A Talmudic Source for R. Shimon Shkop’s Principle of Consistency (Column 617)
To Rivka, my dear daughter
In columns 407 and 466 I described and explained R. Shimon Shkop’s proposal for stopping halakhic loops based on what I there called the “principle of consistency.” We saw that this is not a logical principle but a meta-halakhic one (the paradox is not resolved on the logical plane but by introducing an additional meta-halakhic principle, which is a halakhic innovation). We further saw that the foundation of the solution is the assumption that the order among the events is not in real time; rather, the entire chain of events occurs at a single moment. The internal ordering between them is along the causal axis and not the temporal axis. Nevertheless, that order determines what remains in force and what is nullified.
A few days ago I learned with my daughter Rivka, may she live and be well, a sugya in Yevamot regarding the rule that a prohibition does not take effect upon an existing prohibition (ein issur ḥal al issur), and we understood that prima facie one can find there a source for R. Shkop’s principle of consistency. We will begin with the sugya itself and then return to the principle of consistency.
An Introduction on Yevamot and Mathematics
Many sugyot in Yevamot deal with complex family relationships. The “genealogy” there is a true logical delight. Suddenly you understand why the world needs families, and how boring it would be without them. A mathematical background can certainly help the learner, or at least make things easier. For example, if you speak of “the maternal brother of the son of Reuven’s uncle,” and you ask: what is Reuven in relation to him? (A very common question in Yevamot, and in Sanhedrin regarding disqualifications due to kinship.) Operator theory immediately gives you the answer: to invert the chain of relations from Reuven to Shimon and obtain the chain from Shimon to Reuven, you must reverse the order of the links in the chain and invert each one. Thus, for example, “brother of my father’s uncle” means I am “nephew (the inverse of ‘uncle’) of the son (the inverse of ‘father’) of his brother (the inverse of ‘brother’—the identity operator).” The explanation is very simple: if we assume that the relation between me (I)) and Reuven (R) is as follows:
R = ABCD (I)
Then the reverse relation is:
I = D-1C-1B-1A-1 (R)
If you substitute the previous relation you obtain an identity:
R = ABCD (I) = ABCD D-1C-1B-1A-1 (R) = R
The product of two inverse operators cancels out (nephew of uncle is the identity relation; son of father is the identity relation; etc.)[1]. Note that you can delete the middle D D-1, then delete CC-1, and so on. This is what is called “telescopic cancellation.”
It follows that the inverse of the relation I described above is the following: Reuven is the nephew of the father of his maternal brother. Anyone who has studied Yevamot and Sanhedrin can appreciate how much this simple rule can help. My friends from the “Netivot Olam” yeshiva can tell you how I saved them from these quagmires.
The Sugya of Two Brothers Married to Two Sisters
In the Mishnah, Yevamot 32a, the following simple case appears (when you study it you’ll see that even tracking the developments of this simple double chain is quite difficult):
Two brothers married two sisters. One of them died, and afterward the wife of the second died—she is forbidden to him forever, since she was forbidden to him for even one hour.
Reuven is married to Rachel, and his brother Shimon is married to Leah, her sister (always assign names—preferably from a biblical family while preserving as many relationships as possible; advice worth gold). The complication begins here with the fact that the relationship between any two of this foursome can be described in either of two ways. For example, Reuven is both the husband of Leah’s sister and the brother of her husband. The same holds for Shimon and Rachel. Alas—the worst has happened—and one of them died. As is well known, disasters come in bundles, and the wife of the deceased falls for yibbum (levirate marriage) before his brother. Now let us not forget that he is both the husband of her sister (and therefore she is his wife’s sister, according to the inversion rule above) and the brother of her husband (and she is his brother’s wife, again by that rule).
What do we do? We are not perturbed by the prohibition of “his brother’s wife,” for this is precisely the novelty of the commandment of yibbum: the prohibition of a brother’s wife is overridden by the mitzvah of yibbum. But here there is another incest prohibition: a wife’s sister. This is not overridden by the mitzvah of yibbum; rather, it cancels it. The mitzvah of yibbum applies when the only obstacle is the prohibition of a brother’s wife, but any additional incest prohibition nullifies it.
