Joining Two Witnesses in Monetary Cases – A Probabilistic Perspective (Column 307)

In the previous column I presented the view of the Rif, as quoted in the Rashba on Ketubot, according to which a witness to a loan and a judge who testifies that two witnesses testified before him about that same loan do not combine. The Rashba there raised the issue of special testimony (edut meyuchedet), and we discussed it there. This creates an opportunity to examine a bit the matter of special testimony, and in fact the whole question of joining two witnesses in monetary cases.

Joining witnesses in monetary cases: R. Shimon Shkop

First, let us recall the law we saw in the previous column. The Rif writes that if there is one witness to a loan and another witness who testifies that he himself was once a judge and that two witnesses appeared before him regarding that same loan, they do not combine. The Rashba there asked why we do not treat this as special testimony, which is accepted in monetary cases, and he explains that in special testimony we are dealing with two witnesses who both testify that the borrower owes the lender a maneh (a hundred zuz), and therefore their testimonies combine. But a witness and a judge do not constitute special testimony, because the judge is not testifying about any debt of the defendant (the borrower) but about a case in which witnesses testified before him about the debt.

R. Shimon Shkop, in his novellae to Ketubot there, explains the Rashba’s words, and first precedes this with an explanation of why special testimony combines in monetary cases:

It seems to me that the explanation is that combined testimony (“joining of witnesses”) is effective only if both of them direct their testimony to the reality of one and the same act. But if, with respect to each act, there are not two witnesses, they are not believed at all. However, with regard to loan after loan, joining works, for even though we do not believe them with respect to any particular act of loan, they are believed regarding the existence of a right of lien to a maneh. For according to both of them, Reuven has a right of a maneh over Shimon. For this reason, with six witnesses to particular times we collect only three maneh, just as in a case of three sets of witnesses for three specific times. That is, if the six witnesses testify that from day one to day six Reuven acquired over Shimon a right of a maneh, then from day one to day three there are two witnesses that Reuven acquired over Shimon a right of a maneh, and similarly from day three to day five, and so on.

The novelty here is that in special testimony the subject of the testimony is not the act but the liability (the right of lien, in his words). Regarding that, there are two witnesses even if they testify about two different acts. Therefore six witnesses who testify about six loans on six different days combine into three pairs that obligate the borrower in three maneh.

He now goes on, in light of this, to explain the aforementioned words of the Rashba:

And therefore, in a case of one witness who testifies that he saw the loan and one witness who testifies that the witnesses were examined before him, there is no joining, since with respect to the reality of the act of examination and the act of the loan there are not two witnesses; regarding each act there is only one witness. And with respect to the existence of the liability there are likewise not two witnesses, for the witness who saw that they were examined does not know that Reuven is truly obligated, for perhaps the witnesses lied. When there are two who testify that their testimony was examined, this is as if the witnesses themselves were testifying before us, for any two are believed regarding their testimony. But in such a case, where with respect to the reality of the act there are no witnesses, and with respect to the existence of the liability the witness who testifies about the examination knows nothing, for any two, even though they are believed, this is only by virtue of Torah law, but the witness who sees how they were examined in the court does not thereby know as he would know through direct observation, for perhaps they lied in their testimony. And this is clear.

In the next passage, R. Shimon raises a difficulty on the words of Netivot HaMishpat, who proposes a different understanding of combining two witnesses in monetary cases. In order to understand the discussion, we shall first present the words of Netivot HaMishpat.

Joining witnesses in monetary cases: Netivot HaMishpat

The topic with which Netivot HaMishpat deals is three-year chazakah for land. If Shimon sits on land that is known to be Reuven’s, and Reuven claims against him that the land is his, Shimon replies that he bought the land from him but lost the deed of sale. The law is that Shimon, who is in possession of the land, must bring two witnesses that he sat on it for three years and Reuven did not protest. If he has witnesses for three years, a chazakah is created that serves as evidence that Shimon indeed bought the land from Reuven.

