Logical Loops and Self-Reference – Continued (Column 407)
In the previous column I discussed self-reference. We saw there that such a situation sometimes creates a paradoxical loop, but in many cases it is entirely legitimate. As we saw, it is used both in mathematics and in halakhah. Among other things, we saw the use of such loops to prove or reject claims in various ways, and I wondered, in certain cases, how those who make use of such self-reference stop the loop. In this column I will examine a possible solution.
Three Examples from the Previous Column
There are three examples on which I focused in this context: the Red Heifer, pesik reisha de-lo nicha lei, and migo.
- The Red Heifer is invalidated if a yoke is placed on it with the owner’s consent. The claim was that the owner will never consent, because such consent disqualifies his cow and lowers its value. But that empties of content the disqualification in a case where the owner consents, since he will never consent and the heifer will never be invalidated. The Ran resolved this by saying that if, because of this, we do not invalidate the heifer, then once again the owner will consent, and again we will have to invalidate it. I asked why he stops the loop here and does not continue it ad infinitum. How does such an argument explain the heifer’s disqualification? The conclusion is that at most we cannot determine whether the heifer is invalidated or not. Perhaps the laws of doubt should be applied here.
- So too regarding pesik reisha de-lo nicha lei, which according to the Arukh is exempt. It was objected (in the comments, Sandomilof cited this from Rabbi Ovadia) that a person is never pleased to be liable to stoning; and some answered, like the Ran above, that if we exempt him, then again it will be pleasing to him and he will be liable. Here too I found it difficult: why stop the loop precisely here and not continue it ad infinitum? Why is this an explanation of the exemption according to the Arukh? At most, the laws of doubt apply.
- And regarding migo, we saw that if we adopt the evidentiary force of migo, it undermines itself, for the alternative claim is then no longer better. And there too some argued that if we accept that this undermines it and we do not recognize migo as a consideration, then the other claim again becomes better than this one, and the migo revives. Again, it is difficult: why stop the loop and not continue it forever? Under the laws of doubt, the money will remain in its current presumption. [1]
I thought it may be possible to explain the difficulties regarding these examples through a well-known foundation formulated by R. Shimon Shkop in his Sha’arei Yosher, widely circulated in the yeshiva world, in the following wording: “Any legal status such that if it takes effect it will thereby not take effect—then it does not take effect.” [2] In this column I will try to examine this.
Rabbi Shimon Shkop’s Consistency Principle
R. Shimon discusses a statement of Tosafot in Gittin. By way of introduction: a condition phrased “on condition that (ʿal menat)” is one where the legal effect under discussion operates retroactively if the condition is fulfilled. If a man gives a bill of divorce to a woman in 1980 on the condition “on condition that you not drink wine for ten years,” then if she does not drink wine throughout those ten years (until 1990), the get takes effect retroactively from the moment it was given (in 1980). In Gittin 83a the Gemara discusses one who gave his wife a get on the condition “on condition that you not marry so-and-so,” and states as follows:
R. Akiva responded and said: Suppose she went and married a man from the marketplace and had children, and was widowed or divorced, and then rose and married the one to whom she was prohibited—does it not follow that the get is annulled and her children [from the second husband] are mamzerim?!
That woman, who received a get conditioned on “on condition that you not marry so-and-so,” married another man (which of course does not contradict the condition). After her second husband died or divorced her, she went and married that so-and-so to whom the condition referred. R. Akiva assumes that in such a case the condition uproots the get retroactively. Consequently, the children who had already been born to the second husband earlier become retroactively mamzerim.
On this, Tosafot (s.v. “ve-ʿamdah ve-nisset”) remark there:
“And she rose and married the one to whom she was prohibited—does it not follow that the get is annulled?” And if you will say: But the marriage cannot take effect, since she is prohibited to him as a married woman. In what way is this different from what was taught in the Tosefta: ‘On condition that you not marry my father or your father—this is a get. On condition that you not have relations with my father or your father—this is not a get; we are concerned lest she have relations with them’? This implies that ‘on condition that you not marry them,’ even if she married them, this is a get. So here, why is the get annulled?
Tosafot ask: Why does R. Akiva assume that if she married him the get is annulled? For if the get from the first husband is annulled, then she is still married to the first husband, and therefore her marriage to the second and also to so-and-so (the third) cannot take effect, since she is a married woman. But if she is not married to so-and-so, it turns out that she in fact did not violate the condition of the divorce, and therefore the divorce is valid. [3] Tosafot answer that the case is that she married after the death of the divorcer, but that is not important for our purposes. Their reasoning in the question is that in a case where she married the one prohibited to her (and not after the divorcer died), the divorce is valid—contrary to the simple reading of the sugya. For some reason, Tosafot decided to stop the loop after the first step; and you can already see the analogy to our cases. Here too the obvious question is why stop precisely here and not continue to infinity.
R. Shimon Shkop, in Sha’arei Yosher (Shaʿar 7, ch. 16, p. 258), addresses this question on Tosafot’s words and writes:
“Because such a marriage cannot take effect, for if it were to take effect it would be annulled retroactively due to the condition. And likewise, something that has no possibility of taking effect does not take effect at all; therefore the get stands and the marriage is void.”
His claim is that there is a general meta-halakhic principle stating that any legal effect such that, if it were to take effect, it would uproot itself from the outset—already now it does not take effect. A status whose very existence would uproot itself cannot be effected.
This seems to be a method with the potential to solve our problems as well. It provides a general criterion for stopping loops. To apply it to our cases, we must examine this principle more closely.
The Difficulty with R. Shimon’s Proposal
R. Shimon argues that if there is a marriage whose taking effect would uproot itself from the outset, it cannot take effect. Therefore, Tosafot stop the loop by saying that the marriage to the second [so-and-so] did not take effect, and therefore the get is valid. But one may ask: why not say the same about the divorce from the first husband? If those divorce effects take effect, they are uprooted retroactively; so seemingly they too should not take effect. If so, even after Tosafot’s innovation, the loop resumes. Why do Tosafot choose to say this only about the marriage to the third party and not about the divorce from the first? Apparently, R. Shimon’s words still do not explain the breaking of the loop’s symmetry.
The answer is that there is a difference between the divorce from the first husband and the marriage to the third. The legal effect of the divorce from the first does not, by its very nature, uproot itself. That happens only because afterward she went and married so-and-so (the third) and thus violated the condition—and only then are the divorce effects uprooted. Had she not done this, the divorce would have remained valid. That is, those divorce effects do not inherently include their own uprooting; this happens only because of later events (which, in particular, need not have happened). By contrast, the marriage to so-and-so (the third), by its very definition, uproots itself without any addition beyond that. The marriage to so-and-so occurs after she was already divorced conditionally (without that divorce she could not have married him at all). Therefore, there it is considered an act which, at the very moment it is performed, severs the branch on which it seeks to sit. R. Shimon claims that such a halakhic act cannot create the legal effect it attempts to create.
This is what we called in our fifth book “R. Shimon Shkop’s consistency principle”: an act that effects a legal status must have consistent results (i.e., must not be uprooted by that very act itself). If they are not, the act cannot effect the status in the first place.
An Additional Assumption Regarding the Causal Order of Events
To better understand what this means, we must return to clarify what would happen absent this principle. Without the consistency principle, we would say that when she married so-and-so, the marriage takes effect, and only afterward its taking effect uproots the divorce; now she becomes the wife of the first husband, and the chain continues. Absent R. Shimon’s rule, there would be a loop with its tail in its mouth—very much like the liar paradox.
What changed after R. Shimon’s (and Tosafot’s) innovation? The consistency principle alone is insufficient to solve the problem, since as we saw it could have been applied both to the initial divorce and to the marriage to so-and-so. Our ability to apply it specifically to the marriage to so-and-so and not to the divorce stems from the fact that Tosafot and R. Shimon implicitly add another innovation (which we discussed at length in the fourth book of the series, on halakhah’s relation to the time axis): that this set of uprootings and counter-uprootings—which all occur simultaneously (at the moment of her betrothal to the third party)—is nevertheless viewed as a chain of successive events, as if they occur one after another along a time axis. True, their succession is not on real time but on a causal axis. Each one causes the next, even though they occur simultaneously. R. Shimon’s innovation is that halakhah views the axis of causal production as if it were an internal time axis of the event. Therefore, even if all the events occur at the same instant on the real timeline, we still view them as events appearing successively on that internal timeline (the causal axis), reflecting the fact that each depends on its predecessors.
