CHAPTER 18 – Adin Steinsaltz

1. Qal vachomer and dayo

2. A recurrent fallacy

3. Lack of formalism

R. Adin Steinsaltz, aka Even Yisrael (Israel, b. 1937), translated the Talmud into Hebrew (and other languages) and published it with a new commentary, over many decades, starting in 1965. There is a website called The Aleph Society, where his biography[1]can be read, as well as his commentary on the Babylonian Talmud[2]. I searched there for his comments regarding (using the spelling there preferred)kal va-homerand thedayyoprinciple, and found[3]several posts which I will presently analyze.

I must say I am sorry my analyses turn out to be so critical, because I actually greatly admire R. Steinsaltz’sœuvre. Nevertheless, emotions cannot be allowed to deter us from honest logical assessments. I take Biblical statements like the following as guidelines in such contexts: “Ye shall not… deal falsely, nor lie to one another” (Lev. 19:11), “Thou shalt not respect the person of the poor, nor favour the person of the mighty” (Lev. 19:15), “Ye shall do no unrighteousness in judgment, in meteyard, in weight, or in measure” (Lev. 19:36).

1.Qal vachomer and dayo

In this section, we shall look into R. Steinsaltz’s descriptions ofqal vachomerreasoning and thedayoprinciple in relation to it.

On Baba Kamma 25a-b. Having analyzed Baba Kamma 25a-b in great detail in an earlier chapter (7), I will not here say much about its content. Rather, I will concentrate on R. Steinsaltz’s remarks on the subject and see where he personally stands. What is amazing throughout R. Steinsaltz’s treatment here is the way he blithely ignores all the difficulties involved. He presents the matter very briefly, and on a very superficial level where everything seems obvious and harmonious, and he either does not realize or conceals the inherent difficulties.

As regards the Mishna, R. Steinsaltz only mentions and comments on R. Tarfon’s first argument, without mention of the second. The differences between the two arguments, and between the Sages’dayoobjections to them, are thus completely lost to him or at least skipped over. He interprets R. Tarfon’s first argument as a ‘proportional’ a fortiori (unaware that it could also be read as a mere pro rata argument), and the Sages’dayoobjection to it as a “ruling.” He does not notice that R. Tarfon’s second argument has the distinction that, whether interpreted as pro rata, a crescendo (proportional a fortiori) or pure a fortiori, it has the same conclusion, so that it is immune to the Sage’s previousdayoobjection, so that the Sages’ reneweddayoobjection must be understood differently. His definition of thedayoprinciple is therefore very simple:

“Limiting the conclusions that can be reached by means of akal va-homerin this manner is calleddayyo‘enough.’ It is enough to learn a parallelhalakhahfrom akal va-homer, but not more than the original law itself.”

With regard to the Gemara, he has only this to say:

The Gemara explains that the concept ofkal va-homeranddayyostem from the story of Miriam who spoke inappropriately about her brother Moshe (see Bamidbar 12). As punishment, she was struck withtzara’at(biblical leprosy), and was forced to leave the encampment for seven days. The Torah explains that had her father banished her, surely she would have been embarrassed for seven days – now that she was banished by God, she will have to be removed for that length of time. Although logically banishment because of God’s anger should have lasted twice as long,dayyolimits the punishment to the same amount of time that she would have been embarrassed by her father.”

He does not notice that the Gemara takes for granted, on the basis of thebaraita[4]it is quoting, which refers to the story of Miriam as its model, thatqal vachomeris “logically” a crescendo in form, i.e. goes ‘proportionately’ from seven days banishment to fourteen days in the case under consideration, and that thedayoprinciple “limits” this penalty to seven days. This is of course, as we have shown, not true –qal vachomermay equally well be purely a fortiori argument, in which case there is no call for adayoobjection to it. This means that, in the Miriam example, the conclusion may well be immediately as the Torah has it seven days, rather than fourteen days reduced to seven as the Gemara naïvely claims.

Interestingly, although the Gemara does not explicitly say so, R. Steinsaltz claims that it says that “the concept ofkal va-homer” – and not only that ofdayo– “stems from the story of Miriam.” This is inaccurate, sinceqal vachomeris found earlier in the Torah than in Num. 12:14-15; and as just explained, even the reading of thedayoprinciple into this passage of the Torah by the Gemara (or thebaraitait quotes) is open to debate on logical grounds (though not impossible). These inaccuracies show that R. Steinsaltz has not studied the mechanics of a fortiori argument, and instead simply taken erroneous traditional views for granted.

To these criticisms we should add that R. Steinsaltz fails to mention and analyze all the subsequent issues arising in the Gemara. First, the troubling fact that the Gemara does not notice or take into consideration R. Tarfon’s second argument in its explanation ofqal vachomeranddayo; had it done so, it would have had to admit that a fortiori argument may be non-‘proportional’ and therefore that thedayoprinciple of the Mishna Sages is of two types. Second, in its headlong pursuit of proof that thedayoprinciple is “of Biblical origin,” so that R. Tarfon must know it and essentially agree with the Sages, the Gemara makes up an intricate scenario about their different viewpoints, which upon detailed logical scrutiny turns out to be specious. Unfortunately, none of this is hinted at in R. Steinsaltz’s treatment.