Now, in Shulchan Aruch, Choshen Mishpat 145:2, it rules:

One [witness] testified that he ate (possessed) it in the first, third and fifth years, and the second testified that he ate it in the second, fourth and sixth years – they do not combine, because in the year that this one testifies, that one does not testify, and the land and the fruits return [to the original owner].

One witness testifies that Shimon sat on the land in years 1, 3 and 5, and the other witness testifies that Shimon sat on the land in years 2, 4 and 6. The Shulchan Aruch rules that although we are in the realm of monetary law, here the rule of special testimony does not help, and the testimonies do not combine. Indeed, there are two witnesses here, and if we were to combine their testimonies a three-year chazakah would be formed. Nevertheless, in this case they do not combine. According to R. Shimon, this ruling is obvious. The two testimonies have no common content, and therefore there is no way to combine them into one testimony. The testimony at issue concerns the years of possession of the land, not any debt, but the two witnesses are not speaking about the same years. Moreover, had each of them testified to three consecutive years, one could say that both testify that Shimon has ownership of the land, and perhaps their testimonies could be joined. But when each witness’s testimony concerns scattered years, then even if we were to accept the testimony of each of them as worth two witnesses, no chazakah would result.

The Sema there, in se’if katan 2, adds that even if six witnesses came, each testifying about a different year, their testimony does not combine to create a chazakah. At first glance this follows naturally from what we have seen. But Netivot HaMishpat (there, se’if katan 2 in the Biurim) disagrees. In his opinion, six such testimonies do combine (like special testimony). He of course must explain how this fits with the ruling of the Shulchan Aruch, and in fact how he understands the institution of special testimony in general. He certainly does not understand it like R. Shimon, for according to the explanation we saw, the conclusion of the Sema follows naturally. Netivot HaMishpat there explains the Shulchan Aruch’s ruling, and from that derives his surprising conclusion:

“First, third and fifth.” See Sema sec. 2, who writes that even six witnesses, etc. At first glance this is puzzling: why should there not be a chazakah when one testifies regarding years 1, 3, 5 and the other regarding 2, 4, 6? For if there were six witnesses, each testifying about one year, they would combine; now, merely because the one who testifies about year 1 also testifies about year 3, the testimony is nullified? Let this witness not be worse than another witness who would testify about year 3. Shall a witness be disqualified from another testimony just because he already testified once? And what is the difference from a case where one says: a maneh in Nisan, a maneh in Sivan and a maneh in Av, and another says: a maneh in Iyyar, a maneh in Tammuz and a maneh in Elul – where we extract from him three maneh?”

“And the reason seems to be that two witnesses in special testimony are believed only in a case where, if we were to say that he is not liable, we would necessarily have to say that two witnesses are lying; for example, when one says: a maneh in Nisan, and one says: a maneh in Iyyar, and he (the lender) claims both, for if we say that he is not liable at all, we must say that two witnesses are lying. And we do not say this, and thus he is in any event contradicted by two. This is not so in the case where one says: ‘on her back’ and one says: ‘on her belly’, which is considered half-testimony in the Talmud [Bava Batra 56b], for the reason that even if we suspect only one witness of lying, she is a minor. According to this, our case works out well: for in a case where one says 1, 3, 5 and one says 2, 4, 6, since they are scattered, there is no chazakah. Therefore, even if we suspect only one of them of lying, there is no chazakah, and the challenger is not contradicted by two, and it is unlike the case where one says 1, 2, 3 and one says 4, 5, 6, for according to each of them there was a chazakah. And the challenger, who says that there was no chazakah by the possessor, is contradicted by two. This is not so in the case of six witnesses, each testifying about one year: it is impossible to say that there was no consecutive chazakah, unless we say that two witnesses are lying. And we do not say this, and thus the challenger is contradicted by two.”

