Eilu va’Eilu part II

[Updated 1/9/2014. The story so far: In part I I gave a survey of opinions from rishonim discussed in essays by RM Halbertal and Rav Michael Rosensweig.]
RMHalbertal spelled out three approaches to machloqes: (1) retreival — all machloqes are about recovering forgotten laws, attributed to many ge’onim; (2) accumulative — Torah is built analytically, which means different people can reach different legitimate conclusions (eg the Rambam); (3) constitutive — the halakhah is constructed by the poseiq.
As I noted in the last section, I am not sure the latter two categories are necessarily different. But in any case, the Yerushalmi (Sanhedrin 4:1, vilna 21a-b) seems to assume at least one of them:

Rabbi Yanai says, had the Torah been given clear-cut [predecided] there would be no place for the leg to stand. What is the source, “Vayedaber Hashem el Moshe leimor — and Hashem spoke to Moshe to say”.

Usually this is taken to mean “… saying”. But it can also, and perhaps more grammatically, taken to mean that Hashem told Moshe and the sages to say something. The verse implies rabbinic development of the initial revelation. Continuing:

[Moshe] said before Him: Master of the world! Please let me know how the halakhah should be.
[Hashem] said to him: “Follow after the majority. It the majority find merit, then merit, if the majority obligate [either a duty or a punishment], obligate him. So that the Torah is expounded 49 ways tamei and 49 ways tahor. From where do you know [the number]? It is the number [of the gematria], “vediglo” [and His flag].
Similarly [Tehillim 12:7] says, “The words of Hashem are tahor words, as silver tried in a crucible on the earth, refined seven times.” And [Shir haShirim 1:4], “they love Him meisharim — sincerely.”

As the Penei Moshe explains, the verse in Tehillim is taken as proof of the 49 ways by being read as “seven times seven”. And Shir haShirim is cited to find balance, meisharim, through the conflicting opinions. The Yershalmi is advocating a dialectic approach, in which the Torah’s truth is in the process as much or more than the conclusion.

But in any case, the entire discussion starts from and elaborates on Rabbi Yanai’s idea that the Torah does not give one true ruling for us to recover.

My personal inclination is close to the philosophy of the Maharal’s. If I can use a variant on Plato’s metaphor, we are like people looking at shadows of an object. Since reality can not capture all “three dimensions” of “divrei E-lokim Chaim“, we see what looks like conflicting “two dimensional” shadows. Shapes that accurately represent the whole, but only from the direction from which we are shining the light. The process of pesaq is that of deciding how we should grow and develop given where we stand; what are angle ought to be in relation to that 3 dimentional object and therefore what shadow it casts.One can’t adopt two conflicting positions, neither leniencies (as would the Conservative movement do) nor stringencies (as per the insufficiently fictional “Chumrah of the Month Club”). That would be combining two different angles, to produce a “shadow” the object could never really cast. One is no longer representing the “object”, the Word of G-d.True pluralism (within a range of valid positions) seems to be a compelling conclusion from the Gemara (Hagigah 3b) is concerned about the person who will note when “those [Rabbis] prohibit, yet those [authorities] permit [the very same thing]… how can I possibly learn Torah today?” The answer is found in the words of Koheles 12, “Nasnu meiRo’eh echad – both views were given by the same shepherd.”

Rav Tzadoq haKohein (Resisei Laylah sec. 17), defines a different kind of logic when it comes to thought than when it comes to action, and uses this to understand the nature of pluralism.

Whenever a new thing found about the Torah by any wise person, simultaneously arises its opposite…. When it comes to the realm of action (po’al) it can not be that two things true simultaneously. In the realm of the mind (machshavah), on the other hand, it is impossible for a man to think about one thing without considering the opposite.

This model differs from the Maharal’s. The Maharal assumes that truths can’t contradict. Rav Tzadoq denies the applicability of the rule of contradiction. The two ideas can coexist: Man’s thoughts are designed to be able to handle conflicting truths because it is the best way to approximate a full understanding of the Divine Truth. Like the famous parable of the blind men and the elephant: the elephant is not a fan, a wall, a rope or a tree trunk, and the complete picture is closer to the contradiction as a whole than any one position.

This is actually the literal meaning of the word “teiqu“. When the gemara’s debate can not reach a conclusion, it says teiku. Most students are taught the medrashic meaning, that it’s an acronym for “tishbi yetzareitz qushyos ve’ibayos — Eliyahu the Tishbi will answer all questions”. But the word itself means “let it stand”. Not that there is a question left unanswered, but that both positions stand — despite the contradiction.

For the mathematically inclined, then there’s Goedel’s Theorem. Everyone else may choose to stop at this point.In short and without lots of formula and Greek letters, Kurt Goedel presented a set of theorems that boil down to showing that any sufficiently robust finite formal system that is consistent (i.e. does not claim both something and its opposite — A and not A) must be incomplete. This includes all systems that have formal rules from getting from a finite set of givens to an infinite set of conclusions, and are robust enough to be used to describe mathematics. All such systems must either be able to produce contradictory conclusions, or be unable to produce conclusions that are known to be true.According to the Malbim (intro. to Vayiqra), all of the Oral Torah could be reconstructed from the Written Torah and 613 rules of logic and derashah. Even if we add the halakhos leMosheh miSinai, to fit the understanding of most that these have no source in the written Torah (the Malbim’s statement would imply they do), this is a finite number of postulates and a finite set of rules for elaborating on them. What about Goedel’s Theorem.Given eilu va’eilu The question could be resolved on a number of levels:

As Rav Tzadoq haKohein writes, Divrei E-lokim Chaim are not consistant. Either inherently so, or — as the Maharal takes it — our comprehension is limited to inconsistent approximations. Divrei E-lokim Chaim can therefore be complete.

Halakhah as ruled would have to be constitutive, Rabbanim given the power to define which position is correct. If we took a “retrieval” (Rabbanim try to reconstruct the forgotten) or “accumulative” (deductions from the known) model without a constitutive component, then when we rule out contradictions we would necessarily create areas in which no ruling could be produced.

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