Paradox and Anti-Paradox in the World and in Jewish Law (Column 195)
With God's help
In the recent lectures in Petah Tikva we have been dealing with paradoxes (there are recordings on the site). In the lecture a week ago, a very interesting connection occurred to me, and I decided to write about it here. Among other things, I defined two additional kinds of statements: paradox and anti-paradox, and I will begin with that here. In the next column I will continue and connect the discussion to Buridan's ass and to other examples.
On paradox and anti-paradox[1]
The liar paradox is one of the oldest paradoxes. In its well-known formulation it is presented as follows: a resident of Crete says: "All the inhabitants of Crete are liars." It is commonly thought that this is a paradox, because if indeed all the inhabitants of Crete are liars, then this resident too is a liar, and therefore this statement is false, which means its content must be denied. That is, the situation is that the inhabitants of Crete are not liars, from which it follows that this statement is true, and so on…
But this is a mistake. On the logical plane, this statement is not paradoxical at all, since the loop described here is based on an error in applying the negation operator. The negation of the statement "All the inhabitants of Crete are liars" is not the statement "All the inhabitants of Crete tell the truth," but rather the proposition "There is at least one inhabitant of Crete who tells the truth." If we assume that in Crete there is indeed only one truth-teller, and that this resident is not the speaker himself but his friend, the loop stops immediately. The conclusion is that there is someone among the inhabitants of Crete who tells the truth, but it is not the speaker himself[2].
By contrast, the following statement is genuinely paradoxical:
Statement A: Statement A is false.
This is a statement about itself (without any universal quantifier, that is, without any generalization), and here the loop really cannot be stopped; if this statement is false, then its content must be denied, from which it follows that it is true. But if it is true, then its claim is correct, namely that it is false, and so on…
And what about the following statement:
Statement B: Statement B is true.
At first glance there seems to be no problem here, since the content of this statement does not contradict its truth value. But it turns out that here too there is a logical problem, only this time the problem is the opposite one (which is why one can call it an anti-paradox).
Some define a proposition as a sentence that can take one of two truth values: true or false. A sentence is true if its content corresponds to the facts (=the state of affairs in the world), and false if it does not correspond to the facts. The proposition "The sun is currently shining" is either true or false. If in fact the sun is currently shining, then that proposition is true. And if in fact the sun is not currently shining, then that proposition is false. For every ordinary proposition, only one of these two possibilities is correct. It can take one and only one of the two possible truth values, 'true' or 'false'.
It is precisely here that the special character of statement B appears. If we decide that it is true, then examining its content shows that it is indeed true, and therefore the truth value of the statement is 'true'. That is, the assertion that this statement is true is consistent with its content (=the state of affairs it describes), and therefore the truth value appropriate to this sentence is 'true'. But if we decide that it is false, this means that statement B is false, that is, that the content of statement B is not correct. That is, this determination too leads us to a consistent result (=a match between the statement's truth value and the state of affairs it describes). Therefore the truth value appropriate to this proposition is 'false'.
So we have here an anti-paradox: in a paradox like the liar paradox, that is, statement A above, there is no possible truth value at all. By contrast, in an anti-paradox like statement B, two truth values can be assigned, and both are consistent with the 'facts' (=the content of the proposition).
Graphic representations
A graphic representation of such an anti-paradox can be seen in M. C. Escher's famous drawing called Drawing Hands (Drawing Hands, 1948):
Something that brings itself into being creates an anti-paradox (this is the assumption that the proposition is true, which keeps confirming itself). Incidentally, if both hands were holding erasers, that would be the second way of construing the anti-paradox (to assume that the proposition is false, which also confirms itself). I found such a drawing online as an advertisement for shirts, and here it is:
In the book Goedel, Escher, Bach , by Douglas Hofstadter, this drawing is brought to express the idea of self-reference. Self-reference is of course relevant both to the liar paradox and to the anti-paradox. If we were to place an eraser at the end of one of the hands instead of a pencil, and leave a pencil in the other, the resulting drawing could represent the liar paradox.
Formal solution: the theory of types
Bertrand Russell, in the introduction to his book Principia Mathematica, proposes a general solution to paradoxes of self-reference (like the liar paradox). He proposes a formal language that divides its statements into types arranged hierarchically. A sentence that belongs to a type at level n cannot refer to sentences that belong to its own type and above (only to types below it).
Clearly, in such a language it is impossible to formulate paradoxes, and ostensibly we have here a solution to the entire class of self-referential paradoxes. But this is only a formal, ad hoc solution. It has no independent rationale. By the same token, I could have forbidden sentences that include the word 'false,' or forbidden sentences longer than two words, or any other rule that would succeed in excluding all problematic sentences from the language. That is not a solution to the logical problem, but merely a prohibition against expressing it. Constructing a language in which the problem cannot be formulated does not solve it. Put differently: these rules also forbid innocent and ordinary sentences, through no fault of their own. Hence there is no justification for them, and this is an ad hoc solution.
One may say that this is a practical solution (what we should do on the practical plane), but it does not solve the logical problem that the paradox expresses. I once wondered what a poem written in Russell's language would look like. I suspect not much…
So what should a genuine solution to a paradox look like? If we find a distinction that has its own intrinsic rationale, and as a result the paradox disappears, that would be a solution—as distinct from a distinction adopted ad hoc only in order to make the paradox disappear.
Is this a real paradox?