Netivot HaMishpat begins with an explanation of the advantage that two witnesses have over one. His claim is that this is a statistical advantage (a reduction in the probability of an erroneous judgment). If the probability that one witness is lying is P, then the probability that two are lying is of course smaller; let us denote it by Q.[1] Essentially, Netivot HaMishpat prefers to formulate this from the opposite side: when one witness comes before me, if I do not accept his testimony then I am effectively assuming that he lied (or erred). What is the probability that one witness lies? P. This is indeed a small probability, but still large enough that we must worry about it and therefore do not extract money based on this one witness. But if two witnesses come before me and nevertheless I do not accept their testimony, I am effectively saying that both lied. The probability of that is Q, which, as stated, is smaller than P. This is too small a probability, and therefore it suffices to prevent us from refraining from extracting money based on the two witnesses.[2] For this reason we extract money based on two witnesses but not on one.

Now we must consider what happens when we have more than two witnesses. His formulation is that we must always assume the opposite of what they say, and then calculate the probability of that assumption. If it is smaller than Q, we may not adopt it. That is, if the assumption of the opposite means that at least two witnesses lied, we must not reject their testimony. The significant implication of this thesis is in a situation of split testimonies, and therefore let us now examine all the cases of split testimonies with which Netivot HaMishpat deals in the passage cited above:

1. Special testimony. When there is one witness about a liability of a maneh due to a loan on day A and another witness about a liability of a maneh due to a loan on day B, then the assumption that the defendant does not owe a maneh means that both are lying (for even if only one of the loans occurred, the borrower owes a maneh). Therefore we cannot adopt this assumption and rule against the two witnesses. This is why special testimony in monetary cases combines.[3]

Notice that his explanation differs from the one we saw in R. Shimon Shkop. R. Shimon explained that in order to accept testimony about some case, there must be two witnesses about that same matter. Therefore he must explain why witnesses are combined in special testimony in monetary cases. He explains that the “case” about which they testify is the liability itself (and not the act of the loan). According to Netivot HaMishpat, this is a simple conclusion that requires no explanation. In his view, we do not need to say that the content of the testimony relates to the liability and not to the loan, but only that de facto this is what follows.

2. Half a matter. One witness testifies that there is a hair on the girl’s belly, and another testifies that there is a hair on her back. The testimony is not accepted, because even if we rule that she is still a minor, this does not mean that both witnesses lied. It suffices to assume that one of them is lying, for one hair does not indicate puberty (he assumes that the two hairs are not a probabilistic accumulation but a substantive sign of maturity: as long as there are not two hairs, there is no adulthood). Therefore special testimony is accepted, but testimony about half a matter is not.
3. When we have two witnesses, one about three odd years and the other about three even years, the assumption that there was no chazakah does not require that both lied. It suffices that one of them lied in order to explain the situation. If so, such testimony cannot be accepted, for the possibility that one lied remains acceptable.
4. When we have two witnesses, one about the first three years (1–3) and the other about the three that follow (4–6), then according to Netivot HaMishpat we do accept their testimony. According to R. Shimon Shkop, this should seemingly be rejected, because there is no combined content. According to Netivot HaMishpat, however, it is accepted, because if we decide that there were not three consecutive years of chazakah, it emerges that both witnesses lied (it suffices that one of them is telling the truth in order for there to be three years of chazakah), and this, as explained, is not acceptable.
5. When there are six witnesses, each about a different year (the case of the Sema): if the court rules that there was no chazakah, this means that in its opinion there were not three consecutive years of chazakah on the land. But how can that be? There must be at least two witnesses who lied. In the case where only one lies, there will always remain a chazakah of three consecutive years based on the other witnesses. But if, for example, the second and fourth witnesses lie, there is no longer a chazakah. In such a case we accept the testimony, because the assumption that two witnesses lied is not acceptable.

What is his dispute with the Sema? The Sema claims, like R. Shimon, that the basis is a formal requirement that there be a joining of two witnesses regarding the same case. In this scenario the “case” at issue is the year of chazakah. Regarding none of the six years do we have two witnesses, and therefore we cannot accept their testimony about any one year. From the court’s perspective, he did not hold the land even for a single year. As stated, for R. Shimon this is almost self-evident, since there is no common content for which we could combine the two testimonies.

