Logic in the Talmud

A Thematic Compilation by Avi Sion

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7. Traditional Teachings

A brief overview of the ways Judaism traditionally presents the art of “Talmud Torah”, followed by some suggestions on same.


1.   Hermeneutics

Talmudic law was decided, with reference to the Torah, after much debate. In a first stage, the debate crystallized as the Mishnah; in a later stage, as the Gemara. The methods used in such discourse to interpret the Torah document are known as ‘hermeneutic’ principles (or, insofar as they are prescribed, rules). In Hebrew, they are called midot (sing. midah), meaning, literally, ‘measures’ or ‘virtues’. This Talmudic ‘logic’, as we shall see, has certain specificities, both in comparison to generic logic and intramurally in the way of distinct tendencies in diverse schools of thought. Various Rabbis proposed diverse collections of such methodological guidelines, intending thereby to explain and justify legal decision-making[1].

Readers may find it useful, in this context, to study: the articles on hermeneutics in the Jewish Encyclopedia[2] and the Encyclopaedia Judaica[3], as well as Bergman’s Gateway to the Talmud[4], and the Reference Guide to Steinsaltz’s English edition of the Talmud.

The earliest compilations were: the Seven Rules of Hillel haZaken (1st century BCE)[5]; the Thirteen Rules of Rabbi Ishmael ben Elisha (2nd century CE); and the Thirty-two Rules of Rabbi Eliezer ben Yose haGelili, of slightly later date. These lists are given as Baraitot, the first two in the introductory chapter to the Sifra (1:7)[6] and the third within later works. As already mentioned, Baraitot were legal rulings by Tanaim not included in the Mishnah; but they were regarded in the Gemara as of almost equal authority[7].

According to Jewish tradition, at least since Geonic times (notably, Saadia Gaon) and still today, these rules all date from the Sinai revelation and were since then transmitted from teachers to pupils without interruption[8]. This is in part confirmed by statements in the Talmud and literature of that era, in which Rabbis claim to have received knowledge of certain rules from their teachers[9]. But the historicity of the general claim has not so far been demonstrated by any pre-Talmudic evidence: in particular, there is no obvious mention of such interpretative principles anywhere in the Tanakh.

According to JE: “The antiquity of the rules can be determined only by the dates of the authorities who quote them; in general, they cannot be safely declared older than the tanna to whom they are first ascribed. It is certain, however, that the seven middot of Hillel and the thirteen of Ishmael are earlier than the time of Hillel himself, who was the first to transmit them. At all events, he did not invent them, but merely collected them as current in his day, though he possibly amplified them.” Still according to J.E., Ishmael’s rules are “merely an amplification of” Hillel’s; and similarly Eliezer’s rules coincide in many instances with Hillel’s and Ishmael’s, though in other instances they concern the Hagadah rather than the Halakhah.

It does not, in any case, seem likely that such rules would suddenly be ‘invented’, as a conscious act, by their apparent authors or anyone else. The most likely scenario, from a secular point of view, is that they were for some time unconscious discursive practices by participants in legal debates; gradually, it occurred to some of these participants (most probably precisely those whose names have come down to us as formulators, or reporters and collectors, of hermeneutic rules) that they and their colleagues, and their predecessors, repeatedly appealed to this or that form of reasoning or argument, and such implicit premises would be made explicit (thereby reinforcing their utilization). Different such commentators would find some rules more convincing than others and thus compile selections; eventually, contending schools emerged.

Those would be the natural stages of development of such a body of knowledge: first, unconscious practice (which might be correct or incorrect); second, dawning awareness of such practice (due to what we call ‘self-consciousness’); thirdly, verbalization, randomly to begin with (by exceptional individuals, focusing on the most outstanding practices), and then more and more widespread (more insights, by more people, as a cultural habit develops); fourthly, systematization (of the simplest kind, namely: listing) and dispute (as different lists are drawn up by different groups). In the case of Judaism, the next stage was merging results (by later generations, out of veneration making all the lists ‘kosher’ at once); and subsequently, there was a stage of commentary (trying to justify, explain – within certain parameters). However, sadly, as we shall see, the last natural stages of formalization and evaluation never occurred (until recently, outside orthodox circles).