Only because we treat these events as successive events that appear one after another and not all at once can we use R. Shimon’s principle and evaluate each stage in the chain on its own, at the moment (i.e., at the logical-causal stage) when it attempts to operate. We examine each stage separately at its “occurrence,” and only if the stage under discussion passes the consistency test does it successfully effect the relevant legal status; then we proceed to the next causal stage. Let us now describe this in more detail using Tosafot’s example.
At the first stage on the causal axis, the get is given. When we examine this act, there is no problem with it (for it does not inherently uproot itself, so long as she does not marry so-and-so), hence the conclusion is that now the get takes effect. Afterwards she goes and marries a second man (which is, of course, permitted), and that too takes effect because there is still no contradiction to the condition of the divorce from the first. Afterwards the second dies or divorces her, and she goes and marries so-and-so (the third, to whom she is prohibited by the condition of the first). Here the evaluation already reveals a problem, for if these betrothals take effect, they immediately uproot themselves then and there (without dependence on anything else; everything has already happened in the “past,” i.e., earlier on the causal axis). Therefore, at this stage we stop the loop and declare that the betrothal to so-and-so, the third, does not take effect from the outset (not that it takes effect and is annulled, as the simple reading of the Gemara suggests). It is important to understand that these nuptials are not annulled by the condition or its consequences—i.e., they do not take effect and then the condition that nullifies the divorce to the first husband returns and nullifies them. Rather, they do not take effect at all due to R. Shimon’s consistency principle, by which a legal effect that uproots itself cannot take effect. Thus the loop stops. It is important to see that there is now no reason to return and discuss the divorce, for if she did not marry the third, then the condition of the divorce was not violated, and everything remains as it was: she is not married to the first (because she divorced him) and not to the third (because the attempted marriage to him is a self-uprooting legal effect, which therefore does not take effect).
R. Shimon’s principle created here a state that, from the ordinary perspective, is impossible: she is not married to the first and also not to the third. [4] This is why Tosafot stop the loop with the conclusion that the divorce from the first remains in force. Thus, R. Shimon holds that in the end the divorce is valid and the marriage to the third is not—because of his special principle that any legal effect which uproots itself does not take effect from the very first moment.
Another Example
In the fifth book we analyzed in this manner a whole series of paradoxical halakhic loops, and we saw that in almost all of them the consistency principle solves the problem and provides a criterion to stop the loop. However, we found at least one case where the loop can be stopped using assumption 1 alone, without invoking the consistency principle (assumption 2). First I will illustrate the standard analysis with one more example—concerning the validity of a get written on Shabbat—which requires both of R. Shimon’s assumptions.
The loop here is based on the following premises: Halakhah prohibits writing on Shabbat. However, if one writes over existing writing, that is not considered writing—unless the upper writing corrects something lacking in the lower writing. In addition, a get must be written by a qualified person. One who writes something on Shabbat is considered a mumar (apostate), and therefore is not qualified. Furthermore, a get must be written lishmah (for the sake of the divorced woman). If a get was not written lishmah, it can be corrected by tracing over that word with the quill while intending lishmah.
In light of all of these premises, the author of Minḥat Ḥinukh (commandment 32, “Mussach HaShabbat,” sec. 34) raises the following question:
“A get that had been written not for her sake, and on Shabbat he traced over it for her sake intentionally—what is the law? Now, if he wrote a get intentionally on Shabbat he is a mumar and it is not a valid get; but here, if we say it is not a get because he is a mumar—in truth, if it is not a get then he did not desecrate Shabbat at all, since writing over writing is permitted on Shabbat unless it corrects, and if it is not a get then it was not a correction. If so, he is not a mumar and the get is valid. But if the get is valid, then he becomes a mumar and it is invalid. This depends on that. How are we to judge this matter? If the get is valid it is invalid because of mumar; and if we say it is invalid because of mumar, then he is not a mumar, for he did not desecrate Shabbat. This requires further inquiry.”
A man wrote a get for his wife not lishmah. The get is invalid, so he wishes to fix it and traces over it with lishmah to render it valid. But he does this on Shabbat. If indeed the second writing succeeds in validating the get, then it is considered writing prohibited on Shabbat, since it corrected something that was lacking in the lower writing. But if this is prohibited writing on Shabbat, then the writer is deemed a mumar (a Shabbat violator is considered an apostate for the entire Torah) and therefore disqualified from writing a get. Consequently, the upper writing added nothing, and again it is not considered prohibited writing; then he is not a mumar, and the get is valid. But if it is valid, then the writing is prohibited and he is a mumar, and so on ad infinitum.
This is a causal-normative loop, and it can be analyzed according to R. Shimon’s method: posit an order of events as if temporal (according to causal sequence), and at each stage apply the consistency principle. Let us follow this process. Initially he writes a get not lishmah; the get is invalid. Now he traces over it again on Shabbat. Does the get become valid? This is a normative, not factual, question, and the answer is negative. If the get were to become valid, then the writer would thereby become a mumar, and then the get would revert to being invalid (for it was written by a mumar). In other words, this is a legal effect that severs the branch on which it seeks to sit; by the consistency principle, it does not take effect at all.
Therefore, in the end this get remains invalid, since the legal effect that would validate it does not succeed in taking effect. Hence, clearly, the person also does not become a mumar. It is important to understand that the invalidity of the get does not stem from the fact that the upper tracing was done by a mumar, for ultimately we determined that he is not a mumar. The invalidity is due to the consistency principle, which prevents a legal effect that uproots the branch on which it sits from taking effect.
Interim Summary: Two Distinct Assumptions Underlying the Application of the Consistency Principle
As we saw in this example, the application of R. Shimon’s consistency principle rests on two different assumptions:
- Causal order. Despite the simultaneity of the entire occurrence, we initially ignore the consistency principle and arrange the events along the axis of causation as if it were a timeline on which the events appear in sequence, each leading to the next.
- Consistency principle. We then examine each such event: does its validity neutralize itself at the stage of its performance (i.e., at the point where it is placed in the causal chain)? Once we reach an event that neutralizes itself, the chain stops, since the result of such an event cannot take effect. Here the process ends.
I note that the consistency principle seems somewhat ad hoc, akin to Russell’s theory of types. R. Shimon adds an assumption whose justification is only that it offers a systematic way to stop loops. Can it be justified on its own terms? There is an intuition that it can. It is reasonable for a normative system to declare that it will not recognize a legal effect whose taking effect uproots itself. We are not dealing with facts but with norms; as such, they are entrusted to the normative system, which can decide whether or not to grant them force. Russell’s theory, by contrast, deals with facts and propositions about them, and there it appears entirely ad hoc.
On Halakhah and Logic: Can Logical Paradoxes Be Solved Similarly?
How did R. Shimon manage to solve a problem that seems equivalent to the liar paradox? Can all self-referential logical paradoxes be solved in a similar fashion? Take, for example, the “barber of Seville” paradox: a barber whose policy is to shave all those who do not shave themselves. Does he shave himself or not? If he shaves himself, then he belongs to the group of people he does not shave (those who shave themselves). But if he does not shave himself, then he is included among those whom he does shave (those who do not shave themselves). Can we apply R. Shimon’s consistency principle here too?
Apparently not. There are two main differences between the get paradox—halakhic—and the analogous logical paradoxes, which consist of factual propositions:
A. In a logical paradox, like the barber paradox, we cannot declare one of the statements false, for we assume they describe facts. This differs from the get paradox, which concerns normative-legal determinations (of divorce or betrothal taking effect). Regarding such determinations, we always have the option to rule that the legal act did not produce a status that took effect (in legal terms: it did not “crystallize”), i.e., that the woman is not divorced or not betrothed (though indeed we cannot say that a document was not given or that a condition was not stipulated—those are physical facts).
This difference is not relevant to the liar paradox, for there we are not dealing with statements that describe facts but with a statement about the truth values of statements (in particular, of itself). There, ostensibly, we can declare any of the statements false, since there are no factual premises but rather a judgment (albeit a logical one, not a legal one). But that is not correct, for even for such statements we are not the ones to decide their truth values. These are not normative claims. Their truth values begin in facts and are not subject to our decision. A claim is true if it corresponds to the fact it describes, and false if it does not. Therefore, this too is not in our hands.
B. Logic, by its nature, is atemporal. Therefore, a logical paradox is, by definition, atemporal. Let us use the liar paradox formulation, where this is easier to see.
(a) Statement (b) is true.
(b) Statement (a) is false.
This is the same loop as the paradox formulated in the previous column, but here there are two statements, each referring to the other. The enumeration a/b is arbitrary and could have been reversed. On the logical level, they must be treated as simultaneous—or atemporal. Therefore, one cannot perform an analysis like that of R. Shimon (for, as we saw, his analysis is based on viewing the events as if they were successive and causally linked).