At first glance, the Sema’s ruling is proven from the ruling of the Shulchan Aruch (which we discussed above in case 3). But Netivot HaMishpat claims that he did not understand the Shulchan Aruch correctly (see the explanation in case 3), since the calculation is probabilistic and not a formal joining of two witnesses. In order to reject their testimony and decide that there was no chazakah, we must assume that at least two of them lied. Therefore here we accept their testimony.

But now Netivot HaMishpat raises a not-simple question against his own approach:

“And one should not ask: if so, when there are six witnesses, each testifying about a maneh at a different time, the borrower should be obligated to pay five maneh, since we do not suspect two witnesses of lying.”

If there are six witnesses, each testifying about a maneh due to a different loan (say, one on each of the six days of the week), then according to his approach one should seemingly obligate the borrower for five maneh and not only three. For if we rule that the borrower is liable for only three maneh, it emerges that three witnesses lied. If we rule that he is liable for four maneh, two lied, and that too is not acceptable. Therefore, according to Netivot HaMishpat’s explanation, we would seemingly have to rule in such a case that he is liable for five maneh.

He proposes the following answer:

“This is not so, for every two witnesses constitute one combination, and we always consider two witnesses as one testimony. And as soon as two witnesses have testified about two maneh, the combining of their testimony regarding a liability of a maneh is complete. Similarly, the second pair of witnesses completes a combined testimony regarding a second maneh, and likewise the third pair regarding a third maneh. For each combined testimony we consider it as a separate testimony, and we treat one witness as the liar, and we validate in each combination of testimony only one maneh, so that not both will be lying in each testimony.”[4]

This is a formalistic answer that seems forced. Every two witnesses are combined into one testimony. Therefore, once two have testified, their combination is completed and they drop out of the calculation. We shall return to this below.

The point of dispute with R. Shimon Shkop

We have seen that Netivot HaMishpat bases the combining of two witnesses on a probabilistic consideration. In his view, the explanation of special testimony is obvious, and there is no need to speak about a combination of the two witnesses regarding the liability instead of regarding the case (as R. Shimon Shkop explained). The criterion for accepting a testimony is: what does its rejection presume? If it presumes that one witness lied, that is acceptable; but if it presumes that two lied, that we are not prepared to assume. This is of course a very reasonable and compelling explanation for the rule of special testimony.

By contrast, R. Shimon understood the combination of two witnesses regarding the same case as a formal requirement (like the Sema). Therefore he needs a specific explanation for special testimony. In his view, it is not clear why special testimony is valid in monetary cases, for in other areas of halakhah the subject is the case and not the liability (for example, in homicide we saw that the witnesses must testify about the event and not about the liability of death of the murderer). By contrast, according to Netivot HaMishpat we can understand why there is a difference between monetary law and other areas of halakhah. One can formulate this in several ways.

The first formulation is rooted in a distinction brought by the Rambam between monetary rulings and capital ones. At the beginning of chapter 20 of Hilkhot Sanhedrin he writes:

“A court does not punish based on estimation of the mind, but only on the basis of witnesses and clear seeing. Even if the witnesses saw him chasing after his fellow [to kill him] and they warned him, and they then averted their eyes, or they entered after him into a ruin and afterward entered and found him murdered and writhing and the sword dripping with blood in the hand of the slayer – since they did not see him at the moment he struck him, the court does not execute based on this testimony.”

In capital cases we judge only on the basis of the testimony of two witnesses. Strong circumstantial evidence is not enough for us (circumstantial evidence is not necessarily worse than the seeing of witnesses).

By contrast, at the beginning of chapter 24 there he writes regarding monetary law:

“A judge may judge monetary cases according to those matters toward which his mind inclines as being the truth, and the matter is strong in his heart that it is so, even though there is no clear proof. And needless to say if he knows with certainty that this is so, that he should judge according to what he knows.”