According to JE, these various lists were not, even in their own times, viewed as exhaustive. I am not sure how true that remark is, i.e. whether there is any statement in the Talmud or related literature which confirms the assumption that Hillel, R. Ishmael, R. Eliezer, or whoever compiled a list, did not consider himself as having succeeded in making a full enumeration of valid midot. At the other extreme, the view of traditionalists today, that these lists were all equally complete, is (as we shall see) just as conjectural, and based on anachronistic and circular arguments.

What is in any event evident, is that the rules in each list were not in their own times uncontested. The school of Hillel was opposed by that of Shammai, and Rabbi Ishmael’s formulations were challenged by Rabbi Akiba ben Yossef. It is interesting to note that, at first, these opposing views were considered mutually exclusive; but, over time, they came to be used indiscriminately[10].

It apparently came to be considered that, although two dissonant rules may indeed lead to conflicting interpretations, the selection of one or the other of them as the finally applicable rule in any given single context, was a matter of tradition or majority decision; effectively, the correct conclusion was predetermined, and the rule selected only served as an ex-post-facto rationalization. Thus, the ontological status ascribed to the hermeneutic rules is that they were conditional on material factors – formalities activated or left dormant by textual content (which details were, one by one, designated by authorities, on the basis of transmissions or by vote).

Although R. Akiba’s approach usually prevailed in practice, R. Ishmael’s thirteen midot are the most popularly known: they have become part of the daily liturgy and can be found in most Jewish prayer books. Since the above mentioned initial formulations, many attempts have been made to compile more complete lists (for instance, by Malbim). We will in the next chapter analyze all the hermeneutic principles systematically with examples; here, we will be content to only make some introductory comments.

At the outset, it shall be pointed out that the rules are not all of a purely deductive nature, contrary to what may be thought at first glance. When the rules suggest a “derivation”, they do not necessarily refer to a mechanical relation between premises and conclusion. Most of the rules’ results are partly or entirely inductive; that is, they are, at best, a good working hypothesis within the given context of knowledge, which may possibly be replaced by another hypothesis or a deductive inference in an altered context of knowledge.

Some of the rules, wholly or partly, represent deductive or inductive principles which can readily be justified by natural logic. Of these, some may be validated in formal terms (i.e. substituting symbols for specific contents); whereas others describe discursive acts which are rather intuitive – responses to material data without fixed patterns – and which can be approved with reference to broader epistemological considerations. However, some of the rules, wholly or partly, seem, from the point of view of natural logic, rather obscure and arbitrary, and remain acceptable only due to a claim that they are of Divine origin.

The Talmud itself at least implicitly recognizes the inductive nature of many of the arguments in it. This is evidenced by the fact that when several alternative premises are given for a certain conclusion, it is viewed as being weak. The Rabbis argue: Nu, if each of the sets of reasons given was sufficient, why bother to adduce the others? From a deductive point of view, there is indeed no utility in giving many reasons; but nor is there any harm in it. It is only in inductive logic that giving more reasons increases the probability of the result, and therefore also suggests (incidentally) its relative weakness.

Our remark that Talmudic (and indeed later Rabbinic) reasoning is very often inductive, rather than purely and exclusively deductive, should be emphasized. It is contrary to popular belief (people are rather surprised when I suggest it), and so manifestly ignored by other writers that I would tend to claim it as original. If it is original, then it should be stressed as very important, among the most significant insights of the present work. In any case, it is evident and incontrovertible fact.

The idea is disturbing, not to say devastating, to many people, because induction is thought of as inherently more fallible than deduction, and it is difficult to juggle with doubt and dogma. But in all fairness the truth of the matter is that deductive reasoning can also in principle and often does in practice err, and that inductive reasoning is not in principle necessarily weak nor does it always go wrong in practice. Each case must be considered on its own merits; one cannot make sweeping statements for or against such broad categories of mental process.

Let us now briefly take a look at the tenor of the 13 Midot of R. Ishmael; we will have occasion further on to analyze them more fully[11]. We may distinguish three groups:

  1. Midot whose purpose is to infer information from the text, i.e. to make explicit what is implicit in it; this includes rules Nos. 1-3 and 12.
  2. Midot used to elucidate terms in the text, especially their extensional aspect; this includes rules Nos. 4-7.
  3. Midot serving to harmonize seeming or manifest incongruities in the text, including, as well as inconsistencies, mere redundancies, discrepancies, and other sources of perplexity; this includes rules 8-11 and 13.