On Baba Kamma 63a-b. R. Steinsaltz’s commentary on Baba Kamma 63a-b is essentially the same, repeating verbatim the above quoted paragraph about Miriam. What is added here is his definition ofqal vachomer, and accessorily (though he does not here name it) thedayoprinciple, as follows:

“The method ofkal va-homerusually translated as an A fortiori argumentallows us to learn one law from another by arguing that if the less stringent law included a stringency, we can conclude that the stricter law includes that stringency, as well. Although the method ofkal va-homeris considered to be a powerful one, it is limited in cases where there is an attempt to derive more than the original law included.”

This is of course a traditional rabbinic definition; we have previously seen other very similar statements. R. Steinsaltz is of course not claiming it as original, though he does not mention its historical author (perhaps because he is unknown[5]). We can better analyze his statement by presenting it more formally, as follows:

Law P is more stringent (R) than law Q,

and, law Q is stringent (R) enough to imply stringency S;

therefore, law P is stringent (R) enough to imply that stringency S.

Notice firstly that this argument is purely a fortiori: the conclusion hasthe same(“that”) stringency as the minor premise. R. Steinsaltz does not remark on the difference between such argument and the a crescendo form assumed by the Gemara in Baba Qama 25a, where the conclusion would be ‘proportional’, i.e. containa greaterstringency. Yet, R. Steinsaltz goes on in the same breath telling us that “the method ofkal va-homer… is limited in cases where there is an attempt to derive more than the original law included.” This is, as already pointed out, an allusion to thedayoprinciple. But then we have a contradiction, or at least a mix-up of genres! If the argument is as he depicts it here purely a fortiori (i.e. non-proportional), thedayoprinciple is irrelevant to it and should not be mentioned. If on the other hand thedayoprinciple is to be mentioned, then the argument must be presented as a crescendo (i.e. as proportional). He can’t have it both ways.

Secondly, said in passing, the above definition ofqal vachomerlacks the usual reverse statement:

Law P is more lenient (R) than law Q,

and, law Q is lenient (R) enough to imply leniency S;

therefore, law P is lenient (R) enough to imply that leniency S.

This statement is implied, for examples, in R. Chavel’s definition: “A form of reasoning by which a certain stricture applying to a minor matter is established as applying all the more to a major matter. Conversely, if a certain leniency applies to a major matter, it must apply all the more to the minor matter;” and again in R. Feigenbaum’s: “Any stringent ruling with regard to the lenient issue must be true of the stringent issue as well; [and] any lenient ruling regarding the stringent issue must be true with regard to the lenient matter as well.”[6]

There is of course no doubt that R. Steinsaltz knows this; but he does not say it here. We do find a broader definition ofqal vachomerin R. Steinsaltz’sReference Guideto the Talmud. There he says[7]that this hermeneutic rule sets up a parallel between two laws, one of which has some stricter aspects than the other. If the stricter law has a certain leniency, then the more indulgent law must have it too; and “vice versa,” if the more indulgent law has a certain severity, then the stricter law must have it too.

Thirdly, note the change in the relative positions of P and Q, in the above two arguments. In the first, P is more stringent than Q; in the second, P is more lenient than Q. But as regards their form, both arguments are positive subjectal (or more precisely antecedental, since the subsidiary item S is implied). Therefore, both proceed (despite appearances) “from minor to major.” It follows that R. Steinsaltz’s definition ofqal vachomerhere, even if expanded as we have proposed, is too narrow, because it ignores the corresponding negative moods as well as all predicatal (or consequential) a fortiori reasoning. His definition is also too narrow because it is focused on legal matters, whereas in fact (even in the Bible and the Talmud) a fortiori argument can be used with regard to non-legal matters. But we can assume that R. Steinsaltz is well aware of the possibility of such wider use, since he quotes in hisReference Guidethe example of Jer. 12:5: “If thou hast run with the footmen and they have wearied thee, then how canst thou contend with horses.”

Moreover, R. Steinsaltz makes no effort at validation of a fortiori reasoning. He does not explain why it is indeed logical to reason in this manner. He takes it for granted without further ado, which attitude is quite curious for a man who was trained in the ways of modern science and mathematics. In hisReference Guide, he informs us that this is the exegetical rule most often encountered; but he does not go any deeper into the subject than that.

As regards the above definition thedayoprinciple, it looks commendably broad because it is sadly vague. Disappointingly, R. Steinsaltz does not delve into the nature, source and justification of this principle, nor analyze when it is applicable in any detail. However, in hisReference Guide, he lists various traditional specifications concerningqal vachomer, such as the possibility of applying it to new situations without the sanction of tradition, and (of significance to analysis ofdayo) the impossibility to infer by a fortiori (as unanimously admitted) a prohibition or (according to some opinions) a punishment.