In the case described in the Mishnah, Reuven dies, and then his wife Rachel falls before Shimon for yibbum. Shimon cannot perform yibbum with her because she is also his wife’s sister (Leah). But the righteous Leah also dies in a sudden tragedy (their family name: Reuven and Shimon of the House of Hard-Luck), and now Rachel would be permitted to Shimon (for one’s wife’s sister is not forbidden to him after his wife’s death). Nevertheless, the Mishnah states that since at the moment Reuven died and Rachel fell for yibbum, yibbum was not possible (because Leah was still alive), then even if Leah dies afterward, the mitzvah of yibbum is already void; therefore even now Shimon cannot perform yibbum with Rachel (note that if there is no obligation of yibbum, there is an incest prohibition, for she is his brother’s wife. In the realm of yibbum there is no neutral state of permission: either there is an obligation to perform yibbum, or doing so is prohibited).
The Gemara brings a Tannaitic dispute regarding one who had relations with his wife’s sister (Rachel) while his wife (Leah) is alive:
Our Rabbis taught: If he had relations with her, he is liable on account of his brother’s wife and on account of his wife’s sister—these are the words of R. Yose. R. Shimon says: he is liable only on account of his brother’s wife.
According to R. Yose, he is liable for both wife’s sister and brother’s wife. According to R. Shimon, he is liable only for brother’s wife. R. Yose’s position is more readily understood, for if there is no mitzvah of yibbum then not only the prohibition of wife’s sister exists here, but also that of his brother’s wife (it is not overridden, since there is no mitzvah of yibbum). But R. Shimon’s view is puzzling, for he leaves one prohibition in place—and specifically the prohibition of brother’s wife, which one might have thought would be overridden by the mitzvah of yibbum. The prohibition of wife’s sister, which one would expect to remain, does not appear according to him.
The Gemara brings a contradictory (and more intuitive) baraita in R. Shimon’s view:
But isn’t it taught: R. Shimon says, he is liable only on account of his wife’s sister.
And resolves:
Not difficult: here (the first source) is where the living [brother] married first and afterward the dead [brother] married; there (the baraita) is where the dead [brother] married first and afterward the living [brother] married.
If Shimon (the living one) first married Leah and afterward Reuven married Rachel, then from Shimon’s perspective Rachel was first his wife’s sister and only afterward his brother’s wife. In such a case only the prohibition of wife’s sister takes effect, and the second prohibition does not, because a prohibition does not take effect upon an existing prohibition. That is the case of the contradictory baraita. But if Reuven (the one who later dies) married Rachel before Shimon married Leah, then relative to Shimon Rachel was first his brother’s wife and only afterward his wife’s sister; in such a case only the prohibition of brother’s wife takes effect, and that is the first baraita.
Now the Gemara asks:
And according to R. Shimon, in a case where the dead [brother] married first and afterward the living [brother] married—since the prohibition of wife’s sister does not take effect, let her undergo yibbum!
In the case where Reuven married first, only the prohibition of brother’s wife takes effect and not that of wife’s sister, and the mitzvah of yibbum overrides the prohibition of brother’s wife. So why not perform yibbum in such a case?
Rav Ashi explains:
Rav Ashi said: The prohibition of wife’s sister is suspended and stands; if the prohibition of brother’s wife falls away, the prohibition of wife’s sister comes and takes effect; therefore it [the prohibition of brother’s wife] does not fall away.
R. Shimon holds that if the prohibition of brother’s wife took effect first, then the prohibition of wife’s sister remains hanging and suspended; if the mitzvah of yibbum were to push aside the prohibition of brother’s wife (as usual), then nothing would prevent the prohibition of wife’s sister from taking effect, and it would prevent yibbum. Therefore the prohibition of brother’s wife remains in place (since there is no mitzvah of yibbum to override it).
The Problem with This Explanation
This explanation seems to stop halfway. For we have now arrived at the conclusion that the prohibition of brother’s wife exists and that of wife’s sister does not; but then one can continue and say: let the mitzvah of yibbum come and override the prohibition of brother’s wife—then the prohibition of wife’s sister will take effect and neutralize the mitzvah of yibbum, which will restore the prohibition of brother’s wife, which will remove the prohibition of wife’s sister and restore the mitzvah of yibbum that will again nullify the prohibition of brother’s wife—and so on ad infinitum. I wanted to end with “Chad Gadya, Chad Gadya,” but that would be a poor ending, since in Chad Gadya there is a clear hierarchical chain and no loop. Here the problem is that there is a loop that does not stop. For some reason the Gemara chooses to stop it at a certain point, and it is not clear why.
We saw similar difficulties in columns 406–407 regarding loops that the Gemara or the Rishonim choose to stop at some point without any apparent reason. For example, a red heifer upon which a yoke was placed with the owner’s consent: if that disqualifies it, then certainly it was not with the owner’s consent; but if it was not with his consent then it is not disqualified; but then it was with his consent; and so on. Likewise regarding pesik reisha de-lo nicha lei: the person is exempt and then he does want the forbidden result; but if he wants it he is liable and then he does not want it; and so on. Likewise regarding migo: if we accept the principle, it destroys itself (for the person chooses the “weaker” claim because it is not weaker but rather better thanks to the migo), so there is no migo; but then the claim is indeed weaker; and so on.
