On a Halakhic Loop and a Goyishe Kop (Column 708)

With God’s help

Disclaimer: This post was translated from Hebrew using AI (ChatGPT 5 Thinking), so there may be inaccuracies or nuances lost. If something seems unclear, please refer to the Hebrew original or contact us for clarification.

Yesterday my friend Nadav Shnerb sent me a passage from Nekudot HaKesef that contains a halakhic logical loop. It struck me as interesting, connects to previous columns, and is worth further discussion, so I’ll devote this column to it.

The words of the Shach

In Shulchan Aruch, Yoreh De’ah §124, which deals with the laws of yayin nesekh (libation wine), the Rema records the following ruling (there in se’if 27):

If a non-Jew touched a Jew’s wine out of spite, in order to render it forbidden to him (Tosafot, Mordechai, and Agudah there), then even if this is known only from compelling indications, the wine is permitted even for drinking; and one should drink it in the presence of the non-Jew so that they not accustom themselves to doing this (Tosafot and Mordechai in the name of the Or Zarua).

Normally, an idolater who touches a Jew’s wine renders it forbidden; but if he does so out of spite, the wine is not forbidden. The rationale here seems related to the idea I developed in my essay on killing a thief, where I explained that if someone cynically exploits halakhah, it “freezes” itself and does not enable that exploitation.

The author of Nekudot HaKesef (the Shach) discusses the following case:

A gentile touched a Jew’s wine to provoke him, etc. This incident occurred while I was in the lands of Mehren, and a non-Jew touched my wine. I did not wish to drink it, and he said to me as follows: “Drink, for the wine is permitted; ask your father and he will tell you that it is permitted, since I did it to provoke you so that you would not drink, and when one does it to provoke it is permitted.” Thus far his words.

The gentile touched the wine and told him it was permitted to drink because his touch was only to provoke him, and in such a case the wine is not forbidden.

There the Shach writes that he indeed asked his father, who answered him so:

And I asked my revered father (z”l) what the ruling is, and he said that the wine is forbidden. For the reason for leniency is that he acted to provoke; but since he knows the law, then he did not act to provoke, and it reverts to the original prohibition, as if he had not acted to provoke.

The claim is that there is a loop here: if indeed the wine is permitted, then there is no act of provocation, from which it follows that the gentile did not truly act to provoke, and therefore the wine is forbidden.

Now he objects:

[Even though when done to provoke] it is permitted to drink even not in the presence of the non-Jew—because his intention was not to perform a libation but only to provoke—so here too his intention was not to libate but to show that he knows the law.

In his words he assumes that the wine is not forbidden because the gentile did not intend to libate it but only to provoke, and not for the reason I suggested above (the “freezing” of the law). This is a bit puzzling, since there would still be room to forbid the wine rabbinically as stam yeinam (ordinary gentile wine), which is forbidden upon touch even without an act of libation and even when it is not a bona fide idolater involved.

In any case, the Shach argues that although he did not intend to provoke but rather to show that he knew the law (to taunt him), that too is not an intention to libate, and therefore the wine is not forbidden. Of course, according to my approach there is no room for this claim, since if he did not intend to provoke, there is no “freezing” of the law. In any case, on his own terms this ruling is indeed difficult.

And he resolves:

However, one can explain that since he knows that “to provoke” is permitted, he never acted to provoke at all but did it to libate; and his telling the Jew to ask the law about “to provoke” being permitted was to cause the Jew to stumble so that he would drink libated wine. This is unlike one who does not know, where the non-Jew acts only to cause the Jew to lose his wine so that he won’t drink it—therefore it is permitted. Not so here, for he knows that “to provoke” is permitted; therefore he acts to libate and it is forbidden. This requires further analysis.

There is a concern that he did it in order to libate, and that his sending the Shach to ask his father was only to ensnare him so that he would drink the wine even though it was forbidden (apparently this gentile was a Talmudic prodigy). Here it already seems that there is doubt (perhaps he did it to libate, perhaps not). Thus, in a rabbinic prohibition (such as stam yeinam) there is room to be lenient, and only in actual libation, which is a Torah prohibition, should one be strict. The question is whether this prodigy-gentile also knew all that…

The difficulty

His father’s reasoning is a bit odd, since for some reason he stops and does not continue the loop onward. For if the wine is again forbidden, then clearly he did act to provoke, and the wine should not be forbidden—and so on ad infinitum. This resembles two loops we saw in columns 406 and 617, which I’ll briefly recall here.