On Zevahim 69a-b. We will skip the legal minutiae dealt with in Zevahim 69a-b, which R. Steinsaltz does not develop in detail anyway, and rather focus on his general comments. He repeats here, as does the Gemara, previous comments regarding thedayoprinciple, and then adds:

“One question raised by therishonimis why logic would lead us to conclude that Miriam should have been banished for 14 days. Why not 8 days? Or forever?

Rabbenu Tam is quoted as connecting this with the idea that there are three partners in the creation of a person – his mother, his father and God. Thus God is the equivalent of both mother and father and offense against Him deserves double banishment.

Rabbenu Hayyim ha-Cohen suggests that Miriam deserved just a little extra banishment, but the minimum time that someone suffering fromtzara’atis banished is a week, so any additional banishment must be for a full extra week.

The Ramban argues that no explanation is necessary, since this is merely the way themidrash halakhahspeaks; that since she deserves more the expression is that she needs twice as much.”

This text is further confirmation that R. Steinsaltz – like many great rabbis before him – firmly believes that “logic would lead us to conclude” that an a fortiori argument yields a ‘proportional’ conclusion. He takes this for granted and merely like his predecessors questions why the Gemara specifies specifically 14 days as the logical inference from 7 days, and not more or less. Neither he nor they realize that (as I have explained in detail in an earlier chapter (8.2)) the issue of the quantity of punishment has nothing to do withqal vachomeras such, but relates to the separate operation of a principle of justice or of our sense of justice. Thus, though the question asked: “Why not 8 days? Or forever?” is pertinent, it is far less important than the unasked question: why not 7 days?

On Pesachim 81a-b.We need not here either be concerned with the legal details treated in Pessachim 81a-b; suffices for us to look at R. Steinsaltz’s following remarks relating to the range of applicability ofqal vachomerreasoning:

“Although the Gemara on ourdaf(=page) tries to find a source in the Torah for thishalakha, its conclusion is that there is no clear reference in the Torah for it, rather it is ahalakha le-Moshe mi-Sinai, a law that was transmitted orally to Moses on Mount Sinai that was not recorded in the Torah.

… Although Rabbah tries to apply the rule ofkal va-homer(a fortiori) to this case…, the Gemara rejects this, arguing that we cannot learn akal va-homerfrom ahalakha le-Moshe mi-Sinai.

Although we usually perceive the rule ofkal va-homeras being a straightforward logical one, it cannot be used in the case ofhalakha le-Moshe mi-Sinaibecause of the unique quality of suchhalakhot. In general, a law that appears in the Torah can be used not only for itself, but also as a source for other laws that can be compared to it. Ahalakhah le-Moshe mi-Sinai, even as its strength and severity are equal to those of a law written in the Torah, is not seen as being grounded in the same set of rules as the writtenhalakhot, so we cannot extrapolate other laws from it.”

This commentary contains three items of information: (a) a definition of the termhalakha le-Moshe mi-Sinai; (b) the ruling of Rabbah that new laws cannot be deduced throughqal vachomerargument from a premise characterized ashalakha le-Moshe mi-Sinai; and (c) a highlighting of this logical phenomenon as exceptional. As commentaries go this strikes me as a bit thin, so I will now try to add my own reflections.

Regarding (a), what can be said (perhaps rather cynically) is that a law designated ashalakha le-Moshe mi-Sinaiis so labeled precisely because there is no written evidence that it was given to Moses at Sinai ! If anything, what we have here is an early example of the power of advertising, where the jingle counts for more than the product. What many modern commentators say (more moderately) is that such laws were so called simply because they were considered very ancient and already well-established in Jewish jurisprudence.

Regarding (b), the question logicians must ask here is: If X formally implies Y, does it logically follow that ‘X is imperative’ formally implies ‘Y is imperative’? That is, if we can deduce Y from X, can we deduce the legal necessity of Y from the legal necessity of X? Answer: suppose Z is our ultimate standard of judgment (in the present context, say Obedience to Divine Will). Then our question is: if Z is impossible without X, does it follow that Z is impossible without Y? The answer is, clearly, yes: given X implies Y, and not-X implies not-Z, it follows that Z implies X, then Z implies Y, then not-Y implies not-Z[8]. Thus, as regards formal logic, we ought in principle to accept anystrictly deductiveinferences, including those made through properly formulatedqal vachomerarguments. This cannot be disputed, as just demonstrated syllogistically.

Nevertheless, I do not deny that the conclusions of certainqal vachomermay be regarded as having less legal weight than their premises, in acknowledgment that the premises used usually have some inductive origins. In the context of Jewish law, laws that are evidently and incontestably Scriptural are treated as axioms (i.e. as purely deductive in origin), and therefore formal inferences drawn from them are likewise considered reliable; whereas laws transmitted orally are more inductive in nature and thus retain some measure of uncertainty[9], so that even if they areper seconventionally granted credence, laws derived from themper accidensmay still credibly be refused equal weight. In other words, Rabbah’s ruling is reasonable, even if it could have been otherwise.