One may wonder whether the liar paradox or the dual anti-paradox I have presented are real or not. It is commonly thought that real paradoxes cannot exist, since in reality there is one truth and none besides it (and likewise with regard to an anti-paradox). Hence a paradox is necessarily the result of a mistake in thought or of linguistic deception. This is probably the reason analytic philosophers assume that the solution to a paradox always lies in language. I think they are mistaken, for although it seems correct to me that in the world itself there are probably no paradoxes (a fact is either true or not), the failure may lie in our logic and not necessarily in the language.
But specifically regarding the two sentences presented here, the analytic claim does seem correct. These sentences have no real content. In neither case do they add any information about the world, and therefore no comparison can be made between the content of the sentence and some state of affairs in the world in order to test whether it is true or not. This is a word game that deals with the truth value of the sentences themselves, not with any facts. There is no fact that I need to examine in order to determine whether this sentence is true or false; it is a 'floating' definition (not anchored in any reality). If that is indeed the situation, then these are not propositions at all, and therefore no truth value can be attached to them.
And indeed Ron Aharoni argues in his books that these are only apparent paradoxes (like every paradox), since the question whether sentences that say nothing are true or false is meaningless. But ostensibly there are applications of such structures to sentences that do make some claim about something outside themselves, and then it certainly is meaningful to discuss whether they are true or not. This reawakens the question of what one does with such paradoxical sentences.
Paradoxes in factual systems and normative systems
We will now see two applications of such structures in Jewish law. Let me only preface by saying that Jewish law is not a collection of facts but a collection of norms. Therefore, precisely within its framework, it seems to me that real paradoxes may be possible (only with regard to the world is the assumption true that a fact is either true or false and that there are no real paradoxes). There may be within Jewish law a genuine contradiction that cannot be eliminated.[3] Of course, the question still remains what we are to do in such a situation, but here there may also be a practical solution rather than a substantive logical one.
A stipulation concerning overcharging
In Bava Metzia 51, Rav and Shmuel disagree about a condition concerning overcharging in a sale transaction. Reuven sells some object to Shimon. According to Jewish law, if the price of the object is higher by one-sixth than its market price, the law of overcharging applies and the sale is rescinded. The object returns to Reuven and the money returns to Shimon. Now Reuven wants to sell an object to Shimon but is not willing to return the money in the event of overcharging. He makes a condition on the sale that the buyer will have no claim of overcharging against him. On this law the Amoraim Rav and Shmuel disagree there in the passage:
It was stated: If one says to another, "On condition that you have no claim against me for overcharging," Rav said: he does have a claim against him for overcharging; and Shmuel said: he does not have a claim against him for overcharging.
Rav holds that the condition is void and the law of overcharging remains in force even with regard to this sale. Shmuel, by contrast, holds that the law of overcharging is set aside and the sale stands in any case; that is, on his view the condition is valid.
To understand the continuation of the passage, let me preface that Jewish law does not allow one to make conditions against the law. That is, if a person makes a condition that contradicts the Torah's law, this is 'stipulating against what is written in the Torah,' and the condition is void (while the act remains valid). But there is a dispute among the Tannaim over whether, when such a condition is made in a monetary transaction, the condition is likewise void, or whether in monetary matters the condition stands. The Tannaim disagreed about this: Rabbi Meir holds that the condition is void even in monetary matters, whereas Rabbi Yehuda holds that in monetary matters the condition stands.
Later, the Talmud in Bava Metzia there begins an analysis of Rav and Shmuel's dispute regarding a condition about overcharging. It is natural to compare it to the dispute of the Tannaim (Rabbi Meir and Rabbi Yehuda) regarding stipulating against what is written in the Torah in monetary matters:
Shall we say that Rav stated his view in accordance with Rabbi Meir, and Shmuel stated his view in accordance with Rabbi Judah? For it was taught: If one says to a woman, "Be betrothed to me on condition that you have no claim upon me for sustenance, clothing, or conjugal rights," she is betrothed, but his condition is void—these are the words of Rabbi Meir. Rabbi Judah says: In monetary matters, his condition stands.
At first glance it seems that the Amoraim are disagreeing within the earlier dispute of the Tannaim. The assumption is that their dispute (regarding a condition about overcharging) concerns a monetary matter, and therefore the Tannaitic dispute applies to it as well: Rav holds like Rabbi Meir and Shmuel holds like Rabbi Yehuda.
The Talmud rejects this and argues that there is no dependence between the disputes. It does so in its usual fashion, with each of the Amoraim offering an explanation for why both Tannaim could agree with his own view:
Rav could say to you: I could state my view even according to Rabbi Judah. Rabbi Judah says that only there, because she knew and waived it; but here, does he know what he is waiving? And Shmuel said: I could state my view even according to Rabbi Meir. Rabbi Meir says that only there, because he is certainly uprooting something; but here, who says that he is uprooting anything at all?