First example: “A yoke came upon it”

The Gemara in Bava Metzia 30a cites a statement of Rav Pappa regarding the eglah arufah (the “decapitated heifer”):

Rav Pappa said: Had it been written “oved” and read “oved,” I might have said even if [the work] occurred on its own; and had it been written “avad” and read “avad,” I might have said only if he himself did work with it. Now that it is written “avad” and read “oved,” we require “oved” similar to “avad”: just as “avad” [implies] that it is pleasing to him (nicha lei), so too “oved” requires that it be pleasing to him.

When a corpse is found and it is unknown who murdered him, an eglah arufah is brought. The heifer must be one upon which no yoke has come (lo alah aleha ol). The Gemara states that the disqualifying “yoke” is only one that was put upon it with the owner’s consent (or at least where it is pleasing to him). One sees there that the same is the law regarding the parah adumah (red heifer; see the Hiddushei ha-Ran there, who discusses whether the whole sugya refers only to the red heifer).

And Tosafot there, s.v. “af oved,” ask:

If a male mounted it, why is it disqualified? Surely it is certainly not pleasing to him to render the cow—whose price is so high—invalidated for the sake of a trifling benefit.

That is, the condition that the yoke must come upon it with the owner’s satisfaction empties the law of content, since the owner will never like the idea that his cow loses all its value (a valid red heifer is extremely expensive).

Tosafot resolve:

One can say: if it were valid, it would be pleasing to him; therefore we cannot validate it.

The owner’s lack of satisfaction stems from the very fact of the cow’s disqualification; such dissatisfaction does not remove the disqualification. The dissatisfaction the Gemara has in mind (that would validate the cow) is objective—independent of the legal consequence that the cow becomes disqualified.

The Ran there also struggles with this and offers two answers:

“If a male mounted it, it is disqualified.” You might ask: why? Since you have disqualified it, it is not pleasing to him—for for a small benefit he will not suffer a large loss, as we say in Perek Ein Ma’amidin. One can say: since the act in and of itself is pleasing to him, we cannot validate it on account of its disqualification [for then the disqualification would be the cause of validation, which is impossible]. And furthermore: if you validate it, it will certainly be pleasing to him.

The first answer resembles that of Tosafot (though in that column I explained there is a difference). But what interests us is the Ran’s second answer: suppose we indeed validate the cow because the owner is not pleased with its disqualification. Once we validate it on that ground, the mounting now is pleasing to the owner, and therefore we should again disqualify it, since it was with his consent.

This second answer raises a difficulty: suppose we take one more step and say there is no justification to validate the animal—so we disqualify it. But then once again the owner is not pleased, and it should again become valid. Why stop the loop specifically at disqualification and not continue? This is parallel to the difficulty I raised above regarding the Shach’s father.

Second example: Psik reisha d’lo nicha lei

A similar example concerns the well-known principle of R. Natan of Rome, author of the Arukh. The Tannaim dispute the case of an unintended consequence. For example, someone drags a bench from place to place and, in the process, creates a furrow (the labor of plowing or building on Shabbat). Is he liable for creating the furrow (R. Yehudah), or, since his intention was only to move the bench and not to dig a furrow, is he exempt (R. Shimon)? The halakhah follows R. Shimon: an unintended act is permitted. But the Gemara adds a caveat: where it is a psik reisha—an outcome that necessarily follows from the permitted act—even R. Shimon agrees one is liable. For example, when the ground is very soft and it is certain that dragging the bench will create a furrow. In such a case, even without intent, he is liable. The Arukh adds a third layer: based on difficulties in several sugyot, he argues that if the person is not pleased with the forbidden outcome (d’lo nicha lei), he is exempt even in a psik reisha. For instance, if the furrow ruins his plans (it damages the ground), then even where it is certain that a furrow will be made—he is exempt.