The Principle of Consistency: A Reminder
In those columns and in column 466 I also brought Tosafot’s example in Gittin regarding Reuven who divorces his wife on condition that she not marry so-and-so, and then she goes and marries so-and-so—this cancels the divorce (for the condition was not fulfilled). But then she is still Reuven’s wife and therefore her marriage to so-and-so does not take effect; but if so she did not violate the condition and her divorce from Reuven stands; but then her marriage to so-and-so stands (for she is single), which in turn cancels the divorce; and so on.
For this loop R. Shimon Shkop innovated his principle of consistency, whose core is the following meta-halakhic rule: any legal effect (status/act) whose taking effect would uproot itself cannot take effect. In the yeshiva idiom: any effect such that “if it takes effect, it does not take effect”—does not take effect. In our case, her marriage to so-and-so cannot take effect, because if it were to take effect it would uproot itself; therefore it does not take effect. Here the loop stops. One could continue and ask: if she is divorced from Reuven, why should she not be considered married to so-and-so—after all, she is not a married woman? The answer is that she is not married to so-and-so not because she is a married woman, but because the marriage to so-and-so would uproot itself, and there is a halakhic rule that a self-uprooting effect cannot be effected. We remain with a state that seems self-contradictory (a state we did not encounter at any stage in the infinite loop): she is divorced from Reuven but not married to so-and-so—and there we stop.
I explained that this halt has no logical explanation. Logically, the loop continues to infinity. There is here a meta-halakhic assumption about the imposition of effects that uproot themselves. This assumption is not logically necessary, but halakhah presumes it (according to R. Shimon). I also noted that this meta-halakhic assumption alone is insufficient; we must add another assumption: that we view each stage in this process as if it temporally follows the previous stage. If this were not so, then even the divorce from Reuven could not take effect, for its taking effect would uproot itself (because of the marriage to so-and-so).
But if we assume there is a kind of “as-if temporal” sequence, then we begin our journey on the true time axis at the stage where she divorced Reuven. At that stage there is no problem with that divorce, and it does not uproot itself. Afterward real time moves on, and in the next stage she goes and marries so-and-so. At that stage those marriages cannot take effect because they are an effect that uproots itself (for the divorce already preceded them). How do they uproot themselves? That occurs along an internal time axis: after she “marries” so-and-so we go back “in time” and it emerges retroactively that the divorce from Reuven was canceled. But that is a mistake. We do not really go back in time; rather, we move along an internal time axis that, from the perspective of ordinary time, all occurs at a single instant (the instant she “marries” so-and-so). At that instant the marriage to so-and-so uproots the divorce from Reuven, which in turn cancels the marriage to so-and-so. But this entire process is not a real return to the time of the divorce and a forward progression back to the marriage to so-and-so. All of this occurs along a fictitious internal time axis that is entirely hidden within the moment when she “marries” so-and-so. Within that moment she as it were progresses along another, internal, axis whose ordering is causal rather than temporal: the divorce enables the marriage to so-and-so to take effect—yet the marriage to so-and-so uproots the divorce, and therefore, on this internal axis, it comes before the divorce (because causally it precedes it), even though on the external time axis the marriage to so-and-so comes after the divorce. We regard this ordering as if there were an additional (internal) time axis here, but in truth it is not time but causal order.
In column 407 we saw that this principle, together with the additional assumptions, stops all these loops and many others (I there referred to the fourth volume in the “Talmudic Logic” series, which surveys very many examples of halakhic loops). I also showed there a case in which the internal-time assumption alone suffices to stop the loop, even without adding the principle of consistency. For our purposes: can such a mechanism explain Rav Ashi’s words in our sugya in Yevamot?