Rav explains that according to Rabbi Yehuda, stipulating against what is written in the Torah in monetary matters is a matter of waiver, and therefore in the case of overcharging—where the buyer does not know what he is waiving (because he does not know the market price, and so he may think there is no problem here, in which case there is no waiver, and perhaps for that reason he agrees to the condition)—the condition is ineffective. Shmuel, by contrast, explains that such a stipulation is possible even according to Rabbi Meir, for the very same reason. Since in overcharging the price is not clear and there is no certain uprooting of Torah law, in such a situation Jewish law does not forbid stipulating against what is written in the Torah. The rule that when one stipulates against what is written in the Torah the condition is void applies only in a situation where there is a certain uprooting of Torah law.[5]
Paradox in deciding Jewish law
How should Jewish law be decided in this dispute? The rule we have is that the Jewish law follows Shmuel in monetary matters and Rav in matters of prohibition (see Bekhorot 49b and Niddah 24b). That is, in monetary disputes that belong to Hoshen Mishpat, the law follows Shmuel, whereas in disputes that concern forbidden and permitted matters (Yoreh De'ah), the law follows Rav. The question now is how we should define the domain of the dispute over stipulating against overcharging. Plainly, this is a dispute in monetary law, since it concerns the law of contracts, and the question is whether the contract is valid and what its content is. Therefore, at first glance, one should rule here in accordance with Shmuel, that the condition stands.
In Tosafot, s.v. 'Bameh' (ibid. 51b), they cite the view of Rabbeinu Hananel, who ruled like Rav on the ground that the Jewish law follows Rav in matters of prohibition:
When does this apply? In an unspecified case. Rabbeinu Hananel ruled in accordance with Rav, for the law follows Rav in matters of prohibition. This is difficult, for they do not disagree about whether it is permitted to do this; rather, they disagree about whether he is obligated to return the overcharge, and in monetary law the law follows Shmuel.
Rabbeinu Hananel rules like Rav because this is a discussion of prohibitions, and Tosafot indeed express surprise at him, for this is a dispute in monetary matters (contract law), and in monetary matters the Jewish law follows Shmuel.[6] Rabbeinu Hananel himself presumably held that this is a question of prohibition rather than money, since the dispute is over whether the law allows one to make such a condition against what is written in the Torah or not.[7]
A close look at the arguments brought by the Talmud shows that what is created here is a loop structure like that of the liar paradox. According to Rav's position, the principle of stipulating against what is written in the Torah in monetary matters belongs to the law of contracts, and therefore he explains that according to Rabbi Yehuda one may stipulate because there is waiver here. According to Shmuel's position, however, this is a halakhic question (about the law of conditions in general, and not specifically about monetary conditions); in his view, the fact that according to Rabbi Yehuda a stipulation in monetary matters takes effect is not connected to the laws of waiver, but rather to the laws of conditions in Jewish law.
We thus learn that according to Rav this is a dispute in contract law, which is part of Hoshen Mishpat, and if it is a monetary matter the law should be like Shmuel. According to Shmuel, by contrast, this is a halakhic dispute of forbidden and permitted matters (whether or not one may make such a condition according to Jewish law), and therefore the law should be like Rav. This is a paradox of decision, parallel to the liar paradox: if Rav is right, then the law is like Shmuel; and if Shmuel is right, then the law is like Rav.
At first glance, neither Tosafot nor Rabbeinu Hananel understood the passage this way, since they make use of the ordinary decision-rules for disputes between Rav and Shmuel (and differ only over which rule applies here). But according to the analysis I have presented here, it follows that in this case one cannot use those decision-rules at all, because if the law is like Rav then it is like Shmuel, and vice versa.
But this is not necessary. Tosafot's position can also be understood in light of the analysis I have proposed. Tosafot say that according to Rav it follows that the law is like Shmuel, and according to Shmuel it turns out that although the issue is indeed not monetary (contractual), neither is it a question of forbidden and permitted matters (for there is no prohibition against stipulating against what is written in the Torah; the condition simply does not take effect). Therefore the rule that the law follows Rav does not apply here, because this is not 'matters of prohibition'. If so, Shmuel will hold that the law follows him, and Rav holds that the law follows Shmuel (because in his view this is a monetary issue), and therefore Tosafot say that one should rule here like Shmuel. But Rabbeinu Hananel's position is entirely unclear. Rav certainly holds that this is a monetary issue, so how can it be defined as a matter of prohibition?
Between a practical ruling and a solution to the paradox
Even without Tosafot's reasoning, we have here a paradoxical loop structure. If the law is like Rav, then it is like Shmuel; and if it is like Shmuel, then it is like Rav. This is a loop parallel to that of the liar paradox. So what does one do in practice in such a case? It seems that from the halakhic standpoint one proceeds according to the laws of doubt. Before us is a sale transaction with a condition. The sale certainly exists, and the only question is whether the condition is void. Since we have a doubt whether the condition is void or not, doubt does not displace certainty, and therefore the sale stands and the condition remains in force. If it turns out that there was overcharging (the price was higher than the market price by more than one-sixth), the sale is not undone, because the buyer who demands rescission of the sale must prove that the law is like Rav, and that cannot be done here. In effect, even on the level of practical conduct the law comes out like Shmuel.
But of course this is not a solution to the paradox, but only guidance about what to do in practice. The question of what the theoretical law is in such a case remains open, and there seems to be no solution. This solution parallels Russell's solution to the liar paradox that we saw above (the theory of types). There too, a solution was proposed that ostensibly offers us a way to conduct ourselves without encountering the problem and without its troubling us, but it does not provide a genuine solution.
