On the one hand, this may fall into that long series of specious kal va-homers which are strewn throughout the Talmud. That would be significant enough, and at some point I think we should stop to analyze the deeper significance of the fact that the rule of kal va-homer is so much honored in the breach. But it seemed to me on studying this passage that it took a somewhat different tack, and was trying to offer a paradigm of:
A > B, B > C, but C > A
Namely:
Met mitzvah overrides Avodah, Avodah overrides Shabbat, but Shabbat overrides met mitzvah.
To a Western logician, this is a slap in the face of a Euclidian axiom:
If A > B and B > C, then A > C
This issue is referred to in the contemporary literature of philosophical ethics as “transitivity.” (A recent student of mine referred me to Joseph Raz’s discussion of this issue in The Morality of Freedom, pp. 322ff.) If there is one uniform scheme of human values applying to all rational agents, then certain goods should be universally deemed to be better than others in a consistent hierarchical progression, but (alas?) they are not: one agent prefers A and another prefers B and the attempt at establishing a universal, consistent hierarchy of all goods is bound to fail.
It seems to me that both the Talmud and the modern discussion are running up against the limitations of abstract logic when the attempt is made to apply it to human experience. Human experience has so many variables that a simple-minded logic of abstract consistency is bound to fail when trying to account for it. Thus the anomalies of Talmudic logic (as in this case) may be a tribute to the complexity of human (or human-and-divine) reality, that demands a more subtle and at times paradoxical approach rather than a simple-minded straightforward one.
Case #2: The Case that Falls Between the Cracks of Classification
The following narrative is brought in Bavli Bava Batra 22a: R. Dimi wanted to sell his load of figs, and Rava authorized Rav Adda bar Abba to test his expertise to see if he could qualify to get a visiting scholar's commercial privileges for a day. Rav Adda posed the following stumper to Rav Dimi: "If an elephant passes a basket, what is its status [is it a "vessel" and thus susceptible of defilement, or as excrement is it immune to defilement]?" R. Dimi was unable to provide an answer, so he lost his chance at market-privilege and could not sell his figs. [The tragic sequel of revenge is irrelevant for my current purpose.]
What is characteristic of Rav Adda's question is that it serves to prove the incompleteness of the halakhic thought-system (in the sense that Gödel used a similar theorem to prove the incompleteness of the system of mathematics in his famous Proof, cited by Gordon Tucker in his Gerson Cohen Memorial Lecture, published a few years ago in Conservative Judaism). The halakhic thought-system puts everything into categories. Women are either eligible or not eligible for matrimony to men of specified relations (if you want an exhaustive list, check out Yevamot 1:1); certain cases are either eligible or ineligible for payment of damages; certain foods are either permitted or forbidden; certain items either are susceptible of ritual impurity or not; etc.; and the whole world of objects and cases is classifiable in this way. Or is it? Rav Adda gives a counter-example. It seems in retrospect that he was looking for the Achilles heel in the system, and found it in a similar way to how Gödel found it in mathematics: by looking purposely for a case that confuses the paradigm, by belonging to two opposite classes. The basket that passes through an elephant is at one and the same time a member of the class of "vessels" which are susceptible to impurity, and of "excrement" which is insusceptible.
How is this possible? One reason is that there is a transition of thought-mode from Biblical to rabbinic thought from narrative mode to static-analytical mode. The Bible is full of narratives, and the basic evaluative mode of the Bible is narrative-based. Every narrative is unique; the narrative of what transpired between Jacob and Esau is different from anything that transpired before it (though bearing some similarity to what will transpire between Jacob and Laban in the next episode), and the parties are judged on how they respond spontaneously to the unique features of that episode, having to make instantaneous judgments based on the logic of events as they unfold. Even the laws of the Bible are often presented in narrative form: "If two men are fighting, and one of them pushes a pregnant woman and a miscarriage results...and other damage ensues..." Judges must decide the unique cases that come to them on the basis of the always-imperfect analogies between the presented case and precedent cases, employing that elusive quality of "hokhmah" which is illustrated in the famous story of Solomon and the two mothers: the ability to invent a solution that is also unique and adequate to the unique case presented, while remaining true to time-honored criteria of fairness.
But along come the Greeks and tell us that everything is classifiable: that there are objects and essences, and all you have to do is determine what kind of object is before you, and what is its essence. This works in a static universe, where the objects have no history. The objects classified in the rules of "kelim" are by and large static and can be examined in their current, unaltering state to determine whether they are tamei or tahor. But along comes Rav Adda and introduces narrative into the picture. The basket that he proposes has a history, and it is its history that confounds the paradigm, for at one point of its history it is clearly in one class, but then it passes into an opposite class. By re-introducing narrative into a system that is based on static essences, Rav Adda demonstrates its incompleteness.
But by telling the story of Rav Adda and Rav Dimi, the editors of the Bavli were doing one of the things that they do best: pushing the rabbinic thought-system itself to its limits.