True, even in normative paradoxes we are not dealing with real time, but with a causal axis (an internal time). However, the notion of “causation” we used can only appear in contexts involving relations between events in factual reality, whether physical or legal. The ability of a condition to operate forward and backward in time creates the paradox, but also enables its resolution. By contrast, logical relations are atemporal (as we demonstrated at length in the first part of the fourth book of the Talmudic Logic series). It is therefore incorrect to speak of a causal relation between statements logically related to one another; for this reason, R. Shimon’s analysis does not apply to them. As I showed in column 301 (in the discussion of logical determinism), the falsity of a sentence does not “cause” its truth value to be false. There is no causation here but rather a description of the same thing in other words. This is a logical dependence, not a causal relation, and on such a basis one cannot define a fictitious time axis as R. Shimon did.
For the liar paradox this is obvious. Clearly, the relation between the two statements comprising it is logical (one is true if the other is false, not because the other is false), and there is no causal relation between them. [5] And what about the barber paradox, which “shaves everyone who does not shave himself”? There, ostensibly, we are dealing with empirical facts and not abstract logic (like truth and falsity of statements). Yet even there the relation between the two links that create the paradox is not causal but logical. To see this, let us present this paradox in a three-line structure:
- X shaves every Y who does not shave himself.
- Y shaves himself.
- X shaves Y. [6]
It is easy to see that the relation between these statements is not one of causation, unlike the relation between conditional divorce and the fulfillment/violation of the condition. It is a logical relation between propositions, not a causal relation between facts. Once there is no causation, the events cannot be viewed as successive links on the causal axis. Consequently, R. Shimon’s consistency principle does not apply to these problems. Because of the symmetry in the relations between the statements, it cannot determine which of them is void and which remains valid.
Of course, one could artificially define such an axis even for logical paradoxes and arbitrarily decide that there is some order of succession between the statements, and then apply R. Shimon’s consistency principle. But that would not yield a real solution to the paradox; at best it would propose a formulation in which the paradox cannot be presented (i.e., it prevents its formulation). That is an ad hoc solution, much like Russell’s theory of types.
A Loop that Stops without the Consistency Principle
In analyzing the previous loops, we needed both components of R. Shimon’s method: arranging matters along the causal axis and the consistency principle. As noted, in our book we identified one case where assumption 1 suffices to stop the loop, even without assumption 2 (the consistency principle). This loop consists of a conditional divorce and the annulment of vows.
According to halakhah, one who vows not to eat something is prohibited from eating it. In addition, a husband can annul his wife’s vows (on the day he hears them), but only if he is indeed her husband. In light of these premises, R. Ḥayyim Berlin, in the journal Yagdil Torah (cited in responsa Menachem Meshev §1), raises the following question:
“A man divorces his wife on condition, effective from now and after thirty days, that during those thirty days if she refrains from eating any prohibited item the get shall be valid, but if she tastes any prohibited item the get shall not be valid. Within the thirty days she vows a loaf as konam, and her husband annuls her vow; she then eats the loaf relying on his annulment—Is she divorced or not? If we say she is retroactively divorced, then his annulment was no annulment, and she ate a prohibited item and is not divorced. But if we say she is not divorced, then his annulment is effective, and she ate a permitted item, and consequently she is divorced.”
A man divorces his wife on condition that during the month following the divorce she not eat anything halakhically prohibited. After ten days the woman vows not to eat a certain loaf of bread, rendering that loaf prohibited to her. But on that same day the former husband comes and annuls her vow. She then eats the loaf, since it is no longer prohibited to her, for her husband annulled it. What is the law in such a case? If the eating of the loaf was indeed permitted, then she is divorced from the moment the get was given; but in that case he is no longer her husband and cannot annul her vows. If, however, the vow was not annulled, then she ate a prohibited item, which cancels the divorce retroactively, so that he is indeed her husband and can annul it. To analyze this situation, we proceed in causal order and apply R. Shimon’s consistency principle at each stage.
At the first stage she divorces, and there is no impediment to that, for it is possible she will not eat any prohibited item in the coming month. Therefore, this act passes the consistency test. Next she vows, and of course that too takes effect, for she may vow and such a vow does not inherently neutralize itself. Next, the husband annuls it, and here the discussion begins. Does such an annulment fail to take effect? At this point he is not her husband, since the divorce took effect; hence the annulment has no meaning. Now she eats the loaf, and at this stage the loaf is prohibited. If so, the divorce now lapses retroactively. Crucially, this happens by virtue of an act and a condition. We did not need to invoke R. Shimon’s consistency principle (assumption 2). We now return to examine the husband’s annulment, and this time it turns out his annulment is valid, for he is her husband (the divorce lapsed). Now she eats the loaf, and it is permitted; consequently, the divorce should return and be established. But this is the stage at which the loop stops, for the divorce has already lapsed. A lapsed divorce cannot simply “re-establish” itself. For that to happen, the husband would have to give her a new get. Therefore, it seems that in such a case she remains the wife of the first husband.
Note that here we used only R. Shimon’s assumption 1, namely that such a chain of events should be treated as if they follow one another along the causal axis (as if there were a timeline), but we did not need to use the consistency principle at any stage. Every legal step taken here could have remained valid (depending on what she chooses to do—eat or not), and thus no step could be voided by the consistency principle as such. The reason is that here everything depends on a physical act (eating) and not on a legal status (betrothal or vow). When the matter depends on a legal status, we examine the validity of that status in light of the consistency principle. But eating a loaf is a physical act, and there is no room to say that it “does not take effect” due to the consistency principle. This is an example of a loop that can be resolved without R. Shimon’s consistency principle, relying only on his assumption 1.
We now come to the three loops from the previous column.
Application to the Three Halakhic Loops from the Previous Column
Our three loops are ostensibly similar to a logical, not a normative, paradox; thus, at first glance, the consistency principle would seem inapplicable. There is no legal effect entrusted to us such that we can decide whether it takes effect or not. Yet we must note that we are dealing with laws and not bare facts, and this allows us to formulate a principle similar to R. Shimon’s to stop such loops. In particular, nothing prevents us from assuming assumption 1 regarding them—i.e., to present the loops as if there were an internal temporal order between the stages, with the events arranged along it. Let us analyze the three examples.
In the Red Heifer loop, everything begins when a yoke is placed upon it with the owner’s consent. Now the heifer becomes invalid. But when it becomes invalid to the owner, that causes it to again become not pleasing to the owner, and therefore it becomes valid again, and so on. Here too, we arranged the events according to the internal causal order. One can say that the Ran stops the chain by noting that the owner’s pleasure cannot be voided, for that is a fact. What can be voided is the heifer’s invalidity or validity, because that is halakhah (a norm, not a fact, and therefore dependent on a halakhic decision rather than reality itself). The claim is that once the owner’s pleasure arose at the first stage, the heifer was invalidated. Halakhah fixes that legal state. Afterwards we no longer revisit the owner’s mindset, for that is already a factual state and we are at a stage where the owner’s mindset is fixed; therefore, the loop stops here. If at a later point the owner again becomes displeased, that occurs later on the (real) time axis, but the heifer has already been invalidated.
This analysis is similar to what we saw regarding R. Shimon’s consistency principle, but note that we are using only his assumption 1 (that the events have an internal temporal order along the causal axis). We did not use his consistency principle (assumption 2), since we are not dealing here with legal effects we ourselves generate, but with rules that the Torah sets. The consistency principle is not relevant to a halakhic status that is not the product of human legal action. Only because of the above analysis—which showed that at the foundation of R. Shimon’s method lies assumption 1 as well—could we apply these ideas to our case, which does not involve legal effects.
A similar analysis can be made for the pesik reisha loop according to the Arukh. A person performs a labor on Shabbat for another purpose (e.g., he drags a bench and makes a furrow, but this is done only in order to move the bench from place to place, not in order to furrow the ground). If it is a case where the furrow’s formation is inevitable (pesik reisha) and also pleasing to him (he needs the furrow in his yard), then he has desecrated Shabbat. But once there is Shabbat desecration, this becomes displeasing to him because he becomes liable to stoning, and according to the Arukh, pesik reisha de-lo nicha lei is exempt. Again, we have a chain that interweaves halakhic statuses with the person’s factual mental states. And again, we say that mental states are not in our hands, for they are facts. The halakhic status is a norm, and as such it is determined by halakhic judgment. Therefore, once it was pleasing to the person at the first stage, he is liable; even if that liability then renders it displeasing to him, his mental state at that stage is already fixed and not in our hands, and hence the loop stops there. Any change that occurs takes place later along the (real) time axis and can no longer alter the state already established.