It is important to understand that with regard to this problem, Ron Aharoni's claim can no longer be made. Here we are dealing with claims that have real content (they do not deal only with themselves). They speak about Jewish law and make halakhic claims that are supposed to be true or not. The rules for deciding Jewish law also obviously have clear meaning, and Rav and Shmuel's claims too have clear meaning. We therefore need to decide which claim is 'true' (that is, which should be adopted as Jewish law), but as we have seen there is no way to do so. No truth value (or halakhic ruling) can be attached to either of the two positions, because what we have here is a paradoxical loop structure. This parallels the loop structure of the liar paradox. We will now see a halakhic example with a structure parallel to the anti-paradox.
Anti-paradox in deciding Jewish law
The Talmud in Eruvin 13 describes a prolonged dispute between Beit Shammai and Beit Hillel, which ends with a decision by a heavenly voice that the law follows Beit Hillel. And in Tosafot here (Eruvin 6b) they ask:
Here, this was after the heavenly voice. And if you ask: why is it different, that we do not rule in accordance with the heavenly voice in the case of Rabbi Eliezer in Hazahav (Bava Metzia 59b)?
They ask how one can follow a heavenly voice, while in the case of the oven of Akhnai it was established that from the verse "It is not in heaven" one learns that no attention is paid to a heavenly voice.
They offer two answers to this. The second is:
Moreover, there it was against the majority, and the Torah says, "to follow the majority"; but here, on the contrary, the House of Hillel were the majority, and the heavenly voice was only needed because the House of Shammai were sharper.
Tosafot's words imply that beyond all the specific disputes between Beit Shammai and Beit Hillel, there was another broad meta-halakhic dispute between them: whether one follows the majority of wisdom or the numerical majority (see also my column 66 and 69). Beit Hillel were more numerous, whereas Beit Shammai were sharper.
The situation now is as follows: there is a dispute between Beit Shammai and Beit Hillel over whether one follows the majority of wisdom or the numerical majority. The facts are that Beit Shammai were sharper (that is, they were the majority of wisdom), while Beit Hillel were more numerous. Hence, if one adopts Beit Shammai's position on the meta-halakhic question—that one follows the majority of wisdom—then on the halakhic plane the law is like Beit Shammai, since they are the majority of wisdom. That is, this claim is consistent. But even if one rules on the meta-halakhic plane like Beit Hillel, it follows that one should also follow them in Jewish law. That is, this determination too is consistent. This is a state of anti-paradox, and therefore we have no logical way to decide this dispute. This is exactly the explanation Tosafot offer for why a heavenly voice was needed here: because it cannot be decided by the ordinary rules of Jewish law.
And again I would note that even in this example there is no place for Ron Aharoni's claim. The claims of the two sides (Beit Shammai and Beit Hillel) have halakhic content on both levels: both on the concrete halakhic level (for example, in the dispute over the rival wife of a daughter, whether she is permitted or forbidden) and on the meta-halakhic level that deals with legal decision-making (whether one follows the majority of wisdom or the majority of people). Thus the structure of the passage is like an anti-paradox, since there are two consistent solutions in parallel. Again we have no way to decide the truth value (the halakhic value) of the question, but it is a real question.
Of course, the solution of the heavenly voice is a practical rather than a substantive solution, exactly as we saw in Russell's theory of types regarding the liar paradox, and regarding the rule that doubt does not displace certainty in the case of a stipulation concerning overcharging. For precisely that reason, resorting to a heavenly voice is not an option in the context of the paradox. There, ruling like Rav, just like ruling like Shmuel, is inconsistent. Even a heavenly voice cannot decide in favor of an inconsistent ruling. At most it can propose a practical rule of conduct. In an anti-paradox, where both rulings are consistent, there is room to resort to a heavenly voice to tell us which of the rulings to choose, but even there it seems that this is not a real solution. It is a practical decision, but one cannot (or at least it is very implausible to) regard a lottery as the true Jewish law for such a case.
In the next column we will see two examples with respect to which one must ask whether they resemble a paradox, an anti-paradox, or neither of the two: Alexander of Afriki and Buridan's ass.
[1] See my article on this here.
[2] I do not mean to say that this was necessarily the speaker's intention, but only to claim that there exists a logically consistent meaning for this sentence. According to what is called in logical interpretation the 'principle of charity,' we assign to every sentence a consistent meaning, even if it is not clear that the speaker intended it.
[3] One must remember that Jewish law is the work of human beings and not the creation of the Holy One, blessed be He, and as such it is certainly exposed to failures and paradoxes. The fact that it is binding does not mean that it is necessarily perfect and correct, or free of paradoxes and failures.
[4] The medieval authorities (Rishonim) discuss why conjugal rights are considered a monetary matter. Some of them wrote that in truth the discussion concerns only food and clothing (and conjugal rights entered merely as a stock phrase), while others wrote that the obligation of conjugal rights is a contractual obligation and therefore like a monetary matter (like an undertaking to provide a service).
[5] Plainly, according to Shmuel, even in matters of prohibition, if a person stipulates against what is written in the Torah in a way that does not certainly uproot it, there too the condition would stand. For example, if a person stipulates: "I am hereby a nazirite on condition that I may drink the contents of this bottle" (and he does not know whether it is wine or water), this is not stipulating against what is written in the Torah, and his condition stands.
[6] See also in Hagahot Maimoniyot (Laws of Sale, ch. 13, law 3, sec. g), who wrote that there were Geonim who ruled like Shmuel, "for the law follows him in monetary matters" ("for the law follows him in monetary matters").