Regarding (c), which is R. Steinsaltz’s own commentary to the preceding, what I would like to remark on is its relative passivity and superficiality. He notes descriptively that althoughhalakha le-Moshe mi-Sinaiis considered as binding as written Torah law, what is logically derived from the former is not as binding as what is logically derived from the latter. But he does not make any effort to reconcile this surprising phenomenon with the universal implications of formal logic. Instead, he claims that each type of law is subject to a different “set of rules” – suggesting, without any formal demonstration, that such relativism is logically conceivable. My contention here is that today’s more religious commentators must learn to overcome such intellectual restraint, and dare to ask difficult questions. They will find that the possible answers are usually not as frightening as they imagined. Credibility nowadays depends on readiness to question and if need be to honestly criticize.

2.A recurrent fallacy

In this section, we shall look into a couple of concrete applications, where the reasoning seems to be fallacious.

On Pesachim 23a-b.R. Steinsaltz presents theqal vachomerargument in Pessachim 23a-b as follows:

“The Gemara considers a number of cases of forbidden foods in an attempt to clarify whether anissur hana’ah– a prohibition against deriving benefit – is an inherent part of theissur akhila– the prohibition against eating something. One of the cases where we find a disagreement on this matter isgid ha-nashe(the sciatic nerve – see Bereshit 32:33), where Rabbi Shimon rules that we cannot derive benefit from it and Rabbi Yossi ha-Galili rules that we can.

The Gemara suggests that Rabbi Yossi ha-Galili learns this from akal va-homer(an a fortiori argument) as follows: We know that the punishment for eatinghelev(forbidden fats) is very severe (karet), and that the punishment for eatinggid ha-nasheis less severe (malkot). Since one is allowed to derive benefit fromhelev(this is clearly indicated in the Torah – see Vayikra 7:24), then certainly in the less severe case ofgid ha-nasheone would be permitted to do the same.”

This presentation would seem to be an accurate rendition of the Talmudic argument. The problem is that R. Steinsaltz accepts its claims uncritically. Notably, the claim by R. Yossi ha-Gelili[10]that he has put forward a validqal vachomer. Notice the former’s qualification of the conclusion as “certainly” following the premises.

However, on closer inspection, it is not obviously valid, because the terms used in the minor premise and conclusion (viz. deriving benefit fromhelevorgid ha-nashe) are not the same as those used in the major premise (viz. eatinghelevorgid ha-nashe). If there is indeed a validqal vachomer, it must be less direct than it is made out to be; i.e. it must involve some tacit intermediate moves.

But further scrutiny shows that the putative conclusion cannot readily be derived from the given premises! Let us symbolize our terms as follows: P=helev, P1 = eatinghelev,P2 = deriving benefit fromhelev; Q=gid ha-nashe, Q1 = eatinggid ha-nashe,Q2 = deriving benefit fromgid ha-nashe; R = degree of punishment, so that R= 0 means ‘allowed’ and R > 0 means ‘forbidden’. R. Yossi’s argument can then be written as follows:

P1 is more R than Q1;

P2 is R not enough to be forbidden;

therefore, Q2 is R not enough to be forbidden.

This is a negative subjectal a fortiori argument; it has to be so, since the terms P, Q are subjects throughout it and the movement of thought is from major (P) to minor (Q)[11]. But this is not a valid argument, as already stated, because the major premise concerns P1 and Q1, whereas the minor premise and conclusion concern respectively P2 and Q2. We can, still, try to make it valid by proving somehow that “P2 is more R than Q2.”

(a) Knowing that “P1 is more R than P2,” we could through a generalization assume that “Q1 is more R than Q2;” but this does not permit us to infer that “P2 is more R than Q2.” More specifically, we are given that “P1 is more R than P2,” since eatinghelevis punishable (R), i.e. forbidden, whereas deriving benefit fromhelev(P2) is allowed, i.e. not punishable. From this, we couldby generalizationsay: “for anything, deriving benefit is less punishable an act than eating.” It follows by application of this generality that “Q1 is more R than Q2,” i.e. that “eatinggid ha-nashe(Q1) is more punishable than deriving benefit from it(Q2).” We are also given that “P1 is more R than Q1,” i.e. that the punishment ofmalkot(lashes) is less severe than that ofkaret(excision). From this we can deduce that: “P1 is more R than Q2.” But we stillcannotdeduce that “P2 is more R than Q2” – and without this proposition the a fortiori argument remains invalid. So this approach is not successful!

(b) Alternatively, we could trygeneralizing immediatelyfrom the given major premise “P1 is more R than Q1” to “P is more R than Q,” i.e. to “anything to do with P is more R than the same thing to do with Q,” and thence by application infer the needed major premise that “P2 is more R than Q2.” Although such more direct extrapolation is more far-fetched than the one tried previously, since it involves two distinct subjects in tandem, it at least yields the desired result!