However, regarding the migo example, it seems difficult to offer a similar analysis. True, there is a similarity to the previous cases, in that the claim that migo provides evidence is indeed a halakhic determination, whereas what the person thinks are facts. But if he truly thinks that one claim is worse than the other, then in practice there is evidence; it does not matter that the factual existence of evidence subsequently changes his mind. Here the important question is whether there is indeed evidence, and that is not a halakhic state subject to our determination. The question of whether there is evidence is a factual question, and factually it is hard to say there is evidence (perhaps there is a doubtful indication). Therefore, with respect to the migo case, it seems the question is a good one, and the answer that invokes the loop cannot work. In the previous column I pointed to various solutions to this difficulty.
[1] In particular, according to most of the Rishonim we do not say migo to extract money (migo le-hotzi lo amrinan), i.e., migo supports the claim of the one in possession. If so, even a doubtful migo could help him maintain possession.
[2] See about this in the fourth book of the Talmudic Logic series, ch. 13, and in greater detail in the fifth book of the same series, ch. 8.
[3] The same point is raised in Tosafot s.v. “hacha,” Gittin 84a; compare the Rashba there. See also in M.M. and in R. Ḥayyim on the Rambam, Hilkhot Gerushin 8:13.
[4] From the ordinary perspective, if she is not married to the first, then she is married to the third; and if she is married to the third, then she is married to the first (for she was not divorced from him). This odd combination can arise because her not being married to the third is not due to the condition or because she is married to the first. She is not married to the third because of R. Shimon’s consistency principle. It is simply an invalid legal act.
[5] An “if” relation can also be presented as directional. But here we are dealing with an “iff” relation, or with an “if” relation without direction. Proof: the second statement is related to the first in the same way. There is no precedence relation between them in any sense.
[6] One could of course replace in (b) and/or (c) the word “shaves” with “does not shave.”
Discussion
From the heights of Senir and Hermon I shall utter words, to the master of my debate, who builds dens for lions and mountains for leopards.
B. You are assuming that laws of doubt apply here, and then perhaps there would be room to go stringently (as certainty). But although I noted this in the column, in practice I am not at all sure that laws of doubt are relevant to a situation where the two directions are entangled, each one’s tail in the other’s mouth. Beyond that, the Torah’s rule to derive stringently by analogy was stated only regarding interpretation of the Torah. And there indeed it is in the category of certainty. Its logic is that the Torah itself certainly understood that there are two directions here and assumed that we would go stringently; and since it assumed this in a doubtful case without resolving it, that is a sign that its intention is indeed that we should go stringently. I seem to recall that something like this is written in Birkat Shmuel in the name of R. Chaim at the beginning of Bava Kamma regarding horns of iron. But here we are not dealing with rules of Torah interpretation, and there is no reason for this to count as certainty. And certainly we would not stone a person on the basis of such a doubt.
C-D. Your proposal is interesting, but from R. Shimon’s wording it seems simple that he meant what I wrote. After all, according to your approach this is a calculation made among the possibilities. You argue that the marriage to the third man cannot take effect because it creates an inconsistent state among the possibilities. But he speaks of an effecting that uproots itself and therefore cannot take effect, and that is exactly like my explanation.
Beyond that, you speak of the possibility that the sale is valid and the designation void, but assuming he performed designation and the sale is valid, the claim that the designation is void is itself also a contradiction. If a person performs an act of designation, the act stands unless there is a reason that nullifies it. Perforce, you too must arrive at the principle of an effecting that uproots itself.
E. Whether halakhah is a consistent system depends on what “halakhah” means. The set of halakhot that I myself rule by (or am supposed to rule by when cases come before me) must be consistent, otherwise you have left no son to Abraham our father. Any ruling you make can belong to your halakhah. From a contradiction one can derive anything. The laws of doubt have nothing to do with this question whatsoever. If I am in doubt between X and Y, and the laws of doubt instruct me to do X, but that contradicts another of my halakhot, then there simply is no doubt here. If X contradicts some other halakhah or principle, then that side is not part of the doubt, and we have decided that the halakhah is Y.
My monism means that there is some divine intention of the Holy One (at the giving of the Torah or in general). This need not exist for every halakhic question, but it exists in some questions (not anything goes), and in my opinion in the great majority of them. Therefore, fundamentally, halakhah is discovery and not creation. Of course, that does not mean that the discovery is always correct and accurately aimed at the original intention. But why is this connected to the consistency of halakhah?
C. One can nullify any legal effect one wants. In principle one can also nullify the get. But situations 1-2 involve an internal contradiction in what we have decided. Not because of the past, but because of the present. To void the get and uphold the marriage brings us to the contradictory halakhic state of a woman married to two men. To uphold the get and uphold the marriage brings us to accepting both the get and the condition that voids it. In situations 3-4 there is no internal contradiction, because we are allowed to nullify (the get and the marriage, or just the marriage), and then we arrive at a stable state.
To choose between 3 and 4 we need R. Shimon’s principle. And he says that after judging full situations, we simplify by components. And because in the final result the marriage cannot take effect, we decide that the marriage does not take effect, and then between 3-4 we can choose the option where the get is valid.
Therefore, the principle explicit in R. Shimon’s words concerning an effect that in any case cannot take effect is of course a necessary principle. It is only the component not written in R. Shimon and generated by your analysis—the issue of analyzing according to time—from that one can avoid.
I very much enjoyed this column, and I did not come to argue with the idea itself (I am still occupied with thoughts about it). Only as for R. Shimon, I think he meant something less complex.
E. In matters where halakhah is creation, then obviously there is no reason to assume a priori that it is consistent. They invented a system and it is not consistent—more power to them. What reason is there to think halakhah is consistent other than the assumption of discovery? The argument that holding a non-consistent system would leave no son to Abraham our father is pragmatism.
Incidentally, I once already wrote here that even the idea that from a contradiction one can derive everything (the principle of explosion) can be found in the Torah: “Turn it over and over, for everything is in it.” Meaning: if something contains two opposites, then it contains everything. But here we are not holding two contradictory principles; rather, we are in a paradoxical situation that halakhah does not know how to decide. From that one cannot derive everything, at least to the best of my understanding.
C. I disagree. R. Shimon explicitly says that this is an effect such that if it takes effect, then it does not take effect (= it is uprooted). According to your approach, there is no process of taking effect and then being uprooted, but rather a logical calculation saying that this effect is inconsistent and therefore cannot take effect. Therefore, in my opinion, his words clearly imply that we are dealing with a causal-temporal process as I described.
E. The argument is not pragmatic but essential. I proved in the previous message that this cannot be, because if your system contains a contradiction, then one of your rulings is rejected by force of proof and is not your halakhah. You cannot create halakhah X if among the rest of the halakhot in which you believe there is a halakhah “not X” that contradicts it. That is evidence against your ruling. If you mean that this is free creation not subject to anything, then there is no halakhah at all, and there you have indeed left no son to Abraham our father (if there is no halakhah, there is nobody who observes halakhah. Alternatively, everyone observes it, including the Hindu and the Shintoist).
I am glad you enjoy it, though it seems, as always with columns like these, that you are almost the only one who does (that is the “master of my debate”). But I write columns for quality, not quantity, and I shall fulfill in myself the Rema’s instruction not to be ashamed before scoffers… 🙂
Your words in the second message repeat what I wrote about why I am not sure the laws of doubt can be applied here. But I explained why this is indeed a contradiction. The contradiction is not between the two sides of the paradox (for the truth value of a paradox is “false,” and here the claim has no truth value at all), but between the ruling you propose and another halakhah that contradicts it.
C. It is not only a logical calculation. Because there is a rule here that after a logical judgment of complete situations one may isolate components. Logic by itself cannot distinguish between situation 3 and situation 4. This rule is R. Shimon’s innovation: “Something for which there is no possibility of taking effect does not take effect at all.”
Do you mean to agree that the idea itself has substance, and we are only discussing the interpretation of R. Shimon? Or is there also a flaw in the idea itself?
You jump to the last sentence and ignore the first. Let me remind you of his wording:
“Because these marriages cannot take effect, for if they took effect they would be retroactively nullified because of the condition. And similarly, something for which there is no possibility of taking effect does not take effect at all, and therefore the get remains valid and the marriages are void.”
The idea seems to me entirely reasonable and possible. But in R. Shimon’s wording, in my opinion, what I wrote fits better.
Do you happen to know of other places where R. Shimon deals with this idea? I have no way to search.
I do not remember such a place.