[7] There is some support for this: in the passage in Gittin 84b they raised the possibility of linking the law of stipulating against what is written in the Torah to a stipulation to commit a prohibition (such as "on condition that you eat pork", "on condition that you eat pork"); but this is not the place to elaborate.
Discussion
In principle, he should examine the issue of customs and act according to his own conclusion.
But in your question there is no paradox. He should act according to the custom of City A. After all, the mara de-atra of A tells him to do as the mara de-atra of B says, and that one tells him to do as A says. So let him do as A says.
Perhaps you mean that there is an additional halakhic dispute between them that is unrelated to this dispute about the laws of custom? I think that even then the reasoning in the previous sentence is correct, and again he should follow the view of the mara de-atra of A.
Unless we say that a dispute over whether a given law belongs to the category of monetary law or not is itself defined as a dispute in ritual prohibition, and therefore the halakha follows Rav. And when we say that the halakha follows Shmuel in monetary matters, that is only when the dispute is not about the very classification as monetary law. Possibly this is what Rabbenu Hananel held.
At first I thought to answer you like this:
Even if you are right, you are assuming that “ritual prohibition” includes everything that is not monetary law. I’m not sure about that. “Ritual prohibition” means forbidden and permitted, and it is quite possible that this is a specific category, just like monetary law. What is the halakha regarding ritual impurity and purity, or sacrificial matters: do you think that in those areas too the halakha follows Rav?
But afterward I thought that this is not merely a dispute about a particular law. Rav and Shmuel first of all disagree about how to understand the point of dispute between Rabbi Yehuda and Rabbi Meir. According to Rav, this is a monetary dispute, and according to Shmuel it is a dispute about prohibition. The disagreement in the law regarding stipulating away the law of overcharging is a result of that interpretive dispute. Therefore I do not think that deciding the dispute between Rav and Shmuel is a decision in the dispute about stipulating away overcharging. On the other hand, it is not reasonable to view a decision about how to interpret a tannaitic dispute as a halakhic ruling (since it is an interpretive ruling). This requires further study.
The moment you create a certain construction with rules/claims detached from reality (“in every x the halakha follows so-and-so” is a statement detached from reality in the sense that no matter what the case is, once it belongs to set x it will be decided as y), you can get a paradox or anti-paradox exactly as in language with similar rules. So I didn’t understand what is novel about examples from halakha compared to the examples at the beginning of the post. That is, how do the halakhic cases show us that paradoxes are real problems, and not just errors originating in language?
I do not understand the argument. In your view, does every sweeping rule lead to paradox? It seems to me that you have gone completely overboard. Here is a sweeping rule: every integer that you multiply by 2 yields an even result. What paradox comes out of that?
And even if from some such rule one can arrive at a paradox, it is interesting and nontrivial to see that it actually occurs in practice (for example, in our case there need not actually be a case where Shmuel claims that a certain matter is one of ritual prohibition and Rav claims it is monetary).
My claim is that in a paradox like the liar paradox one can say that the sentence has no content at all. It is mere wordplay, since it says nothing whatsoever about the world outside itself (=the sentence). But these rules definitely do say something about the “world” (the halakhic one), and therefore it seems that they have meaning in their own right. And if a paradox arises, it cannot simply be dismissed as though we had here a meaningless sentence like the liar paradox. Perhaps it is meaningless, but that has to be shown. In the liar paradox, that claim can be made on its face.
Yosef wrote (I moved it here):
A fascinating issue.
A somewhat similar story appears in the book “HaTorah HaMesamachat”: Rabbi Shlomo Zalman Auerbach had the practice of not answering questions related to the conduct of the city of Jerusalem, and he referred questioners on such matters to the “Minchat Yitzchak” — the rabbi of the Edah HaChareidis in the city. Once a question arose regarding Purim in the Ramot neighborhood: the “Minchat Yitzchak” held that Ramot was too far from Jerusalem, and therefore the Megillah is read there on the 14th. By contrast, Rabbi Shlomo Zalman held that any place that pays taxes to the Jerusalem municipality is considered part of Jerusalem, and one reads there on the 15th. However, when they came to ask him about this matter, he said the following:
“As you know, in questions of public policy in Jerusalem I defer to the mara de-atra. Now, the mara de-atra himself holds that Ramot is not part of Jerusalem, and consequently it is not part of the area under his rabbinate, so ostensibly I can rule on the matter; but I myself hold that Ramot is indeed part of Jerusalem, and therefore I cannot rule…”
My comment:
Very nice. It is even trickier than the example brought here, because it is not clear whether in the question of what is included in Jerusalem the mara de-atra has authority, since this is a question at one level beneath his authority (it determines the scope of his authority). It is like a discussion in the High Court of Justice about the scope of the High Court’s own powers.
But in the end these rules too are meaningless and contentless when they contain a contradiction (because a contradictory statement has no meaning).
And here they contain a contradiction (if one accepts them without qualification), because it follows from them that in certain laws the halakha follows Rav, namely that the halakha does not follow Rav. (This is not essentially different from a case in which Rav were to say explicitly: “Halakha: the halakha is not like me,” which is the classic liar paradox. Only here Rav did not say it; the rules of decision did).
My claim is this. The reason for the paradox in the case of Rav and Shmuel is the set of tools and rules defined within the halakhic world that create the possibility of such a paradox. The fact that we treat halakhic language as binding is nice, but I really do not understand why that adds anything compared to the liar paradox. One could just as well create a conceptually and behaviorally binding framework in which the assumption is that either the whole group are liars or truth-tellers, and under that belief the framework would drag us into a paradox. In other words, the fact that we treat these rules rigidly, with no exceptions, does not make the paradox more real.