In monetary law what determines is the information in the judge’s possession. Testimony is required only in order to bring the information to the knowledge of the judges. If they themselves know the information in some other way (and it seems that even if they merely have an impression), they may rule based on other evidence. There is no requirement specifically for two witnesses. If so, special testimony is no worse than any other testimony (according to Netivot HaMishpat, its reliability is exactly the complement of the probability that two witnesses are lying).[5]

A second formulation is based on a distinction of R. Akiva Eiger in Gilyon HaShas, Makkot 5a.[6] There he determines that in monetary law the obligation exists even before the court’s ruling. A borrower is obligated to repay his loan irrespective of the court’s decision. The court only reveals the law if it is not known to the parties and/or enforces it when necessary. By contrast, in capital cases and other areas the liability is created by the ruling. In these areas the ruling has a constitutive status, and without it the liability does not exist. A person who desecrated Shabbat with witnesses and warning is not liable to death until a court rules so with regard to him. In light of this distinction we can perhaps say that in monetary law information must be brought to the judges’ knowledge, and they merely uncover the obligation that already exists. Therefore no specifically formal testimony is required, and it suffices that reliable information is presented. The probabilistic consideration tells us that this information is reliable (the probability that it is false is very low). By contrast, in capital cases formal testimony of two joined witnesses is required as a formal requirement (and not just as a way of bringing information to the judges); it is part of the very act of establishing the ruling.[7] There, testimony is required according to all the formal rules.

Incidentally, at the beginning of Sha’ar 7 there, he discusses the status of testimony as part of the halakhic determination. (Indeed, there he is speaking also about monetary cases, and this is not the place to elaborate.) By the way, at the beginning of Sha’ar 5 he notes that the discussion in court regarding monetary cases concerns the facts and not the law. This too fits with what I wrote above.

In passing I would just note that seeing testimony as functionally needed only in order to bring information before the court leads us to the halakhic rule “hearing is not superior to seeing” (lo tehei shemi’ah gedolah mi-re’iyah). What the judges know themselves (they themselves saw the event) is certainly no worse than testimony transmitted before them. However, according to most Rishonim this rule applies in all areas of halakhah and not only in monetary law.[8]

The difficulties of R. Shimon Shkop

Later in his words there, R. Shimon raises difficulties on the words of Netivot HaMishpat:

“And in Netivot, sec. 145, se’if katan 2, he wished to say that the reason for joining witnesses is that any two do not lie, and only one lies, and therefore with six witnesses we assume that only one lies. On this basis he strained himself in the case of six witnesses about six maneh at specified times: why do we not collect five maneh; see there. But any serious student can see that his words are far from the line of truth. For if so, if one witness testifies that Reuven betrothed a woman and one witness testifies that he caused damage, we would have to assume that one of them certainly did not lie, and there would be a doubt of betrothal and a doubt of liability for damages, for according to Netivot, regarding the maneh as well there is no joining between them, and they are not directing their testimony to one and the same thing. Moreover, how will he handle this sugya, that if only one of them is telling the truth we must obligate in a kal va-chomer, just as two who testified about a loan or about the examination in the court.”

R. Shimon raises here three difficulties: (1) The explanation of Netivot HaMishpat for the case of six witnesses who testify about six different days – why we do not collect five maneh but only three – is forced. (2) He further raises a difficulty from the words of the Rif in the Rashba that we saw above, where he says that a witness and a judge do not combine and this is not like special testimony. According to Netivot HaMishpat it is exactly the same, for the probability that both are lying is too small to be taken into account by the court. (3) He also raises a difficulty from a case where we have twice a single witness about two utterly different matters. For example, one witness testifies that Reuven betrothed a woman, and another testifies that Reuven’s ox caused damage. According to Netivot HaMishpat, the probability that two witnesses are lying is small, and the court should not rule in that manner. If so, we ought to be in doubt about both matters (doubt whether he betrothed and doubt whether his property caused damage).