Back to Rav Ashi
It seems to me the answer is yes. Recall that we are dealing with a case where Reuven (the one who dies) married first. In such a case, the prohibition of brother’s wife is the first to take effect on Rachel relative to Shimon. Now Shimon marries Leah, and the prohibition of wife’s sister “wants” to join and take effect on Rachel as well. But it does not take effect, for a prohibition does not take effect upon an existing prohibition. Yet, as the Gemara says, it does not dissipate and disappear; rather, it remains “hanging and suspended” (if the prohibition of brother’s wife falls away for some reason, it will take effect in its place). Now Reuven dies, and his wife Rachel falls to Shimon for yibbum. The mitzvah of yibbum “awakens” and seeks to push aside the prohibition of brother’s wife. But if the prohibition of brother’s wife disappears, the prohibition of wife’s sister will take effect and neutralize the mitzvah of yibbum. Here the loop stops, because we see that if the mitzvah of yibbum were to take effect, it would uproot itself; therefore, according to R. Shimon Shkop’s principle of consistency, the mitzvah of yibbum cannot take effect. Note that this occurs even though the prohibition of wife’s sister has not taken effect on Rachel (it is merely suspended), and therefore it is not that prohibition that “stops” yibbum. The reason it does not take effect is not the prohibition of wife’s sister, but R. Shimon’s principle of consistency: its taking effect would uproot itself (because it would remove the prohibition of brother’s wife, which would then allow the prohibition of wife’s sister to take effect and cancel the mitzvah of yibbum). As we have seen, such a mitzvah cannot take effect.
Up to this point we applied the principle of consistency to the mitzvah of yibbum. An alternative formulation applies the principle to the prohibition of wife’s sister: suppose the mitzvah of yibbum pushed aside the prohibition of brother’s wife; the neutralization of that prohibition would allow the prohibition of wife’s sister to take effect on Rachel, which would prevent the mitzvah of yibbum from taking effect, which would leave in place the prohibition of brother’s wife, which would again prevent the prohibition of wife’s sister from taking effect. In other words, the prohibition of wife’s sister uproots itself, and therefore it too does not take effect. The only status that remains in such a case is the prohibition of brother’s wife—neither the prohibition of wife’s sister nor the mitzvah of yibbum. How does this happen? The prohibition of brother’s wife took effect on the real time axis even before the whole story begins—at the moment Reuven married Rachel. At that moment, Leah is not yet Shimon’s wife, and certainly there is not yet any obligation of yibbum, so that marriage takes effect and, as a result, so does the prohibition of brother’s wife. Nothing prevents their taking effect. By contrast, both the mitzvah of yibbum and the prohibition of wife’s sister—each one, at the moment it would take effect, would uproot itself, and therefore cannot take effect.
The final state according to R. Shimon (bar Yochai, not Shkop) is that there is a prohibition of brother’s wife, but there is no mitzvah of yibbum and no prohibition of wife’s sister. This seems contradictory, for if only the prohibition of brother’s wife exists, the mitzvah of yibbum should apply (what cancels it if there is no prohibition of wife’s sister?!). But then the prohibition of wife’s sister would take effect, and so on. However, as we saw above, that is not correct. The prohibition of brother’s wife exists, and nevertheless there is no mitzvah of yibbum. There is no mitzvah of yibbum not because of the prohibition of wife’s sister, but because it is a self-uprooting effect.
The sting of this whole move is that we assume that this loop does not actually occur along the true time axis (we do not actually move back and forth in time), but along a hypothetical causal axis. If the process were real, then what would uproot the mitzvah of yibbum would be the prohibition of wife’s sister. But we are speaking of a hypothetical process—something that happens along an internal “time” axis (which is really a causal axis): when the mitzvah of yibbum “wants” to begin to take effect, we make a hypothetical calculation of what would result if it did in fact take effect, and we discover that it would end up uprooting itself. Consequently, it does not begin to take effect. It is not that it takes effect and then the prohibition of brother’s wife is uprooted and then the prohibition of wife’s sister returns. Rather, it is a hypothetical argument: if it were to take effect, it would uproot itself; therefore the entire process does not begin at all. This is why, as I wrote above, the mitzvah of yibbum does not take effect not because of the prohibition of wife’s sister, but because it is self-uprooting. No loop is formed and the earlier difficulty does not arise.
The difficulty was based on our assuming that the entire process actually occurs back and forth along the time axis, in which case there would be no way to stop it. The core of my explanation is that the process is purely hypothetical and does not occur in reality—exactly as we saw in R. Shimon Shkop’s halting of the loop. There, too, the difficulty arose because we thought everything is happening in actuality: the condition is violated and then uprooted and then reinstated, and so on. R. Shimon’s answer is that it is a hypothetical process that does not occur in reality: we merely ask, “If the marriage to so-and-so were valid, what would happen?” When we discover that it would uproot itself (and not that it actually uproots itself—since it does not actually occur), the conclusion is that it does not take effect at all. The entire chain does not begin in reality.
Back to the Question of a Source for the Principle of Consistency
We have seen that Rav Ashi’s “loop” is not real but a hypothetical thought experiment we conduct: what would happen if all this were to occur? This is the meaning of the mechanism innovated by R. Shimon Shkop, and in this sense it seems to me that our sugya is an excellent source for his innovation. Without it, it is very hard to understand, for we remain with an infinite logical loop and Rav Ashi’s words are unintelligible.