Some objected to the Arukh along the lines of the earlier question in Bava Metzia: no one is pleased to incur stoning or a sin-offering; therefore in every psik reisha case the person is displeased and should be exempt. The law of psik reisha would thus be emptied of content, since anyone acting without intent would always be exempt, even where the outcome is inevitable.

Here too one can answer in the two ways we saw above. One can say, like Tosafot and the Ran’s first answer, that the outcome that obligates is one that is pleasing to him if we set aside the legal consequence. Or one can answer like the Ran’s second answer: if we exempt in such a case, we return to a situation where he is indeed pleased, and he becomes liable. But again one can wonder: why is that the conclusion rather than the opposite (that is, how do we decide where to stop the loop)?

A criterion for stopping loops: the Consistency Principle

In column 407 I described R. Shimon Shkop’s “Consistency Principle,” by which one can stop many logical loops. In brief, R. Shimon addresses the following loop: imagine a get (bill of divorce) given on condition that the woman not marry so-and-so. She went and married him; thus the get should be void. But if it is void, then her marriage to so-and-so is void (for she is still the first husband’s wife, and the second’s betrothal does not take effect). But if so, she did not violate the condition, since she is not married to so-and-so—so her get is valid. But if the get is valid, she is free, and her marriage to so-and-so takes effect, and so on ad infinitum.

R. Shimon argues that one can halt such a loop by adopting the following assumption (what I called “the Consistency Principle”): any halakhic effect (chalut) that, if it were to take effect, would thereby uproot itself—cannot take effect at all (in the inelegant yeshiva-student argot: “any chalut that, if it takes effect, doesn’t take effect—then it doesn’t take effect”).

In this case, we trace the iterative process step by step: first, she is divorced from the first husband, and that remains. Next, she marries so-and-so; prima facie that also takes effect, since she is not a married woman. But the moment she marries so-and-so, the get becomes void, and that in turn uproots her marriage to so-and-so. Therefore the marriage to so-and-so cannot take effect (because if it did, it would be uprooted). Here the process stops. Note that the result seems paradoxical: she is divorced from the first husband yet not married to the second—not because she remains the first man’s wife (she does not), but because of the Consistency Principle. This is a halakhic rule that conditions any legal effect: if it would uproot itself, it cannot take effect.

I explained there that this principle is not logical but halakhic (or meta-halakhic). It is a feature of halakhah though there is no logical necessity that it be so. Hence it is not a solution to a logical paradox but a halakhic rule that tells us how to act when faced with this sort of halakhic loop (and there I adduced, and pointed to, many more examples resolved this way).

Is the Consistency Principle relevant to our cases?

It is fairly clear that in the Shach’s case this principle is not relevant. The principle guides us regarding halakhic effects (chaliot) and states that if there is a chalut that would uproot itself, halakhah will not allow it to be created. But in the Shach’s case we are not dealing with chaliot but with a fact (a psychological one): the gentile’s intention. The question here is factual: did the gentile intend to provoke or to prohibit (or perhaps something else, like taunting him with his Torah knowledge)? With facts one cannot say that if facts lead to a paradox they are therefore untrue. What the gentile intended (or not) is a factual question, and we cannot legislate his intentions.

By way of comparison, in the two examples above the situation is a bit different. There the person’s intention arises post factum—it is the result of the halakhic status: if the cow is disqualified, then the person is not pleased with that outcome; and if he incurs a sin-offering or stoning, he certainly is not pleased with that outcome. Therefore, if the outcome does not transpire, that in turn affects the halakhah. But in our case the gentile’s intention is not the result of the halakhic status; it produces it. If the gentile intended to provoke, the wine is not forbidden; if he did not intend to provoke, the wine is forbidden. Thus there is only the question of what the gentile intended, and here there is a single answer and no more (though we may not know it).

The conclusion is that, on the one hand, the Consistency Principle is irrelevant in the Shach’s case (since we are dealing not with chaliot but with facts), but on the other hand the paradox does not truly exist. The gentile’s intention was one thing and only one; we simply do not know it. At most this is a case of doubt, but there is no loop here. Hence the Consistency Principle is unnecessary. By contrast, in the two earlier cases there is a loop, because the halakhic state generates the person’s intention (or satisfaction), and that intention/satisfaction in turn affects the halakhic state. In those two cases the intention/satisfaction is not a simple fact but depends on what happened. Yet since we are dealing with facts and not chaliot, the Consistency Principle does not apply there. Thus in those cases it is needed (since there is a loop) but does not help (since they are facts and not chaliot). Those two are genuine loops.