It is important to emphasize that all these difficulties arise only because of Netivot HaMishpat’s conception. According to R. Shimon there is no difficulty, for he conceives the need for two witnesses as a formal requirement. Therefore it must be a joint testimony about the same case (and in monetary law the liability is the “case”, as we saw above).

We can add another difficulty against Netivot HaMishpat’s position from the previous sugya there in Ketubot. The Gemara there says that according to the Sages of Rabbi, if a witness validates his own signature on a document, he is considered as a witness who testifies about the loan itself and not only about the validity of his signature on the document (in the language of the Gemara: “he testifies about the maneh in the document,” and not “about his handwriting”). From this two conclusions follow, one lenient and one stringent: the lenient conclusion is that if both signatories to a document come, and each validates his own signature, we accept their testimony (because both are testifying about the loan, and therefore they combine as two witnesses regarding it). The stringent conclusion is that if one of the signatories died, and the remaining witness both testifies about his own signature and validates the signature of the deceased, and in addition a second witness comes and validates the signature of the deceased – the testimony is not accepted. The reason is that the living witness contributes three-quarters of the evidential force (he testifies as one witness about the loan and contributes half of the force that validates the second witness’s signature), and the rule is that when combining two witnesses, each must contribute no more than half of the evidential force. In the language of the Gemara: “Three quarters of the money go out on the mouth of one,” i.e. three-quarters of the sum are taken based on one witness. According to Netivot HaMishpat, this rule is seemingly incorrect. In order to reject this testimony and rule that there was no loan, we would have to say that both witnesses lied, something the court does not do. By contrast, according to R. Shimon, who views the joining of two witnesses as a formal requirement, we can understand that within that framework there is also a requirement that each witness not contribute more than half of the evidential force.

A possible explanation of Netivot HaMishpat’s view

Let me preface by noting that it is not clear to me why R. Shimon does not raise a far broader difficulty: seemingly, according to Netivot HaMishpat it should follow that after we have once refused to accept the testimony of a single witness, from then on we should accept, throughout history, the testimony of a single witness in all cases. For if we fail to accept him in one of the later cases, we are thereby assuming that there were two witnesses who lied over the course of history, and that is impossible. In other words, why is there any need at all for a novelty concerning special testimony? Even a single witness should be accepted. I brought the difficulty to the point of absurdity in order to persuade you that it cannot be that Netivot HaMishpat truly meant this.

It thus seems obvious that his intent is that if there are two witnesses about the same case it is not plausible that they are both lying, and therefore we can rule according to them. But if it is one witness about case A and another about case B, then in each of the cases we do not have a high enough threshold even to create doubt (and even if there is doubt, “a doubt does not remove [money] from certainty”). Netivot HaMishpat explains that the joining of two witnesses is a probabilistic matter, i.e. we do not really need a joining between them, but the probabilistic consideration arises only when two witnesses testify about the same matter: it is not plausible that two witnesses are lying about the same matter itself. But with regard to two different matters, clearly there is no such necessity. Does the fact that some witness lied a thousand years ago have any bearing on our case today? Thus the third difficulty of R. Shimon falls away. The first difficulty (regarding six witnesses for six maneh) indeed remains somewhat forced. Netivot HaMishpat himself says that in a case of six witnesses, each testifying about a different year, we collect only three maneh. It may be that even there we can say that when they testify about six maneh, there is no probabilistic joining. We join the probabilities of two witnesses in two cases and view that as one case, but we do not join five cases together to create testimony about one case. And still, there is some force to the objection.

There remains another difficulty, which I added, regarding the extraction of “three-quarters of the money on the mouth of one” (where the two witnesses testify about the same matter – it is testimony about the same loan), and we still have to reconcile the Rashba’s distinction regarding special testimony (the second difficulty of R. Shimon). Regarding the “three-quarters” case, perhaps we can say that the testimonies there are about the maneh in the document and about the second signature, and therefore there is not one matter about which they are lying. The witness who testifies about his own signature testifies about the maneh in the document, and in addition he joins in validating the second signature, but that is already a different subject of testimony (the signature and not the maneh). Therefore we can assume that he is lying about his own signature, for that attributes lying to only one witness. And regarding the second signature indeed we cannot assume that both are lying, and thus we accept that; but one signature does not suffice.[9]

And perhaps we can say that in the “three-quarters” case we can reject the testimony by assuming that only the living witness is lying, whereas the witness who validates the signature of the deceased is telling the truth. In such a situation we do not accept the testimony and do not obligate the borrower, even though we were forced to assume that one witness lied.