Another way to approach this extrapolation would be to write the major premise as a hypothetical: “When (1) eaten,Helev(P) is more severely punished (R) thangid ha-nashe(Q);” then from this generalize to: “Under all conditions,Helev(P) is more severely punished (R) thangid ha-nashe(Q);” then apply the latter to: “When (2) deriving benefit,Helev(P) is more severely punished (R) thangid ha-nashe(Q).” We can now argue, regarding “deriving benefit”: “ifgid ha-nashe(Q) is not punished severely enough (R) to be forbidden, thenhelev(P) is not punished severely enough (R) to be forbidden.” The problem with this approach is of course its credibility: it looks too much like deliberate manipulation to obtain the desired conclusion.

In sum: if deriving benefit fromhelev(P2) is not punishable (i.e. is allowed),it does not necessarily follow thatderiving benefit fromgid ha-nashe(Q2) is not punishable (i.e. is allowed). The latter conclusion is not logically impossible, and may even (as just shown) be produced by inductive means, but as far as deductive logic is concerned it is anon sequitur. There may be another proposition stated elsewhere or tacitly assumed in the Gemara, which makes possible the deductive generation of the required major premise “P2 is more R than Q2,” but I have not found any such intermediary; therefore, as far as I am concerned, the argument has to be judged as formally invalid.

Which means that R. Yossi was arguing in a fallacious manner. R. Steinsaltz, however, like the Talmud before him, takes R. Yossi’s a fortiori argument as essentially valid, though open to rebuttal (“ikka lemifrakh?literally, ‘you can break the argument’”). But note that this rebuttal is not an attack like mine above on the a fortiori process as such, but merely on one of its premises. He writes:

“The Gemara records the response of Rabbi Shimon, who forbids deriving benefit fromgid ha-nashe, as arguing that we cannot seehelevas being more severe, since there are certain rules wheregid ha-nasheis more stringent. For example,gid ha-nasheapplies to all animals, whereashelevis limited to domesticated animals (behemot) and does not apply to wild animals (hayyot).”

The thrust of this counterargument by R. Shimon seems to be the rejection of “Eatinghelev(P1) is forbidden, whereas deriving benefit fromhelev(P2) is allowed.” We are told that the interdiction concerning eatinghelevapplies to domesticated animals, but not to wild ones. For the latter kind of animals, then, eating and deriving benefit are both allowed. Whereas the similar proposition ongid ha-nashe(Q) would have to apply to all animals. In short, the generality of “P1 is more R than P2” is not accepted by R. Shimon.

But anyway, as we have just shown, even if this generality were accepted, R. Yossi’s argument would still not be valid, since we cannot deduce through it that “P2 is more R than Q2.” Both R. Shimon and R. Steinsaltz do not seem to realize this more formal issue. This is a rather disappointing performance on the part of all three of these rabbis, and many others, which goes to show the importance of having formal models to go by.

On Baba Batra 111a-b.R. Steinsaltz describes theqal vachomerargument in Baba Batra 111a-b, after explaining how the premises were arrived at, as follows:

“The Gemara suggests akal va-homer… If a daughter, who has less rights of inheritance from her father’s estate, nevertheless inherits her mother, certainly a son, who has stronger rights in inheriting his father’s estate, will inherit from his mother.”

If we try to present this reasoning in more formal terms, we get the following:

A sonof a man(P1) has more (or stronger) rights of inheritance (R) than a daughterof a man(Q1),

and, a daughterof a woman(Q2) has rights of inheritance (R) enough to inherit from her (the mother) (S);

therefore, a sonof a woman(P2) has rights of inheritance (R) enough to inherit from her (the mother) (S).

This argument looks at a glance like an a fortiori, but is not really one, since the major and minor terms are different in the major premise (P1, Q1) and in the minor premise (Q2) and conclusion (P2), although the middle term (R) and the subsidiary term (S) are uniform throughout. We can turn this argument into a genuine a fortiori, if we manage to deductively or inductively infer the required major premise: “A son of a woman (P2) has more rights of inheritance (R) than a daughter of a woman (Q2).” For a deductive solution, we need appropriate intermediate premises. For an inductive solution, we must accept the generalization of the given major premise, so that the needed major premise can be derived from it.

Alternatively, we could formulate the Gemara’s a fortiori argument with uniform major, minor and subsidiary terms, as follows:

A son (P) has more (or stronger) rights of inheritance (from father) (R) than a daughter (Q),

and, a daughter (Q) has rights of inheritance (R) enough to inherit from her mother (S);

therefore, a son (P) has rights of inheritance (R) enough to inherit from his mother (S).

This would be a valid a fortiori argument if we could ignore the specification “from father” (which I have put in brackets) in the major premise. Otherwise, the middle term R (“rights of inheritance”) would not be the same in the major premise (where “from father” is specified, as given) and in the minor premise and conclusion (where it is irrelevant, and therefore cannot be specified). In order to remove the specification “from father” in the major premise, we need to generalize the given proposition from “A son (P) has more rights of inheritancefrom father(R) than a daughter (Q)” to “A son (P) has more rights of inheritancefrom anyone(R) than a daughter (Q)” – i.e. to move from a relative proposition to an absolute one. In concrete terms, we must presume a son to be generally more privileged than a daughter in matters of inheritance.