You also said that even within legal cause-and-effect we discuss them as if they are truly one after the other and not simultaneously. The idea itself is interesting and unobjectionable (except that it is a meta-legal innovation). I want to present a parallel to it in support, namely from the Rambam’s “wonderful point.” And although I remember that you learn the “wonderful point” differently, still it seems to me that it can also be understood in the way I am suggesting.
Meat cooked in milk is forbidden for benefit (and in particular for eating). Cooked forbidden fat is permitted for benefit and forbidden for eating. Fatty forbidden fat cooked in liquid milk remains permitted for benefit. And the prohibition of meat in milk does not take effect upon the prohibition of fatty forbidden fat, even though seemingly meat in milk adds a prohibition of benefit to the prohibition of fatty forbidden fat. Why?
The Rambam’s wording: “The answer to this is that meat in milk is forbidden for benefit because Scripture forbade it in eating, as we explained earlier, that every prohibition of eating is also forbidden for benefit unless Scripture specifies otherwise. And there is no verse there that forbids its eating and a verse that forbids its benefit; rather, the two matters together are the prohibition of meat in milk. Therefore, when we say that one prohibition does not take effect upon another, the prohibition of meat in milk will not take effect upon the prohibition of carcass, and it will not become forbidden for benefit.” (I copied from Sefaria and emended it slightly.)
And I understand him as follows: in meat in milk there is a prohibition of eating, and from it follows a prohibition of benefit, because that is the Torah’s rule. This is causal generation in every sense. One can now look at the legal result that meat in milk is forbidden for benefit (and for eating), or one can continue to remember that there is a logical structure beneath it, and it is a causal structure: the prohibition of eating meat in milk causes the prohibition of benefiting from meat in milk. The Rambam then says that meat in milk begins only with a prohibition of eating, and if that prohibition takes effect, it causes the prohibition of benefit. But if the prohibition of eating does not take effect, then it does not cause the prohibition of benefit. Therefore, when one cooks fatty forbidden fat with liquid milk, the prohibition of meat in milk arrives carrying only a prohibition of eating, and that does not take effect because one prohibition cannot take effect upon another; therefore, the prohibition of benefit for meat in milk, which stems from the prohibition of eating, also cannot take effect.
In my opinion this is identical to your idea in R. Shimon: that even within legal cause-and-effect we still remember the logical structure and treat it as though it comes one after the other, and not as though we simply have the result lying before us.
Incidentally, it seems to me that the expression “wonderful point” does not mean a beautiful point but a hidden point (“a matter that deceives everyone”—that is, wondrous and far from the eyes of the many, who did not know it). It is also the language of translation, and one should find whether the Rambam writes something like this in Hebrew as well.
That is how I too understood his words (though they should be examined in light of his words in negative commandment 113 and elsewhere).
As for whether this parallels my idea regarding R. Shimon Shkop, I am not sure. In the absence of the cause, there will be no effect. One does not need here the innovation that we see this as an internal time-axis. I think everyone agrees about that.
Incidentally, Greek philosophers already noted that there is no time gap between cause and effect, because otherwise there would be a moment in which the cause existed and the effect did not (though of course this can be debated). Therefore, according to them, the claim that in the absence of a cause there is no effect already implies some fictive time-axis. I do not see anything special in the “wonderful point.” In my opinion the “wonderful point” is not the innovation that without a cause there is no effect (which, as said, is simple), but that this is indeed the relation between the prohibition of eating and the prohibition of benefit—a relation of cause and effect and not two parallel prohibitions.
As for your linguistic comment, I do not see a difference between the two possibilities. An idea is wondrous in a place where others did not think of it or err regarding it. Hafla’ah is saying something explicitly, revealing it. Nifla is hidden and obscure. As is the way of the holy tongue in several matters, two opposites receive the same root (you are much more expert than I am in these matters).
Without an internal time-axis I do not understand the Rambam. In meat in milk there is a prohibition of benefit, and that adds to the prohibition of eating forbidden fat. Why does it matter that this prohibition of benefit was originally caused by a prohibition of eating? Only if one continues to preserve the order does one first judge the prohibition of eating alone.
Incidentally, if the “wonderful point” really introduces the idea of a time-axis within logical emergence, then it truly is an idea hidden from the eyes of many until you found it in R. Shimon.
Well, actually I did not add anything.
It is not in its original source, but rather that the specific prohibition of benefit on this particular object was caused by the prohibition of eating that took effect upon it. We are not speaking of where we learn the general prohibition of benefit from orlah or hametz, but of how the prohibition of benefit is created and takes effect on this specific object. That itself is the Rambam’s innovation: there is a causal relation—the prohibition of eating is created, and from it the prohibition of benefit. That without a cause there is no effect is, as stated, a simple idea and does not require the assumption of a fictive internal time-axis. Consequently, in my opinion, that is also the wonder of his point.
Now I understand.
I also enjoy it very much, except that I do not have Sandomilov’s wisdom to comment and ask as he does… Thank you for the column, Rabbi.
Taking a screenshot and sending it to my mother 🙂
Though it seems to me that I have simply grown used to understanding (or trying to understand) what Rabbi Michi says, so that things in his mode of processing and simplification really “fit” me. Rabbi Zevin also had a gift for writing simply and clearly (except that Rabbi Zevin usually simplified other people’s ideas).
Take a screenshot of this too and send it to my mother. 🙂
Suddenly the memory struck me. You already once explained this understanding of R. Shimon to me, when I did not understand in his words why the get too does not nullify itself (as you asked here in the column), and you gave me in advance the gist of the explanation here: that we treat the get as preceding the marriage, so it may take effect, while the marriage begins the self-severing. And there too you explained that the reason an effect that severs itself does not take effect is because self-reference is illegitimate (for some reason this was not emphasized here in this column. Here the emphasis is different: that an act which in no way was handed over to take effect is a void act, and the normative system does not constitute it just in order to create problems for us). And there too I tried to bring the “wonderful point,” and there too you explained that there is no connection. And this happened in a thread that began from the paradoxes of the red heifer and pesik reisha. Everything exactly as above. Bizarre.
In any case, I mention this because it turns out that there is a link there to another source in R. Shimon’s writings, namely in his novellae to Kiddushin, siman 21
https://www.hebrewbooks.org/pdfpager.aspx?req=40915&st=&pgnum=137.
There the discussion is about someone who gave a maneh to a slave on condition that his master have no rights to it. According to Rabbi Meir, it is impossible for the slave to acquire without the master also acquiring, and therefore the condition is void and the acquisition by the master stands. According to the Rabbis, the slave acquires and the master does not acquire (and in this way the slave is redeemed). And R. Shimon explained, according to the Rabbis, that in any case the master has no acquisition, since if he acquires then the gift is nullified from the outset and he did not acquire; therefore there is no acquisition at all for the master, but the slave does acquire, and only the legal effect of the master’s acquisition is nullified.
But one needs to clarify Rabbi Meir’s view here. For in the case of one who sells his daughter on condition that there be no designation in it, and the master then designated her, Rabbi Meir said (Kiddushin 19b, cited in Sha‘arei Yosher p. 258 as brought in the column) that the sale stands and the designation is void. But in the case of one who gives to a slave on condition that his master have no rights to it, Rabbi Meir says (Kiddushin 23b, cited in the above novellae of R. Shimon) that the gift stands, the condition is void, and the master acquires. What is the meaning of this matter? Why does Rabbi Meir not say that because of the condition the master’s acquisition cannot exist, since it uproots itself, and therefore the gift stands, the condition stands, and the master’s acquisition is void? This seems like a severe contradiction in adjacent sugyot. And if Rabbi Meir in the case of sale and designation says this only because of the local derashah there, then why did R. Shimon bother to explain in it the principle that an effect that uproots itself is void?
Perhaps there is a difference between the master’s acquisition and the master’s designation. The master’s acquisition is inherent in the nature of the slave’s acquisition, and the slave’s acquisition never had a possible moment without the master’s acquisition; therefore the slave’s acquisition without the master’s acquisition is impossible, and this is a stipulation against what is written in the Torah, so his condition is void. But the master’s designation is not inherent in the nature of the sale of the daughter, and the sale of the daughter had a possible moment without designation by the master (only with an option of designation). In that case, according to Rabbi Meir, he is not stipulating against what is written in the Torah, so his condition stands; but the master’s designation in any case does not take effect, since it nullifies itself, whereas the sale of the daughter can take effect, so the sale takes effect and the designation is void. According to the Rabbis, the master’s acquisition too is judged like the master’s designation and is something separate in nature from the slave’s acquisition; therefore the master’s acquisition is void (according to R. Shimon’s explanation, because it uproots itself), but the slave’s acquisition is not.