Regarding the Rashba’s distinction (the second difficulty), it seems that we can perhaps explain as follows. There we are dealing with two different contents (the judge testifies about the act of the witnesses’ examination, and the witness testifies about the loan itself), and therefore they are two different contents of testimony; thus in that case Netivot HaMishpat holds that we do not apply his probabilistic consideration. Indeed, in order to reject that testimony we must assume that both the witness and the judge lied, and apparently we ought to accept the testimony; but as we have seen, these are two different contents, and in such a case we do not perform the probabilistic calculation. One can also reconcile it by saying that in this case it suffices to assume that the witness alone lied. For even if we accept the judge’s testimony, he testifies about the examination of the witnesses and not about the loan itself, and that is not enough to collect the maneh. According to this, the Rif and Rashba too accord with the words of Netivot HaMishpat.[10]

A probabilistic explanation

I suggested here that Netivot HaMishpat’s reasoning does not operate with regard to different cases but only with regard to the same case. I showed that this reconciles his view with the difficulties, but I did not explain the logic of this as such. Indeed, I brought the alternative to the point of absurdity (that if we once rejected the testimony of a single witness in the past, from then on we could no longer reject any witness on earth). It seems that this is precisely the logic. Clearly there are witnesses who lie from time to time, and therefore that there are two liars over the course of history is certainly plausible. But the probability that the two liars will testify about the same case is very small. Therefore, in that very case we do not accept the assumption that two witnesses are lying.

Indeed, there is room for the argument that the two testimonies are not independent. If there is a motive or conspiracy to lie in this case, they will try to recruit two witnesses to do so. Therefore it is not surprising that the two who lied are concentrated in one case. But it seems that Netivot HaMishpat holds that although it is plausible that they will seek two witnesses for the same case, there is no high probability that they will find them. The presumption of the witnesses’ uprightness (chezkat kashrut) implies that we will not succeed in finding two liars for the same case.[11] Clearly one can challenge this in various contexts, but it is still reasonable to establish such a general legal line.

Something similar exists regarding the difference between two cases of crib death in the same house (for the same mother) and two cases in two different houses. See about this in column 144 (example 3, and in my article linked there). We can perhaps bring another example (which of course is not completely analogous, but is instructive as a parable) regarding throws of a die. On the one hand, the probability that in two throws of a die we will get two sixes is exactly equal to the probability that in one throw of two dice we will get two sixes. On the other hand, the conclusion that the die is biased (unfair) is not the same in the two cases. In the first case a (very slight) suspicion arises, but in the second there is not even a trace of suspicion. When there are two witnesses who come about the same case, the suspicion is different from the case of two witnesses who come about two different cases.

[1] At first glance Q = P², but this is not precise. When two witnesses come and say the same thing about the same case, there is no possibility that one is lying and the other is not. There are only two possibilities: either both are telling the truth or both are lying. If the probability that both are lying is proportional to P² and the probability that both are telling the truth is proportional to (1–P)², then the absolute probability that both are lying is:

Q = (P²)/(P² + (1–P)²) chance

And this is on the assumption that there is no dependence between the two witnesses.

[2] There is a subtle point here. The probability that the witness is lying is a conditional probability: given that reality is A, what is the probability that he will say “not A”? But what interests me as a judge is the reverse conditional probability: given that he said A, what is the probability that reality is “not A”? Indeed, if the probabilities of A and “not A” are equal, then according to Bayes’ formula there is no difference between these two probabilities. For simplicity I assume here equal probabilities.