I don’t understand. I am not defining a system of rules here. This is halakha, and if I have trust in it then it is an existing system of rules, not one I created ad hoc. Fine, one can also disagree.
Obviously. If a paradox arises, you can see that itself as proof that the rules contain a contradiction. That is tautological.
But these rules/statements have meaning before one points to the paradox. By contrast, in the sentences of the liar paradox everyone can see that they have no meaning in themselves, even apart from the fact that a paradox arises within their framework.
Where do you give classes in Petah Tikva, and when? (I live there and would be happy to participate.)
By the way, in the past I already asked about the paradox of the ontological argument that does not sit well with me, and I argued that it is simply a paradox, and just as every paradox does not testify to truth (because, as noted, there is a contradiction), so too this argument. And the point is that the paradox in this argument is already in the assumption that the unbeliever in fact does believe, which creates the same loop you talked about, and what that shows is that indeed there is a mistaken conception here even before the assumption in the argument that God exists — an assumption that cannot be refuted and therefore one is supposed to conclude that it is correct. Rather, the very structure is paradoxical, and that is where the problem lies: it is just a paradox and should not be taken seriously.
At Beit Knesset Mishkan Yisrael, 7 Glitzenstein St. Thursdays, 20:45–22:00.
Your argument is absurd. I take paradoxes very seriously, because a paradox is a proof by contradiction that one of the premises is incorrect. Only if you point to the flaw in the argument can you dismiss it. Someone gives you a proof and you reject it because it is obvious that it is not true? That is ridiculous. By that logic, nothing could ever be proved to you and you would never discover that you are mistaken.
But beyond that, the ontological proof is not at all a paradox. It merely shows that a person is sometimes unaware of his beliefs. What is paradoxical about that? Whenever someone proves to you that you were wrong, that is the situation. You discover that you were not aware of your own beliefs.
How does it work there — is anyone who comes welcome?
My claim is that reality shows that this is not correct, and I did not decide on my own that it is obviously not correct, as in the example of Achilles and the tortoise and in many other places where the contradiction is between reality and the argument that proves otherwise; then we assume that the argument is mistaken and not reality. And therefore this gives me some indication that if one of the premises in a paradox is wrong, then usually it will be the conclusion of the argument, and that is what causes the confusion. (In my humble religious opinion, there must be some explanation that accounts for why paradoxes are simply not correct, each in its own way, since they run against reality, and it seems to me that there is some error in the structure of the argument.) Therefore in this case as well I am inclined to assume that the mistake lies more in the way the claim is presented and less in the fact before us — namely, the person who claims that he does not believe.
It seems there is no difficulty with the commandment “Do not stray after your hearts and after your eyes,” and more than that, it is a very natural commandment, because from God’s perspective it is desirable that a person not be seduced into error. Like a father commanding his son not to graze in чужд fields lest he hear other things. And likewise regarding Maimonides’ counting the commandment of faith as a positive commandment — they already challenged him: how can one command a nonbeliever to believe, since he does not see himself as belonging to the system? And the answer is that in any case a believer fulfills a desirable commandment, even though a nonbeliever will not obey this commandment.
Only one could make two claims: a. Is it desirable to the Holy One, blessed be He, that a person believe without the truth having become clear to him, but rather out of simplicity/naivete? (as per the well-known view of Rabbi Nachman)
b. Can this be called a commandment if it cannot be enforced?
What is this doing here? What is it referring to?
Either explain, or move it to the relevant thread, or open a new thread.
Something does not fit with this understanding of Tosafot. If one accepts the conclusion in the Oven of Akhnai that we do not follow a bat kol, one must also accept the conclusion there that we follow the majority, and then one should rule like Beit Hillel. Seemingly, if this sugya is normative halakha, then the possibility of deciding according to a majority in wisdom has already been rejected.
The question is whether one follows a majority in wisdom or a numerical majority. In Yavneh, that question was not decided.
Sorry, could someone explain to me the diagram at the beginning — sentence A, sentence B? I don’t understand the diagram. Could you give a practical example of a sentence? In short, I didn’t understand.
I didn’t understand the question. But if you are asking for a diagram, I have no way to provide one here.
The Tur explains, following Tosafot, that in a dispute over the rules of decision there is no way out except to resort to a bat kol, and therefore they took notice of its words in the dispute between Beit Shammai and Beit Hillel. In the spirit of that Tur on paradoxes, one could suggest an additional explanation (perhaps it is included in the Tur, or in the answer to the question in column 563, but in any case it may sharpen the point).
Beit Hillel’s side, to follow the numerical majority, seemingly presupposes that “It is not in heaven.” And Beit Shammai may have held that it is in heaven, and therefore the majority in sharpness prevails. Or they may have held that it is not in heaven and nevertheless that the majority in sharpness is preferable in order to approximate the truth on earth as much as possible. If Beit Shammai’s view was that it is in heaven, and therefore the majority in sharpness prevails, then it becomes very clear how the bat kol helped. The bat kol came forth from heaven and said to follow the numerical majority — that is, that one should not heed heaven. Then Beit Shammai were caught in a paradox and were forced to assume they had been mistaken and that one does not heed heaven. And therefore precisely in this dispute the bat kol was effective. What do you think?