If you have another answer I would be glad to hear it.
I do not have time right now to get into it, and I am not even sure I understood your intent. Two possibilities occur to me, and perhaps you meant one of them (there are expressions in your wording that point toward each one).
1. One can discuss whether the condition in designation is that he should not have designation rights in her (a stipulation against what is written in the Torah), or “on condition that the master not designate her” (a stipulation about the master). The second stipulation is not in the category of stipulating against what is written in the Torah. This is a logical distinction regarding the relation between the condition and the act.
The transfer to the master follows from the very laws of giving to a slave, but designation is only an option and is not an automatic consequence of selling the daughter. This is of course a continuation of the conception that here the stipulation was about the master and not about the Torah, because if it was a stipulation about the Torah (that is, about the possibility of designation), then it really is the same thing.
2. But according to my approach in R. Shimon’s words, one can draw a distinction that speaks about the time-gap and not the logical relation. In designation, the designation comes after the sale, and therefore the sale certainly takes effect, because it is not uprooted by the very fact of being done. But in a sale on condition that his master have no rights, this is a sale that cannot take effect from the very moment it would take effect.
Thank you. (I was trying to say 2.)
I also enjoy topics like these, but unfortunately people here write at too elevated a linguistic level; it needs to be simplified more for the poor in understanding like us, especially in the debate between the comments.
This passage is repeated because some point in it has become obscured.
A. In the paradox of the get and the apostate, you resolved that the get is invalid and the Jew is not an apostate, because the validity of the get nullifies itself and therefore does not take effect.
When does the get become valid, and when does the Jew become an apostate? Seemingly it is at the same moment: the moment he makes the entire get valid, by that very act he violates the prohibition of fixing and becomes an apostate. The two results occur at the same moment, but logically the validity of the get precedes the apostasy. In such a case, the simple conclusion would seem to be that from that point onward the get is valid and from that point onward the Jew is an apostate. For in the moment before validating the get, the Jew was a valid Jew; and the fixing of the get produces two separate results (the get’s validity and the Jew’s disqualification).
And even if that is not correct and the paradox remains, I would have expected, according to your words, the solution to be that the get is valid and the Jew remains valid, because the get’s validity logically precedes the Jew’s disqualification, and therefore the disqualification of the Jew is the later step that nullifies itself. True, here the validity of the get is worse than a “get on condition that you not marry So-and-so,” because in the latter case there was at least some chance at the moment of giving that the get would have genuine force, whereas here, in the get corrected for her sake, its validity immediately nullifies itself and it is the first in the chain to uproot itself—but still, according to your words, why not say that the get takes effect and the disqualification of the Jew does not? In truth, it seems to me that I did understand what you mean, except that why was the Torah given on a mountain and not in a valley? To teach us that everything must be clear and not deep.
B. What does one do if halakhah lays down two principles and in a certain scenario they lead to a contradiction, and we have no idea how to solve it? Suppose we know that R. Shimon’s idea is not correct. What do we do then? Does that mean we were mistaken in at least one of the two principles? From your words I understood that yes. And I think seemingly not.
If the contradiction is revealed in a certain case, then all that happened is that in this case we do not know what to do and need a heavenly voice or something. As far as I am concerned, let the heavenly voice say, like Alexander of Macedon, to kill all those who generated the problem and dedicate their property to Temple repairs. There can always be solutions in principle; the problem is only that we do not know the practical solution.
It is agreed that one cannot sustain a principled contradiction. If one holds that a carcass is permitted and a carcass is forbidden, that is meaningless, and everything can also be derived from it. But an accidental contradiction can be sustained: one can hold that one simply does not know what the halakhah is in this case. That is, one does not know the status of the get and the status of the Jew who wrote it. And one cannot derive ‘anything’ from this, because we are not actually holding a contradiction; rather, from the contradiction it is revealed that in this case there is a new law that unfortunately was not disclosed to us. Apparently it was forgotten during the mourning for Moses, and Othniel son of Kenaz did not manage to reconstruct this new law.
A. It is hard for me right now to get into the whole matter again. Off the cuff I would say there is no obstacle to retroactively changing a state that has already come into being. That is not the consideration. The question at every stage is whether this stage stands on its own feet or nullifies itself, irrespective of what will happen later. A stage that nullifies itself will not take effect, and the situation is thereby frozen.
B. You are presenting here the distinction I have made more than once between contradiction and conflict (what you call here an “accidental contradiction”—not a good term). A contradiction is a logical matter; a conflict is a practical problem. Indeed, one can hold two principles that lead to a conflict, even if one does not know what to do there in practice. By contrast, a contradiction destroys the system. Thus, for example, preserving life and Shabbat can lead to a conflict in a certain situation (which in principle might never occur). Even if we had no practical solution, there would be no reason to abandon either of those two principles. The problem is only that I do not know what to do, and that is all.
That is exactly the solution I proposed for contradictions between halakhah and morality. I argued that it is a conflict, not a contradiction.
B. Correct. Now, is there any a priori reason to think that halakhah contains a mechanism for deciding every single conflict?
I mean intra-halakhic conflicts, of course. (I am aiming to say that there is no principled motivation to find a mechanism of decision for all halakhic paradoxes. And one who holds that there is no such mechanism is not driven into a forced position.)
That is, whether it is decidable/computable? I see no necessity for this. Even on the banal level (practical implication for betrothing a woman): if one betroths a woman on condition that there is a Turing machine that checks the halting of every Turing machine. Halakhah relates to reality, and if reality is not decidable, then halakhah is not either. But undecidability can also exist within halakhah itself. For example, you have two positive commandments (or prohibitions), one fulfilled by sitting and doing nothing (such as eating matzah) and the other violated by sitting and doing nothing (such as observing Shabbat). And let us assume for the sake of discussion that they have equal halakhic force and the clash between them is simultaneous. What does one do in such a case? Which one overrides which? Here neither has priority, and the rule that passive inaction is preferable does not apply, nor of course do the rules of doubt.
I just thought of matzah lying in the public domain while I am sitting in the private domain on Passover that falls on Shabbat. What is the law if I extend my mouth into the public domain to eat it and bring it into my stomach, which is sitting in the private domain? Assume there is no prohibition on Shabbat here, only a positive commandment, and that the positive commandment is equal in force to the positive commandment of eating matzah (the karet and stoning for Shabbat are for the prohibition). What does one do?
Perhaps one could cast lots between equivalent options, and then perhaps halakhah would indeed be decidable. But that is artificial, of course.
A1. How can there be an example of halakhic undecidability as a result of reality? Reality is always decidable. It is known that there is no machine that decides the halting of every machine, so if someone betroths on that condition, she is not betrothed. And if something is independent of a given system (that is, both it and its negation are consistent with the system), then the truth is that it is independent. So this is just an ordinary factual doubt. Or perhaps I did not understand.
A2. Suppose we do not know what the law is regarding electricity on Shabbat, or whether a koy is a wild or domesticated animal. Could that be an example of undecidability? Seemingly not. If no ground is found to forbid, then it is permitted. If grounds are found in both directions and the decisor cannot decide, then he applies the laws of doubt.
B. In the case you described of internal halakhic undecidability, one could say that a person may choose what to do and everything is fine. Just as if someone sees lost property on his right and on his left and can return only one, he may simply choose arbitrarily which lost object to return. How is that similar to a paradoxical problem in which every decision is bad?
Again I realize this is essentially what you proposed with a lottery. But elsewhere I already expressed my view that where one can cast lots, one can also choose without a lottery. In the case of conjoined twins, you said one must be egalitarian in granting the chance to live. There too I think one may choose arbitrarily (without a lottery), but why in the halakhic case here would I require a lottery and not allow arbitrary choice? Whose rights are being infringed here?
C. In any event, an innovation emerges from your words: there is no a priori reason to think halakhah has something to offer in the realm of solving halakhic paradoxes (or conflicts); it would be nice to find such a thing, but it is not guaranteed to exist.
It is not true that reality is decidable. There is only one reality, but deciding it is our decision. We do not necessarily know everything about reality, and perhaps we cannot determine everything either.
I was mistaken regarding the halting problem, but the principle remains. There are undecidable questions (such as the consistency of a system), and if someone betroths a woman on that condition, there is here a halakhic question that is undecidable.
Ignorance is not undecidability. It may turn out to be essential undecidability, but that requires proof.
Once you allow a lottery or arbitrary choice, then of course everything is decidable. But as I said, that is artificial.
Indeed, in my opinion there is no necessity that halakhah be decidable. On the contrary, it seems likely to me that it is not.