Back to the Shach’s case

Still, there is a loop there—only not in the case itself but in our reasoning as we analyze it. On the one hand, the gentile intended to provoke, and therefore the wine is permitted. But if he knew that (and of course he did, since he himself said it), then he did not intend to provoke. But if he did not intend to provoke, the wine is indeed forbidden. The question now is whether the gentile made that calculation as well or not. One can, of course, keep going—but this is not a loop about the gentile’s state; it is only an analysis that explains why we end up in doubt about his intention. We do not know how to analyze his intention correctly, but there is only one intention: either he intended to provoke, or he did not. We simply have no way of knowing which, because of our “loopy” analysis; that merely tells us that we are in factual doubt about what his intention originally was. In truth, the doubt is: which chain of reasoning did the gentile run, and where did he stop his own loop? This loop is only our attempt to reconstruct the gentile’s thought process and how far he went in his halakhic calculations.

Goyishe kop

To end, this story in the Shach about the gentile who was a Talmudic prodigy reminds me of a well-known joke about the difference between a Jewish head and a gentile head when it comes to learning Gemara:

One day a priest said to the rabbi, “You’ve taught me many things, but there’s one thing I want to learn and you refuse—I want you to teach me Gemara.” The rabbi said to him, “You’re a gentile and you have a gentile’s head; there’s no chance you’ll manage to understand Gemara.” The priest persisted until the rabbi agreed. The rabbi said, “I’ll agree to teach you Gemara on one condition: you must answer one question.” “Fine,” said the priest, “what’s the question?” The rabbi asked, “Two people fall down a chimney. One comes out dirty and one comes out clean. Which of the two goes to wash?” “Very simple,” said the priest, “the dirty one washes and the clean one does not.” “I told you you wouldn’t succeed,” said the rabbi. “It’s exactly the opposite—the clean one looks at the dirty one, thinks he too is dirty, and goes to wash. The dirty one looks at the clean one, thinks he too is clean, and does not wash.” “I hadn’t thought of that,” agreed the priest. “Ask me another question.” “Fine,” said the rabbi. “Two people fall down a chimney. One comes out dirty and one comes out clean. Which of the two goes to wash?” “Very simple,” said the priest confidently. “The clean one looks at the dirty one, thinks he too is dirty, and goes to wash; the dirty one looks at the clean one, thinks he too is clean, and does not wash.” “Again you’re wrong,” said the rabbi. “I told you you wouldn’t understand. The clean one looks in the mirror, sees he is clean, and does not wash; the dirty one looks in the mirror, sees he is dirty, and goes to wash.” “But you didn’t say there was a mirror,” protested the priest. “That’s what I told you,” said the rabbi. “That’s your head—you’re a gentile and you won’t understand—according to the Gemara you have to consider all possible angles—all the possibilities.” “Fine,” sighed the priest. “Let’s try again. Ask me another question.” “Last time,” said the rabbi. “Two people fall down a chimney. One comes out dirty and one comes out clean. Which of the two goes to wash?” “It’s very simple,” smiled the priest. “If there’s no mirror—the clean one looks at the dirty one, thinks he’s dirty, and goes to wash; the dirty one looks at the clean one, thinks he’s clean, and does not wash. If there is a mirror—the clean one looks in the mirror, sees he’s clean, and does not wash; the dirty one looks in the mirror, sees he’s dirty, and goes to wash.” The rabbi said to him, “I told you you wouldn’t understand—you’re a gentile and you have a gentile’s head—explain to me how it could be that two people fall down a chimney and one comes out dirty and the other clean?!”

For my part, I’d resolve it easily: after the first fellow went down the chimney, he scraped off all the soot onto himself, so the second came out clean. Even a Jew who learns Daf Yomi can’t grasp that—unless he’s an analytical lamdan. Incidentally, I recall hearing a funnier version, but I couldn’t find it now (see here for the various incarnations of this joke. The best version is, of course, Amnon Yitzhak’s video).