[Whereas if Beit Shammai held that it is not in heaven and nevertheless one follows the majority in sharpness, then indeed they would not heed a bat kol, and it also would not have gone forth for nothing; rather, they held that it is in heaven, and therefore the bat kol came forth and they were influenced by it. And the practical upshot is that today one could say that it is not in heaven and that one follows the majority in sharpness rather than the numerical majority, because one does not heed a bat kol. This also explains how anyone can have the authority to say “It is not in heaven” and to dispute a bat kol (if, for example, a bat kol were to come forth and say that “the morrow after the Sabbath” is indeed as the Sadducees say): if there are the words of the master and the words of the disciple, whose words do we obey? But since a bat kol came from heaven, and from the words of heaven themselves we learned that they concede that it is not in heaven. Personally, however, I think that in truth it is in heaven, and aggadic statements have their place of honor, and no one has authority to say otherwise.]
Hello,
I only recently began learning Gemara, so I apologize in advance if the questions are basic or not entirely clear. I read all the posts on the site about paradoxes, contradictions, and loops in the Gemara and halakha, and I want to ask a question about the paradox in stipulating away overcharging.
1. In your opinion, is the solution one could propose for Tosafot’s ruling — that stipulating away overcharging is not part of the laws of ritual prohibition — correct? If so, then there really is no paradox and this is genuine halakha. How can one determine on a firmer basis whether stipulating away overcharging is not part of ritual prohibition, in which case there is no paradox, or is part of ritual prohibition, in which case there is a paradox and the halakha is not genuinely true but only a practical ruling? If it really is a paradox, why write a halakhic rule for passages in the Gemara that says nonsense at all? If there is a contradiction, one cannot determine halakha, and the Gemara is not really saying anything with respect to the sugya; everyone should act according to what seems right to him.
2. Are there examples in the Gemara of paradoxes/contradictions that cannot be solved in the way suggested for Tosafot’s ruling about stipulating away overcharging? Or in other words, are there really contradictions in the Gemara that cannot be resolved by a plausible solution? I read the posts about solving paradoxes in the Gemara by distinctions of time and consistency — are there contradictions to which that sort of solution cannot be applied (as perhaps with stipulating away overcharging, if one accepts that this is a matter of ritual prohibition)?
3. If there really are genuine contradictions/paradoxes that emerge from the Gemara, do you think these are contradictions written by mistake, or is this intentional? Is there any indication of awareness of the paradox within the Gemara itself? If it is by mistake, then as I asked, why derive halakha from them at all? If it is intentional, what do you think the reason is? Can one understand something special about the passage / about the Gemara itself through the fact that it contains a paradox?
In addition, I want to ask a similar question regarding the anti-paradox in the dispute between Beit Hillel and Beit Shammai that was decided by a bat kol. Why establish halakha if both X and Y are true? Is it forbidden to have two legal halakhot for the same question, and therefore one must decide? Or is it simply to prevent a person from ending up in the situation of Buridan’s donkey that you described in the next post?
Thank you very much!!
1. I believe I addressed this in the column. I did not understand your question at the end.
2. I don’t know of any. But an ad hoc solution is always possible. Even if not by means of the principle of consistency, then in some other way.
3. A contradiction is generally between different sugyot, not within the same sugya itself. There is no need to assume that something there was written by mistake. When there are contradictions, it is a dispute between sugyot.
There cannot be two legal halakhot, otherwise there is a contradiction in the system. At most one can refrain from ruling and leave the matter open. You can find in several places in the Gemara: “One who acted like this master acted, and one who acted like that master acted.”
A small addition to the second question — is there really an anti-paradox there at all? Why can’t one decide the meta-halakhic dispute between Beit Hillel and Beit Shammai over whether we follow the majority or the sharper sages, and then there would be only one correct answer? Why does the fact that both positions are consistent indicate that both are true?
Of course one can. That is what they did. But only by means of a bat kol. A decision within the rules of halakha is impossible, because there is no way to determine the method of decision itself. That is the situation of an anti-paradox that necessitated the appearance of the bat kol.
You wrote: “Thus we find… this is a decision paradox parallel to the liar paradox: if Rav is right then the halakha follows Shmuel, and if Shmuel is right then the halakha follows Rav.”
Why?
As the Gemara says in Eruvin, only when there are two contradictory rulings, like spine and skull, is there a problem. But here this is like a dispute between two different or similar topics. For example, if I ruled like Rabbenu Tam that the time for the evening Shema is from plag ha-minha, am I also required to rule like him that plag ha-minha is determined according to his own view of plag ha-minha (that is, Rabbenu Tam’s sunset)? In other words, why should I care that according to Shmuel the dispute between him and Rav is a dispute in ritual prohibition? On that point I can certainly disagree with him.
And similarly later regarding what you wrote about the dispute between Beit Shammai and Beit Hillel: here too, seemingly there is no paradox regarding whom to follow. Because even if we decide like Beit Hillel that we follow the majority, then in other cases where Beit Hillel are not the majority, the halakha would not follow them.