I do not understand what an essentially undecidable question is. Either the system is consistent or it is not. And for every question, either only it or its negation is consistent with the system, or both are. What is there besides lack of knowledge?
Exactly—that is what I answered you. You said that reality is decidable, and I argued that decidability pertains to epistemology and not ontology, that is, to my understanding of reality and not to reality itself.
But when we are not speaking about physical reality but about norms, there is the possibility that the norm is not defined in itself, and not merely that I do not know it. That is undecidability of halakhah in itself. I also added that if you introduce the possibility of casting lots (or choosing arbitrarily) in every case that is not decidable, then you have emptied the question of content, because in that sense halakhah is obviously decidable by definition. Like Buridan’s donkey with the possibility of a lottery.
I understand.
An opportunity that came to hand—how could I let it pass? In the column there appears the Minchat Chinukh’s paradox regarding one who traces over the letters of a get on Shabbat for her sake: what is the status of the get, and what is the status of the Jew writing it? For if the get was validated by this writing, then the Jew violated the prohibition of fixing and is an apostate. And if an apostate Jew writes a get, then the get is invalid. It follows that validating the get leads to its invalidation, because it disqualifies the writer and thereby invalidates the get. And from the invalidity of the get it follows that the Jew did not fix anything and is not an apostate, so the get should be valid. [And you solve this according to your explanation of R. Shimon, that the validation of the get comes first and cannot take effect, so the get remains invalid and the Jew remains valid.]
Above I wondered: throughout all the time of writing until the moment the get became valid, the Jew had transgressed nothing, since he had not written any letter (he merely traced over an existing letter) and had not fixed any get, since he still needed to complete the required writing. And after he did everything required to fix the get, he thereby performed two actions at once: he fixed the get and became an apostate—meaning that from that point onward the get is valid and the Jew disqualified, whereas until that point the get was invalid and the Jew valid. This is a normal action with two implications, and they both take effect immediately at the completion of the action; and although they are not one after another, still they exist simultaneously, because each matter is entirely distinct unto itself. And the paradox vanishes.
I have now seen Mishnah Hullin 1:1: one who slaughters on Shabbat (unintentionally), his slaughter is valid. And there, in the commentary to the Mishnah: “And perhaps you will ask: why should not slaughter done intentionally on Shabbat be valid, since he does not desecrate Shabbat and his slaughter is not invalid except after the completion of slaughter, so that if he slaughtered again afterward, only the second slaughter would be forbidden? Know that from the moment he begins to make a wound in the neck of the animal, he desecrates Shabbat before he has slaughtered any part of the esophagus or windpipe. And if you wish for more explanation than this, say that when he slaughters some of the signs before he completes the slaughter, he desecrates Shabbat, and when he completes the slaughter he is disqualified.”
Accordingly, it emerges clearly that if one takes a blank parchment and writes a get for her sake, then certainly by the first word or even before that he becomes an apostate, and whatever more he writes is no longer for her sake. But if he traces over the letters of a get for her sake, then since the validation of the document and the disqualification of the person come together, then indeed “they stand together, and one does not crowd another; each walks in his path, and when they fall through their weapons they are not cut off”—and the Minchat Chinukh’s paradox falls.
Possible, but I think there is a difference. In slaughter, the act ends at the end and the transgression comes first. But in tracing over writing in a get, what ends is the transgression, not the act. The significance of the act is obtained at the end, but the act in itself is an act of prohibition throughout its whole length. When the result is obtained, it is revealed retroactively that he was writing all along.
I did not fully grasp your point. Could you explain more? (And perhaps this should also be examined from the perspective of the view that slaughter is one continuous act from beginning to end.)
When you trace over writing in a get, you are writing from the beginning. It is only that this fact is revealed only at the end, when it becomes clear that everything you did was writing. The claim is that the act of writing does not occur in the result that there is a valid get, but in the action. Writing is making letters, not validating a get. True, only when the get becomes valid is it revealed that everything you did in the past was an act of writing, but still it was done from the beginning. Therefore, in my opinion, it is not necessarily correct that the writing occurs only at the final moment, as you assumed in your analogy.
One must discuss whether this is a case of “it becomes revealed retroactively” or “from now on, retroactively.”
But he transgresses because of fixing, not because of writing. Throughout all the writing he performed acts of fixing, and in the last correction they combine into fixing the get, at which point he transgresses because of fixing. I cannot understand how this differs from slaughter, where he slaughters continuously from beginning to end until he reaches the majority of the signs, and if not for the fact that he was desecrating Shabbat from the beginning, the Rambam said the slaughtered animal would be valid and the person disqualified from then on. According to you, what is the law if he began before Shabbat either fixing the get or slaughtering, and only a small part remained at the onset of Shabbat, which he then completed on Shabbat?
Not at all. The transgression under discussion is writing, not fixing. There is no primary category of labor called “fixing.” It might perhaps be under the category of the final hammer blow. But in my opinion the final hammer blow does not apply to a get. This is not preparing a tool for use.
If he completed it on Shabbat, then he wrote both on the weekday and on Shabbat. He is liable only for the part he wrote on Shabbat.
Ah. You are saying that in completed writing he becomes an apostate retroactively after the first two letters because of writing. But in completed slaughter he does not become an apostate retroactively at the cutting of the first sign, for example, because that is not a labor; rather, only when he removes life and prepares the animal for eating [the completion of the slaughter and the desecration of Shabbat occur simultaneously]. Therefore in slaughter the two results (the permissibility of the ox and the apostasy of the Jew) take effect from then onward, but in the get one runs into the paradox that if the get is fixed, then the Jew is considered an apostate already before the completion of all the writing, and therefore the get is not fixed. Now I understand and accept; thank you.
According to this, it seems to follow that if he had only two letters left to write for her sake and wrote them on Shabbat, then indeed this is like the Rambam’s question regarding slaughter, and the law would be: from then onward the get is valid and the Jew is an apostate, without paradox. The paradox exists only when one writes over four (or three) letters for her sake.
Possible. Incidentally, I think three letters may suffice.
I just opened the Minchat Chinukh there, and it turns out that I overlooked the issue of writing over existing writing, because he already brought there the case of one who slaughters on Shabbat (immediately after the passage quoted in the column. https://hebrewbooks.org/pdfpager.aspx?req=14093&st=&pgnum=110&hilite=).
However, he did not cite the words of the commentary to the Mishnah. And he wrote there that according to Tosafot in Hullin, from one single act he does not become an apostate, and therefore if he wrote only the last two letters for her sake, he desecrated Shabbat and nevertheless is not an apostate, and the get is valid.
That is, according to the Minchat Chinukh, if by one act he does become an apostate, then even in writing only the last two letters for her sake there is also a paradox. But seemingly according to the above and the words of the commentary to the Mishnah, it comes out not so; rather, in writing only the last two letters for her sake there is no paradox at all, and the two results are born together from the cause. Only in four (or three) letters is there a paradox.
Incidentally, I just thought: if a minor wrote one letter on Shabbat, then became an adult and wrote a second, is he liable to stoning? According to the side you raised that if a minor fasted on Yom Kippur and then became an adult and ate, he is liable to karet because fasting is a pre-halakhic concept (that is how I understood it, at any rate), then perhaps here too he would transgress by the second letter alone, because there is writing here. And if he ate half, then became an adult and ate another half to the measure of satiation, it seems even more obvious that he is obligated in Grace after Meals by Torah law. And if he slaughtered one sign as a minor and then became an adult and slaughtered the second, perhaps it is not slaughter, since that is only a halakhic concept. It seems to me one could develop this much further.
And if he stuck bread to the oven and then became an adult but did not remove it, it seems obvious that he is exempt.
Only in matters whose definition is as I explained—namely, where the requirement is conceptual and not halakhic. Therefore each of the cases you raised must be judged on its own merits.
Of course. But could you give a non-binding off-the-cuff opinion as to the law in the above examples:
He became an adult and wrote a second letter on Shabbat
He became an adult and completed eating to satiety for Grace after Meals
He became an adult and completed slaughter (regarding slaughter, my first impression was that the requirement is halakhic and not conceptual)
He became an adult and completed eating an olive’s bulk for prohibited foods
He uprooted an object on Shabbat, became an adult, and carried it out to another domain
Two letters are the required measure for writing, and therefore I think only two letters together count as writing; it is not that the second letter reveals that the first was already writing. So here it seems quite clear that he would be exempt. He did not write two letters while obligated.