Such generalizations are legitimate provided they are performed overtly and explicitly acknowledged to be inductive acts. From a deductive point of view they are of course akin to circular argument or tailoring a premise to obtain the desired conclusion (see similar comments of mine relative to Pessachim 23a-b above, though the present case is a bit simpler). Thus, the author(s) of the Gemara containing this argument may be reproved, either for failing to realize and admit the inductive underpinning of the argument or for unconsciously engaging in fallacious deduction. In other words, there would have beenno logical inconsistencyif the Torah had prescribed that sons inherit from fathers more readily than daughters do, and daughters inherit from mothers more readily than sons do.

R. Steinsaltz next presents us with an attempted application of thedayoprinciple:

“Following this argument, the Gemara continues and concludes that since both sons and daughters inherit their mothers, the sons have priority in this case just as they do in cases when their father passes away. This position is rejected by Rabbi Zekharia ben ha-Katzav who believes that sons and daughters should share equally in the mother’s estate, because of the concept ofdayo….

The Gemara relates that several amora’im wanted to accept Rabbi Zekharia ben ha-Katzav’s ruling, and the Talmud Yerushalmi reports that the Babylonian sages had a tradition that followed his teaching. Nevertheless, thehalakhahfollows the other opinion, and boys receive preference in inheritance laws also in the case of a mother’s estate.”

Apparently, the rabbis read the previously mentioned purely a fortiori argument as a crescendo, i.e. an argument involving a quantitative comparison, in this case a comparison of ‘priority’. For instance, the second version of it may be supposed to contain an additional premise about ‘proportionality’ as follows:

A son (P) has more (or stronger) rights of inheritance (from father) (R) than a daughter (Q),

and, a daughter (Q) has rights of inheritance (R) enough to inherit from her mother with some ‘priority’ (S1);

the ‘priority’ of inheritance (S) is proportional to the ‘rights’ of inheritance (R);

therefore, a son (P) has rights of inheritance (R) enough to inherit from his mother withgreater‘priority’ (S2).

Thus, the subsidiary term (S) is different in the minor premise (S1) and conclusion (S2), with S2 > S1. According to R. Zekharia, this inference is to be interdicted by means of thedayoprinciple; whereas others accept it as is. Is this indeed, as the former claims, an argument subject todayoapplication? We could say so, with reference to the daughter’s position, since the conclusiondiminisheswhat might be supposed to be her rights (to equal or even prior inheritance). On the other hand, from the son’s viewpoint, since the conclusionimproveshis position, giving him first priority,dayois not called for. So, there is room for debate[12].

Perhaps a few more words on thissugyawould clarify matters a bit more. The Torah laws of inheritance (specifically, Num. 27:8) give the daughters of a man second priority compared to his sons: “If a man die, and have no son, then ye shall cause his inheritance to pass unto his daughter.” The term “priority” used in this halakhic context refers to a “winner takes all” order of precedence.

The sons inherit (almost)allof their father’s wealth, his wife and daughters being effectively excluded (except for certain provisions that need not concern us here). If a son predeceases his father, his own sons are next in line for his share, then his daughters[13]if sons are not available. If no sons, or male or female offspring of theirs, are alive, then and only then do the daughters (of the father), and their offspring, get the (whole) inheritance. Thus, the “right of inheritance” of daughters is potential, not actual. It is contingent: it isconditionedon there being no male child, or grandchild through a male child, available to receive the (whole) inheritance.

This concerns inheritance from a father. What of inheritance from a mother? The Torah does not explicitly answer this question; so, the rabbis try to answer it, inBaba Bathra, 111a, as follows[14]:

“[It is written.] And every daughter that possesseth an inheritance in the tribes of the children of Israel; how can a daughter inherit [from] two tribes? — [Obviously] only when her father is from one tribe and her mother from another tribe, and both died, and she inherited [from] them. [From this] one may only [derive the law in respect of] a daughter.”

Thus, as already mentioned, the rabbis first establish the rights of daughters to inheritance from their mothers. This serves as the minor premise of the a fortiori argument they use to derive the rights of sons to inheritance from their mothers:

“Whence [may the law respecting] a son [he derived]? — One may derive it by an inference from minor to major: If a daughter, whose claims upon her father’s property are impaired, has strong legal claims upon the property of her mother, should a son, whose claims upon the property of his father are strong, not justly have strong legal claims upon the property of his mother?”