Admittedly, Tosafot in Gittin itself would seem to be a source for the principle of consistency, for without it there is an infinite loop. Moreover, that is proof from the Gemara and not merely from Tosafot, since Tosafot is only challenging the Gemara. It emerges that without the principle of consistency one cannot understand the Gemara. So why is our sugya in Yevamot a better source than the sugya in Gittin itself? In Gittin it is a question, and in principle someone might have proposed another answer to resolve it. Here it appears that Rav Ashi states the principle of consistency explicitly. It is not merely the result of a difficulty and calculation within the sugya. Therefore, in my view, the Yevamot sugya is truly a source for the principle of consistency, and now we can use it to resolve the sugya in Gittin as well as all the other loops I mentioned.
Another Example of Moving from Practical to Hypothetical Reasoning: The Categorical Imperative
I wish to conclude with another example of the significance of moving from practical reasoning to hypothetical reasoning, as in the principle of consistency. In columns 122, 344, and elsewhere I discussed the categorical imperative, and I pointed out that there too a similar error occurs.
Consider a person who claims there is no point in going to vote in elections or in paying income tax because this step has no effect (I explained there why my vote will not change the outcome of the elections, and why one person’s tax evasion does not change the country’s economic situation at all). The usual response to such a person is the consequentialist one: what will happen if everyone does as you do? Clearly, if everyone evades taxes the state coffers will be empty, and if no one goes to vote there will be anarchy. His reply is that those would indeed be very undesirable states, but they will not actually occur—at any rate not because of him. After all, every person makes his own calculation privately (and does not talk about it with anyone else, certainly not regarding tax evasion): whether to evade taxes and whether to go vote. Everyone makes his own decision as he did, and the decisions of all people are not affected by what I decide. Therefore we return to the claim that my step has no effect. Even in a situation where everyone decided to evade taxes, the state’s condition would indeed be dire, but my hundred shekels would still make no difference. They did not cause everyone else’s decisions. Thus, prima facie, there is no argument here that should make me change my policy.
I explained that one can propose a solution to this in terms of Kant’s categorical imperative. The claim against such an offender is not consequentialist (“If you do this, everyone else will do so as well”). The consequentialist claim is indeed mistaken. The claim against him is philosophical-hypothetical: make a hypothetical calculation of what would happen in the hypothetical case that everyone behaved as you do (even though in reality this will not happen—at least not because of you). If the result seems bad to you, then the act in question is bad—and therefore you must not do it. If the result seems positive to you, there is no problem—do it. This is no longer a claim that can be dismissed in the same consequentialist way, since it does not deal with practical consequences. The consideration here is not what will actually happen, but what would happen in the hypothetical case that everyone decides to act thus. The hypothetical consideration does not seek to examine the consequences of your act; rather, it is a gauge for determining the goodness or badness of the act under discussion. The state that would emerge if everyone did X determines the nature of the act X. If that state is bad, then X is a bad act (even though my own X did not produce that state). If it is a bad act, it is forbidden; again, irrespective of consequences. If the state is positive, then X is a good act, and therefore there is no barrier to doing it—again, irrespective of consequences.[2]
Thus, here too, our problem arises because we raised a practical consideration regarding the actual consequences of the act in question (a consequentialist consideration). It is resolved by our moving from a practical-consequentialist consideration to a hypothetical one (what would happen if), exactly as we saw in R. Shimon Shkop’s principle of consistency.
Admittedly, there is no loop here, and therefore the similarity between the cases is not complete. But if you consider the point I raised in column 122—namely, the consequentialist consideration—you will obtain a genuine loop (there are bad consequences, but still it makes no difference to me because my act by itself has no effect; but then everyone will say it makes no difference to them for the same reason, and then there will be an effect; and so on). The way to solve the problem is to stop the loop by moving to hypothetical reasoning. Now the similarity between the categorical imperative and the principle of consistency is much stronger.
[1] There is non-uniqueness, because a person can have several brothers; therefore “brother of my brother” is not necessarily me, and likewise “son of my father” or “nephew of my uncle.” Hence such a chain does not necessarily pick out a single definite person; but in principle the chains of family relations obey these relations. I have always wondered whether it is correct to say that I am my own brother, since we have the same parents (see column 81).
[2] Admittedly, in column 122 I showed that one can translate this consideration into a consequentialist one via the Prisoner’s Dilemma. But for our purposes here that is not important.