On Undecidable Propositions in Judaism

A conversation with a friend reminded me of this talk that I delivered three years ago this week, so I rescued it from my old livejournal obscurity.

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Shabbat Shalom,

This week’s parsha [Torah portion] is parshat Balak, where among other things we are introduced to Pinḥas, and we get to ask ourselves whether extremism in defense of morality is or is not a vice.

That, however, is not what I wanted to talk about. Balak is qualitatively different from all of the other parshiot since Lekh Lekha in one major way: the Jews are not the focus of the story. Pretty much all of the events, from Balak hiring Bilam, to the repeated cases of erstwhile curses being transformed into blessings, happens outside of earshot of any of B’nei Yisrael [Jewish people]. We have a tradition that none of the words of the Torah are wasted – we learn different lessons from each of the identical offerings of the nasiim [heads of the tribes], and the presence or absence of a word, or even a single letter can be the subject of vast exegetical teachings. So what is this doing here?

I have a possible answer, but we’ll need to take a short detour away from the parsha to get there.

There was, among the gentiles, a long and storied tradition of rationalistic systemization with the idea that the use of reason would uncover truth. The purest example of this found its expression in the union of philosophy and mathematics in Europe. The goal of their pursuit was a deterministic rational approach to determining the truth or falsehood of any statement – in a phrase, formal logic. They believed that once they had achieved this, they would be able to map out all of the possible true statements in a formalized way, and both prove every truth, and refute ever falsehood. Lebniz, one of the co-creators of calculus (and the one whose notation for derivatives is actually used), famously said

Quo facto, quando orientur controversiae, non magis disputatione opus erit inter duos philosophos, quam inter dous computistas. Sufficiet enim calamos in manus sumere sederque ad abacos, et sibi mutuo dicere: Calculemus! [“if controversies were to arise, there would be no more need of disputation between two philosophers than between two accountants. It would suffice for them to take their pencils in their hands, sit down with their slates, and say to each other, “let us calculate!”].

The zenith of this desire was Bertrand Russell’s Principia Mathematica, which spent hundreds of pages laying out a fully rational foundation for mathematics and deriving that addition worked the way everyone thought it always had.

This desire for a fully rational system to understand capital-T Truth was never monolithic within the Jewish world. There is a coherent rational strain down through history; The Mishnah includes an explanation of God’s creation of miraculous elements in the last possible moments before ceasing His creating, such as the mouth of the world which swallowed Koraḥ, or more timely to this week, the mouth of the donkey that spoke to Bilam. These serve as a proof-text of a desire to have all of the pieces of the narrative “fit” in a rational manner.

Further, the whole enterprise of rabbinic argument is itself a testament to rationalism – the height of this is the case of the oven of Akhnai, in which Rabbi Eliezer disagreed with the other rabbis regarding whether an oven with a certain construction was susceptible to tumah [ritual impurity] or not. Rabbi Eliezer was unable to convince the other rabbis with “all the arguments in the world,” in the words of the Gemara, and then proceeded to perform a series of escalating miracles, concluding with the proclamation by a heavenly voice that the decision should go according to his opinion.

Rabbi Joshua’s response, Lo bashamayim hi [it is not in Heaven], is a stunning example of the chutzpah which is only found in Jewish thought (that is, quoting the Bible to God), but is also a clear rejection of non-rationalist thinking. At that moment revelation could be said to be defeated in the face of an ascendant rationalism. No new source of information would be allowed to outweigh the decisions reached by the process of analysis and examination of that which was set down before.

Maimonides and the other codifiers largely continued with this approach, although some cracks appeared in the foundation – custom had and continues to have a force which is stronger than reasoning, and a tension between “what the law said” and “what people did” became the norm, and increasing layers of rational argument were built on the foundation provided by the Gemara and the codes in an attempt to formally define the answers to all of the questions which could possibly arise.

Back to Russel and the late 19th century logicians. Their hopes were soon to be dashed: Kurt Gödel proved, without a shadow of a doubt, that any formal system which is sufficiently powerful as to be able to express truths about itself, is either inconsistent or incomplete. That is, it can either prove that both a thing and its opposite are true, or there are cases whose truth is beyond the ability of the system to prove. He proved this about mathematics, but the same argument applies to any formal system which is able to describe its own workings. One relevant aspect of Gödel’s argument is that you can demonstrate truths that the formal system cannot prove via the method of “stepping outside the system” – they are completely unprovable from within, but obvious from a different perspective. Gödel’s proof was a trauma from which Western philosophy has not fully recovered.

Halakhah [Jewish law], like any other formal system, it bound by Gödel’s theory – it is necessarily inconsistent, incomplete, or both. However, we have known that this is true for a long time: we have both the case of eilu v’eilu divrei Elokim Ḥayim [these and those are the words of the living God], and of teku, which is an acronym for Tishbi yetaretz kushiyot ve’abayot [the messiah will solve all the difficult questions]. Rav Soloveitchik said that the lesson we should learn from the presence of teku is that we should not presume to believe that we have all of the answers.

Even earlier than that, we have the idea of a Ḥok – a decree for which we do not know the reason.

So if the inevitable failure of rationalism is no ḥiddush [novel insight], what is the relationship to parshat Balak?

I propose that the episode is reminding us that although God has taught us everything we know, this is not the same thing as God teaching us everything He knows.

Balak approached his purpose rationally – seeing that he had a problem on his hands, he set out to arrange for troubles to befall those he viewed as enemies. His rational approach did not discern the Truth behind Bilam’s reticence, and could not grasp the nature of the failure of his mission – because the leap of faith required is precisely the type of “stepping outside the system” which is so hard to do when one is deeply attached to a certain perspective. Balak’s problem isn’t merely that he was unable to discern capital-t Truth; lacking a frame of reference where he could understand correctly what the Jewish people represented, he embraced a falsehood and elevated that to the status of Truth itself. However, Balak made a category error: he treated God like a vending machine – behaving as if he could just have the right words said, then God would enact his will. This is the idolatry of creating god in the image of man. This point of view is rejected resoundingly, and Balak’s mission ends in dismal failure. We embrace instead the idea that God rewards goodness and punishes wickedness, but often in ways we will not understand or be able to predict.

Jews are the chosen people of God, and we have a special mission as proponents of ethical monotheism; this does not mean that God only talks to us, or works only through us. In the same way that the book of Jonah shows a Jewish prophet reluctantly saving a gentile city, Nineveh, parshat Balak shows a gentile prophet reluctantly blessing the Jewish people.

The manner and form of God’s interaction with the gentile nations of the world will occasionally be made clear to us – either through our prophets or theirs, but that clarity should not be taken to mean that we understand the whole of those interactions. Consider: God lingered over creation, and considered the creation of the means by which He would confront Bilam important enough that He delayed the first Shabbat.

The unrevealed nature of God’s actions in this world is worth remembering as we enter into the three weeks, the darkest time in the Jewish calendar. Just as the blessings of Bilam become part of our daily liturgy, so too can noting the presence of the manifold interactions of God in the world become an additional cause for us to sing His praises.

May we merit to see the handiwork of God in His creation. Shabbat Shalom.

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About thegameiam
I'm a network engineer, musician, and Orthodox Jew who opines on things which cross my path.

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