This purely a fortiori argument is thereafter, as already shown, turned into an a crescendo (i.e. a ‘proportional’ a fortiori) argument, and the question ofdayoarises at this stage:

“And by the same argument: As there, a son takes precedence over a daughter, so here, a son takes precedence over a daughter. R. Jose son of R. Judah and R. Eleazar son of R. Jose said in the name of R. Zechariah h. Hakkazzab: Both a son and a daughter [have] equal [rights] in [the inheritance of] a mother’s estate. What is the reason? — It is sufficient [etc.]” … “And does not the first Tanna expound. ‘It is sufficient [etc.]’? Surely, [the exposition of] Dayyo is Pentateuchal!” … “Elsewhere he does expound Dayyo, but here it is different, because Scripture says, in the tribes, thus comparing the mother’s tribe to the father’s tribe: as [in the case of] the father’s tribe a son takes precedence over a daughter, so [in the case of] the mother’s tribe a son takes precedence over a daughter.”

In this way, the law for inheritance from a mother is made to mirror that for inheritance from a father. Note that the sons are given precedence over daughters with regard to inheritance from the mother, even though the sons’ rights are inferred from the daughters’ rights; but this is not logically problematic, since the daughters’ rights referred to are only potential and therefore not altogether displaced by the inferred sons’ rights.

Here again we may express disappointment at the rabbis in general, and R. Steinsaltz in particular, for not analyzing the various logical issues dealt with in this section with appropriate rigor; and here again, their lack of formal understanding ofqal vachomerand thedayoprinciple is to blame. I am of course not contesting the law[15], but only wish to point out that it is arrived at by means of logic which is not purely deductive (though it is made to seem so, somewhat) but which depends on some inductive leaps that we have above duly exposed. There is nothing wrong with induction, provided it is frankly recognized as such and not presented as deduction.

Various forms. To recapitulate: we examined the above two Talmudic examples of a fortiori argument to test R. Steinsaltz’s understanding of such reasoning. Both arguments, though unrelated, displayed the same sort of fallacious thinking (judged by strict deductive logic standards) – so it looks like we stumbled upon a recurring fallacy in Talmudic logic, and no doubt in people’s thinking in general. It is interesting to note that R. Steinsaltz did not notice these errors. To be fair, this was an easy mistake to make, even if a little careful reflection would have quickly gotten alarm bells ringing.

This fallacy has many possible forms. The forms we encountered above are the following. The most typical is an argument that resembles positive subjectal a fortiori, except that the major and minor terms (P and Q) are not uniform throughout – being greater in the major premise than in the minor premise and conclusion.

P1 is more R than Q1,

and P1 is greater than P2 and Q1 is greater than Q2.

“Therefore,” if Q2 is R enough to be S,

then, all the more, P2 is R enough to be S.

This argument is fallacious because the givens before the “therefore” do not always imply the formally required major premise “P2 is more R than Q2,” even if the latter is sometimes true. This formal requirement cannot be ignored or vaguely assumed; it has to be proved by some means.

We can show this argument is fallacious by simple mathematics. If we symbolize ‘the value of R for some variable x’ by R{x}, we can put it as follows: given that R{P1} > R{Q1}, and that R{P1} > R{P2} and R{Q1} > R{Q2}, it does not follow that R{P2} > R{Q2}. This can be seen in the diagram below. All we can deduce is that R{P1} > R{Q2}; regarding R{P2} and R{Q2}, the first may be greater (or equal) or lesser than the second.

Clearly, if we can somehow show that R{P2} > R{Q1}, then it would prove that R{P2} > R{Q2}. If on the contrary R{P2} < R{Q1}, the relation between R{P2} and R{Q2} remains undetermined; in such case, to prove the desired relation, we would need to refer to some other intermediary, say R{y}, such that R{P2} implies it and it in turn implies R{Q2}.[16]

Diagram 18.1

Variants of this are: where the major and minor terms are uniform, but the middle term (R) is explicitly or implicitly relative (to some item X, say) in the major premise and the same relativity is not mentioned or intended in the minor premise and conclusion, or where the major premise is explicitly or implicitly conditional (again on some item X, say) while the same condition is not mentioned or intended in the minor premise and conclusion. That is to say:

P is more R (relative to X) than Q,

“Therefore,” if Q is R (relative to something else) enough to be S,

then, all the more, P is R enough to be S.

(On condition X,) P is more R than Q,

“Therefore,” (on some other condition,) if Q is R enough to be S,

then, all the more, P is R enough to be S.

In these two forms, the fallacy lies in ignoring that the tacitly intended ‘relativity to X’ or ‘conditioning upon X’ in the major premise may well not be also applicable in the minor premise and conclusion, whereas the minor premise would still be true if it applied to non-X but did not apply to X. The three arguments are, then, from a strictly deductive point of view, fallacious – i.e. the putative conclusion does not necessarily follow from the premises. This does not mean that there are not special cases where the required premises can be produced inductively or even deductively – it just means that they are not universally present.

We can from these positive subjectal forms predict three negative subjectal ones, where the minor premise is negative with the major term (P) as subject and the conclusion is negative with the minor term as subject (Q). We can also conceive of implicational and hybrid equivalents of these various forms. A similar set of fallacies can be expected to occur with predicatal a fortiori arguments. For instance, the following one would be typical:

More R is required to be P1 than to be Q1,

and P1 is greater than P2 and Q1 is greater than Q2

“Therefore,” if S is R enough to be P2;

then, all the more, S is R enough to be Q2.