Regarding eating, my inclination is that he is obligated to recite the blessing, because now he is satiated as an adult as a result of eating. Put differently: eating obligates the blessing, except that as a minor he is exempt from blessing. But once he is an adult, he becomes obligated to bless even for the eating he did as a minor. According to this, even if he ate everything while still a minor and came of age exactly when he finished, he must bless (if there is a time gap, then perhaps this depends on the law of disqualification by lapse with respect to mitzvot. See the Rosh on Moed Katan ch. 3, siman 96).
Regarding slaughter, I agree that this is not slaughtered. One of the signs was cut by someone not subject to obligation.
Here too it seems to me that he is exempt. As an adult he ate less than the minimum measure. And so too according to the reasoning of the later authorities regarding the prohibition of less than the required measure—namely, that it is fit to combine, meaning that in every tiny amount there is the quality of eating, and only the quantity is lacking.
Exempt, as above. However, this may depend on disputes among the Rishonim in understanding carrying out on Shabbat. If the essence is the transfer and the placement, and the uprooting is only a condition, then perhaps there is room to obligate.
Thank you.
Hi, I do not know what the procedure is here regarding comments on old posts, but I’ll try my luck anyway.
In the post you wrote that when a woman marries So-and-so after her husband made the divorce conditional on her not marrying So-and-so, then the marriage to So-and-so did not take effect because of the principle of consistency. You added that one can say the marriage did not take effect because marriage is a normative matter and not a factual one.
Afterward you discussed a case where a man divorces his wife on condition that she not commit a sin, she vows not to eat bread, afterward the husband annuls the vow, and the woman eats bread. You argued that here the loop ends with the two still married, without any need for the principle of consistency, because eating bread (as opposed to marriage) is not a normative matter but a factual one.
My question is: why do you treat eating the bread as a fact and not as violating a vow (which is indeed a normative matter)? Just as in the first case the woman put a ring on her finger (a fact), but that was not considered marriage (normative), so too here the woman ate bread (a fact), but that was not considered violating a vow (normative). Why in this case is consistency not needed to stop the loop? If the divorce became effective again because of eating the bread (and violating the vow), that means the bread she ate did not really void the divorce (it was just ordinary bread-eating). How is this different from the first example?
Thank you very much!
A vow is indeed a legal effect, but violating a vow is not a legal effect, only a physical action (which has halakhic significance). If the vow took effect and the woman violated it, then she violated the vow. There is nothing here to make take effect or to nullify. Note that the problem is not the very applicability of the vow but the act of violating it.
A. Of cypresses from Senir they built all your planks; they took a cedar from Lebanon to make a mast for you. Words that can be sold for dinars!
B. Regarding the red heifer and pesik reisha: if we do not resort to a halakhic “tips” theory (which is a plausible idea), and we arrive at a stopping of loops, then perhaps one should simply say that we stop the loop stringently. Just as with an analogy (hekkesh) we derive stringently even though one could have derived leniently. And as I seem to recall, the more accepted approach among the later authorities is that this is treated as certainty (that is how the hermeneutical rule was transmitted), not as doubt. Therefore such a stringent hekkesh would entail lashes, would not combine into a double doubt, and its derivatives on the lenient side are indeed judged leniently (regarding extracting from one in possession, one must examine what counts as stringency and leniency). If so, if this is the Torah’s rule, then perhaps we should judge loops by something akin to a binyan av as well. What do you think?
C. Your explanation of R. Shimon seems to me very beautiful, complete, and strong, and I regret undermining it, but what can I do—I understand R. Shimon a bit differently. What bothers me somewhat in your explanation is the treatment of the axis of causal generation as though it were a temporal axis. Still, the explanation I would propose seems simpler to me, though also weaker. Perhaps I will say more about this later from the perspective of how I understand the Rambam’s wonderful point (I understand him as saying roughly this—that a causal axis is judged in stages. But you understand the point differently).
In Tosafot on Gittin there are a priori four possible situations: (1) the get is void and she is married to the second man. (2) the get is valid and she is married to the second man. (3) the get is void and she is not married to the second man. (4) the get is valid and she is not married to the second man. Now, situation 1 is halakhically invalid, because she is married to two men. Situation 2 is halakhically invalid because we are maintaining a valid get contrary to its condition (you cannot accept the get halfway). That leaves situations 3-4 as halakhically valid before us (to choose whether to void the get and void the marriage, or to uphold the get and void the marriage). And in both, she is not married to the second man. Therefore marriage to the second man is not an option, and this is an act nullified from the outset. Such an act is worse than kiddushin that cannot lead to intercourse; it is an act not entrusted with taking effect. It remains to decide whether the get is valid or not—i.e., whether situation 3 or 4 obtains. But since we concluded that she is not married to the second man, there is no reason for the get to be voided. Therefore: the get is valid and she is not married to the second man.
And this is exactly what also happens in R. Shimon’s other example there. One who sells his daughter on condition that she not be designated, and the master then designates her—for Rabbi Meir, the sale takes effect but the designation does not. Just as according to Tosafot the get takes effect but the marriage does not. Here too there are a priori four possible situations: (1) the sale is void and the designation valid. (2) the sale is valid and the designation valid. (3) the sale is valid and the designation void. (4) the sale is void and the designation void. Now, situation 1 is invalid, because designation without a sale is impossible. Situation 2 is halakhically invalid because we are maintaining a valid sale contrary to its condition (you cannot accept the sale halfway). That leaves situations 3-4 as halakhically valid before us (to choose whether to void the sale and void the designation, or to uphold the sale and void the designation), and in both she is not designated to the master. Therefore the designation is null from the outset, because it is an act not given over to take effect (perhaps one can also view this as a “simplification” of the constraints). And now that the designation is void, there is no reason for the sale to be voided. Therefore: the sale is valid and she is not designated to the master. [According to your understanding of R. Shimon, the sale is valid because at the time of sale it was able to take effect if the master would not designate her, and the designation does not take effect because at the time of designation it was not able to take effect, since designation after sale uproots the sale and thereby the designation itself.]
What we gain by this is the breaking of symmetry between the get and the marriage—the break is that for a valid get there is a halakhically valid situation in which the get is not void (this is like your explanation). And there is no need to resort either to temporal order on the axis of causal generation or to the actual temporal order; that is, the fact that the acts of the get or sale came into existence before the marriage or designation is of no importance, and it is not as though we follow some sequence.
Truth be told, this whole matter confuses me. My suggested explanation is really a question whether I have not missed some basic flaw (which would force one to your explanation, or which is itself also at the root of “my explanation”). And if I am right about R. Shimon, then your more complex explanation of R. Shimon is your own original addition.
[Incidentally, in cases of “coming simultaneously” as well, we move to a valid and consistent result without analyzing the process precisely. But that has its own parameters, because it is known that one who transfers ownership by throwing a deed of acquisition into his own courtyard has not transferred anything. In any case, there is a resemblance.]
D. The practical difference between your explanation of R. Shimon and the one I proposed is your further point—which follows only according to your approach (what a surprise). In the paradox of the get and the apostate, you resolve that the get is invalid and the Jew is not an apostate (and the get is invalid “for no reason”), even though there is an internal contradiction here: if the Jew is not an apostate, why is the get invalid, given that it was written by a valid Jew? And in the paradox of the woman and the loaf, you resolve that the get is void and the vow was not annulled (and the annulment does not annul “for no reason”), even though there is an internal contradiction here: if the get is void, why was the vow not annulled, given that it was annulled by a trustworthy husband?
But according to what I wrote in section C, there is no solution to these paradoxes. In both of these, unlike the case in Tosafot on Gittin and the designation of the maidservant, there is no consistent state at all (note this carefully—and I hope I have not missed something here), so we are not required to choose one among several possible consistent states, but rather stand before a shattered trough, with the stone still on the mouth of the well. Therefore these are paradoxes with no resolution. There is no reason to think halakhah is a consistent system. And if there is no resolution, then apparently one must, as you suggested briefly, treat it as a “case of doubt.”
E. As for the assumption that halakhah is a consistent system, it seems that one should discuss the relation between discovery and creation in halakhah. In my opinion, on first glance, even if everything is discovery there is still no reason to think it is a consistent system, because in the end one reaches a practical ruling with meta-rules (such as the law of doubt). Moreover, I am not entirely sure that a monistic conception of halakhah means that everything is discovery (but on this I have only thoughts far from crystallization). Your view on discovery and creation in halakhah, and its connection to monism, is not sufficiently known to me, and if there is a reference I would be happy to read it. The easiest thing to say is that all the true things in halakhah—whether they have practical halakhic ramifications or not—are a discovery of the monistic truth that was in the Holy One’s mind at the time of the giving of the Torah. And indeed, I thought that is how I once understood your words. But I am not sure that is what you mean, so I ask if you could clarify.