[3] One can ask why in prohibitions or capital cases we do not combine special testimony. Seemingly, this consideration exists there as well. Apparently, Netivot HaMishpat too agrees that his reasoning is correct in monetary law, where testimony is needed only to inform the judges. But in other contexts there are formal requirements regarding testimony. We shall discuss this further below.

[4] Netivot HaMishpat concludes with a passage dealing with the testimony of six witnesses regarding land. His words here are not clear to me. Above I omitted them, but for completeness I bring them here:

“And likewise here we consider each two witnesses as one combination, and we combine witness 1 with witness 6, witness 2 with witness 5, and witness 3 with witness 4, and we validate one out of each pair. Thus there is testimony about three consecutive years, for whatever testimony we can validate, we validate, as explained in sec. 30, se’if (3) [2].”

He explains that even in the case of six witnesses regarding six years of chazakah, this calculation leads us to three years of chazakah. But this is not at all clear in light of his words up to that point. In that earlier case, Netivot HaMishpat himself explained (see section 5) that the calculation is global – that there should not turn out to be two liars in general. There he did not combine each pair into one testimony. Moreover, how can he, according to his own view, combine two witnesses about different years?

[5] One can ask why we do not rule based on one witness or disqualified witnesses. It seems that in principle we can indeed rule based on such evidence (including close relatives, etc.), as long as the judges are convinced that this is the truth. According to the Rambam, the laws of evidence in monetary matters were stated only for a situation in which the judge has no clear position of his own. In such cases he judges according to the halakhic rules of evidence (and there two valid witnesses are required, etc.).

[6] Indeed, from his words there it seems that Tosafot disagrees, but he presents this as obvious and remains with a difficulty on Tosafot.

[7] On the status of testimony as part of the establishment of the ruling, see Sha’arei Yosher, at the beginning of Sha’ar 7 (although there he speaks also about monetary law; this is not the place to elaborate). Incidentally, at the beginning of Sha’ar 5 he notes that the discussion in court regarding monetary law is about reality and not about the law. This too fits with what we wrote above.

[8] Therefore indeed, according to most Rishonim it emerges that when a court judges a case based on what they themselves saw, this is not a ruling based merely on knowledge, but their seeing is considered as testimony delivered before them (which of course raises the problem of “a witness cannot become a judge,” and this is not the place to elaborate). One can see more about this in my Ketubot lessons on “a witness cannot become a judge.”

[9] Seemingly, there is still room for difficulty: why reject the validity of the witness regarding his own signature, for in the case of two witnesses, each validating his own signature, this is indeed accepted. But this is not difficult, for the joining of two witnesses, each validating his own signature, is only because they combine in their testimony about the loan itself. Here that does not occur (for the validation concerns the signature and not the maneh in the document).

[10] In any case, there are five other Amoraim in the sugya who hold that a witness and a judge can be combined. The Rishonim there all note that it is very difficult to understand their reasoning (for the contents of their testimony really are different). According to Netivot HaMishpat, even if we do not accept his explanation as the halakhic view (that a witness and a judge do not combine), we can still explain quite comfortably the view of the five Amoraim who disagree (and accept the joining of the witness and the judge) along the lines of Netivot HaMishpat. In their view this is indeed legitimate special testimony (as we proposed above), for in order to reject it we would have to assume that both the witness and the judge lied, and therefore they accept it.

[11] Something like this is the difference between two cases of crib death in the same house (for the same mother) and two cases in two different houses. See about this in column 144 (example 3, and in my article linked there). We can perhaps bring here another example (which of course is not completely analogous, but has value as a parable) regarding die throws. On the one hand, the probability that in two throws of a die we get two sixes is exactly equal to the probability that in one throw of two dice we get two sixes. On the other hand, the conclusion that the die is biased (unfair) is not the same in the two cases. In the first case a (very slight) suspicion arises, but in the second there is not even the slightest suspicion. When there are two witnesses who come about the same case, this differs from two witnesses who come about different cases.