3.Lack of formalism

Although it is pretty obvious that the rabbis involved in the above described fallacious arguments were intending valid deductive arguments, we can ‘save face’ for them by suggesting that (though they did not say so out loud) they did not really mean their arguments as strictly a fortiori, but were consciously engaged in arguments that are ‘roughlya fortiori’. They are mere analogies that resemble a fortiori but are not truly so, being more inductive than deductive. They were ‘pseudo-fortiori’, or ‘quasi-fortiori’, but not really fortiori.

In any event, as I have shown in the present and other chapters (7-9), the maincauseof problems in rabbinic use of a fortiori argument (and this is also true of other forms of argument, of course) is their eschewing formal logical studies. This lack of formalism is confirmed by R. Steinsaltz in his workThe Essential Talmud(chapter 30)[17], where referring to the specificity of the “talmudic way of thinking” he writes:

“A basic factor is the attitude towards abstraction. In the Talmud, as in most areas of original Jewish thought, there is deliberate evasion of abstract thinking based on abstract concepts. (…) The Talmud employs models in place of abstract concepts. (…)Kal va-homer, for example, is a method applied to a certain model in order to adapt it to another model. Thus there is a high degree of mechanical thought, and no attempt is made to clarify practical or logical problems per se; (…) it is not always possible to understand the convoluted methods of the operation itself” (p. 263).

R. Steinsaltz, of course, is not intending any radical criticism thereby. But I would say that this is the core problem, and if we ever hope to modernize and improve upon past Jewish legal thought, and credibly further develop it, we have to learn and adopt more formal methods of inquiry. There is in my view just no excuse for hanging on to ways of thinking that (occasionally, if not often) lead to error. Logic is not something arbitrary, which can be ignored or shunted aside when we dislike its results. Logic is a way to test if a theory is true, together with empirical data. If a theory goes against logic, and/or against empirical data, it must be rejected or at least reformulated. There is no credible escape from this methodological requirement. It is an absolute, applicable to religion as well as to everything else.

[2]The essays there posted are described as “based upon the insights andchidushim[i.e. novelties] of Rabbi Steinsaltz, as published in the Hebrew version of the Steinsaltz Edition of the Talmud.”

[4]Abaraitais a statement of Tannaic origin, i.e. antedating the Gemara.

[5]I suspect that such statements were derived from the MishnaBeitzah5:2; but I do not know who did that first.

[6]Chavel:Encyclopedia of Torah Thoughts, p. 27, n. 106. Feigenbaum:Understanding the Talmud, p. 88.

[7]I do not quote him verbatim, because I have before me the French version of his text. I presume the English edition says pretty much the same thing.

[8]I tacitly assume that the implications mentioned here are all normal; i.e. that not-X does not imply Y, X does not imply not-Z, and Y does not imply not-Z. The first two of these are tacit premises, and the third is a conclusion (demonstrablead absurdum: if Y did imply not-Z, then since X implies Y it would follow that X implies not-Z – which is given as untrue).

[9]Or, if you prefer, such oral laws are more subject to faith, because their emergence in the present cannot be exactly traced all the way back to Sinai. Of course, this is objectively true even of the written law, but a difference of degree can still be claimed.

[10]Who is presumably no other than R. Jose, the father of R. Eliezer to whom the list of 32 hermeneutic rules is attributed.

[11]R. Yossi’s actual formulation, according to the Soncino Talmud, is: “If heleb, for which there is a penalty of kareth [if eaten], is permitted for use, how much the more the sinew [is permitted for use], for which there is no penalty of kareth [if eaten]” (brackets mine). Note in passing that the Socino Talmud wrongly refers to this as argument “a minori” (ad majus) – whereas it is clearly in facta majori ad minus(from kareth to no kareth).Note also in passing that there is no issue ofdayoin this context, and none is raised; yet no one marvels at the fact and its implication that thedayoprinciple is not always relevant.

[12]I would say, however, thatdayois not relevant here, since what is at issue is not strictly speaking apenaltyto be applied by the court.

[13]This logically follows from Num. 27:8 by reiteration, i.e. applying the law first to the father and then to his sons.

[14]I quote from the Soncino edition, because I do not have at hand R. Steinsaltz own English translation (if he has one). The “it is written” reference here is to Num. 36:8.

[15]Although, in all honesty, I personally find the Jewish law of inheritance unfair to women, denying them independence as human beings. It was, no doubt, at the time it was promulgated a reflection of the existing patriarchal society, and probably an improvement in the status of women. But times have changed, and in today’s society women must be acknowledged as equals under the law.

[16]Note in passing that, given R{P1} > R{Q1}, we would likewise be unable to establish that R{P2} > R{Q2}, if R{P1} < R{P2} and R{Q1} < R{Q2}. On the other hand, if R{P1} < R{P2} and R{Q1} > R{Q2}, it would follow that R{P2} > R{Q2}.