Besides, your understanding of Tosafot is not necessary at all — namely, that there was also a meta-halakhic dispute between Beit Shammai and Beit Hillel. A simpler understanding would be that according to everyone — meaning both for us and for Beit Shammai and Beit Hillel — there is a doubt whether “incline after the majority” applies even when it is clear that the minority are sharper. It is even possible that for Beit Shammai it was clear that one follows the majority in such a case, and on the other hand for Beit Hillel it was clear that one follows sharpness in such a case. Of course, this matters only for someone who is uncertain whom the halakha follows, Beit Shammai or Beit Hillel — that is, someone who does not know how to decide based on each side’s proofs. But for the disputants themselves (Beit Shammai and Beit Hillel, and likewise any other person in the world for whom it is clear), these laws of uncertainty do not apply at all, because for him there is no doubt. As brought and as is known, this is obvious; I will only quote the Shakh that you yourself cited in Choshen Mishpat 25:126: “It is obvious that one does not follow the majority of decisors where it appears plainly in the Talmud that the law is with the minority.”
This has nothing at all to do with two contradictory rulings. We are not talking about a contradiction but about a paradox. A loop.
It is not likely that in this doubt everyone agreed to remain in doubt. But even if so, I brought this here only as an example of a paradox.
That is exactly what I am explaining — there is no loop here, because you can certainly rule (or, more accurately, understand) like Rav that the question about the law of the stipulation, “one who says to his fellow, ‘on condition that you have no claim of overcharging against me,’” is a question in contract law (that is, monetary law), and nevertheless (and for that very reason) rule like Shmuel, because the halakha follows him in monetary matters; and vice versa.
But if you ruled like Shmuel, then you assumed that this is not a question in contract law.
And furthermore, why not the opposite? Rule like Shmuel that this is a question of prohibition and permission, and then rule like Rav. Here that is of course an anti-paradox.
Not true; these are two different questions.
The first question (that is, Rav and Shmuel’s first dispute) is whether the stipulation “one who says to his fellow, ‘on condition that you have no claim of overcharging against me,’” is a question in contract law (that is, monetary law), or a general question.
And on that I have no rules of decision for whom to rule like, because this is a question neither in monetary law nor in ritual prohibition; it is only a matter of how to understand the discussion.
And every Rishon can decide as seems right to him.
The second question (the second dispute of Rav and Shmuel) is: after I have decided what kind of question this is, I am obligated to rule according to the rule that the halakha follows Shmuel in monetary matters and Rav in matters of ritual prohibition. (That is, if I decided in question A that this is a monetary question, I must rule like Shmuel, and vice versa.)
(And I didn’t understand your last point at all — it is exactly the last two words that I wrote.)
Shmuel’s position is a ruling in matters of ritual prohibition, not in monetary law. If in his opinion there had been a question here in contract law, that would have been a different question, and on it he might well have ruled like Rav (we do not multiply disputes unnecessarily).
My last point said that this is an anti-paradox, not just an ordinary sugya. If you agree, then fine.
I see no difference at all between the end and the beginning. (The beginning: you can rule — or more accurately, understand — like Rav that the question about the law of the stipulation “one who says to his fellow, ‘on condition that you have no claim of overcharging against me’” is a question in contract law [that is, monetary], and nevertheless [and for that very reason] rule like Shmuel because the halakha follows him in monetary law. And likewise the end: you can rule — or more accurately, understand — like Shmuel that the question about the law of the stipulation “one who says to his fellow, ‘on condition that you have no claim of overcharging against me’” is a question of ritual prohibition, and nevertheless [and for that very reason] rule like Rav because the halakha follows him in matters of ritual prohibition.)
And I also do not understand why you are forcing your interpretation the way you do.
My point is simple: there are two disputes here, and the first dispute is unrelated to the rule that the halakha follows Rav in ritual prohibition and Shmuel in monetary law.
And “multiplying disputes” is irrelevant here, because in any case there are two disputes here:
First dispute:
How to understand the stipulation “one who says to his fellow, ‘on condition that you have no claim of overcharging against me’” — whether it is a question in contract law (that is, monetary law), or a general question.
And the second dispute is the dispute between Rav and Shmuel as to the law regarding that stipulation.
I will explain one more time and that’s it.
If you applied Rav’s view that this is a discussion in contract law, then Shmuel, who ruled as he did, was dealing with a different question (that of prohibition and permission). Therefore you cannot separate the questions and simply rule like Shmuel.
I applied (that is, interpreted) Rav’s view that this (that is, the above stipulation) is a discussion in contract law, and therefore I will rule on the other question that is thereby created — namely, how to rule regarding that stipulation — like Shmuel.
And I do not care at all that Shmuel shouts that the above stipulation is a law in matters of ritual prohibition; and even if Rav himself were also to cry out that according to Shmuel himself the stipulation is a law in matters of ritual prohibition, I would pay no attention to their outcry, because on this point I have the right to rule (that is, to interpret) that the above stipulation is in monetary law like Rav — and nevertheless, or precisely because of that, to rule like Shmuel.
What really is a paradox
is that I understand that you are the one who doesn’t understand (the penny hasn’t dropped for you),
but on the other hand my intuition doesn’t allow me to think that this is true, since your level of understanding and intelligence is vastly above mine.
(You’ll probably decide here in accordance with my intuition; well, at least it works.)
Rabbi A is the mara de-atra of City A, and he ruled that when a Jew is staying somewhere as a guest, he must follow the rulings of the mara de-atra of the host location.
Rabbi B is the mara de-atra of City B, and he ruled that everywhere, a Jew should follow the rulings of the mara de-atra of the place where he lives.
What should a Jew from City A who is staying in City B do?