Admittedly, this grouping of the 13 Midot is a bit artificial. For, in a strict view, all inference of information is an eventual elucidation of terms and a prevention of inconsistency; and similarly, all elucidation of terms constitutes inference of information and harmonization; and likewise, all harmonization results in elucidation of terms and leads to inferences of information. Nevertheless, the immediate goals of these different movements of thought are sufficiently distinct to justify our subdivisions. A nice thing about these groupings is that they show a continuity of sorts in the approach of R. Ishmael, and explain and justify the sequence in which the midot were listed. The only misplaced midah in our view is No. 12, which should be closer to No. 2, or at least in the same group.

a) Inferences of information

Rule 1, qal vachomer (lit. lenient and stringent), refers to a fortiori, a form of argument whose conclusion is essentially deductive, though there are in practice inductive aspects involved in establishing the premises, as we have seen. Within Judaic logic, this form of reasoning has in fact served as the paradigm of deduction, much as Aristotle’s syllogism (with which it is often confused) has had the honour within Western logic. The discovery of a fortiori is, I would say, one of the most brilliant contributions of Jewish logicians to generic logic. It should be noted that a fortiori has Biblical roots, as Jewish tradition has reported since Talmudic times if not earlier.

Rule 2, gezerah shavah (lit. equal rulings), refers to arguments by analogy, or more specifically inferences based on homonymy (similarity of wording) or on synonymy (similarity of meaning). Reasoning by analogy was very common among the ancients, Jewish and otherwise, until the advent of the scientific method in relatively modern times; it could range from far-fetched comparisons to very credible equations. Of course, most arguments, including syllogism, are based on analogies, since conceptualization depends on our intuition of similarities between apprehended objects. However, not until recently was it fully understood that the legitimacy of an analogy rests on its treatment as a hypothesis to be tested, and repeatedly tolerated (i.e. not rejected) and even confirmed (if predictive) by evidence, more so than its alternative(s). So, analogy is essentially an inductive mode of thought.

While gezerah shavah is based on closeness of subject-matter, inferences from context appeal to the textual proximity of topics. Such logistical considerations are relatively incidental, but they lean on the fact that the text in question was written by an orderly mind. This form of reasoning includes: the rules known as heqesh (relating to two items in the same verse) and semukhim (relating to two items in adjacent verses), which are traditionally counted as aspects of rule No. 2 (though probably later inclusions under that heading); and rules classed as No. 12, meinyano (inference from immediate context) and misofo (inference from a later reference). Such reasoning has obviously got to be regarded as inductive, since however intentional the positioning of words, phrases or sentences, there have to be occasional changes of topic.

A matter of related significance, note, is the assumption by R. Akiba that, in a Divine document such as the Torah, the choice and placement of words cannot be accidental; whence, no repeated word is superfluous and no missing word is insignificant, every letter counts, and so on. This view allows, indeed encourages, many an inference (or alleged inference). Be it said, R. Ishmael did not in principle agree on this issue, but considered that the Torah “speaks in the language of men”.

The interpretations involved in analogical or contextual arguments may be intuitively reasonable enough, but they are not readily put in formal terms and are therefore difficult to validate systematically. In any case, applied indiscriminately, such arguments are bound to lead to difficulties – one line of reasoning may lead to one conclusion, and another to its opposite, there being no inherent logical protection against contradiction. And indeed, difficulties were often encountered. For this reason, many limitations were imposed on these rules; and ultimately, they were regarded as unusable without the support of an accepted tradition, or at least the approbation of the majority of the authorities.

Rule 3, binyan av (lit. father construct), seems to refer to causal reasoning; that is, to finding the causes (in a large sense) of differences or changes, and thus predicting similar effects in other contexts. In a legal context, this means finding the underlying basis of known laws, so as to be able to make coherent laws in other areas. Here too, argument by analogy is involved, and the mode of thought is essentially inductive. The way the rule is traditionally worded (“a comprehensive principle derived from one text, or from two related texts”) gives a false impression that it refers to immediate or syllogistic inference; but we must look at its operation in actual practice to understand it, and in such event the role played in it by the process of generalization becomes evident. While such reasoning is relatively easy, nowadays, to express formally and control scientifically, the Rabbis (as we shall see) had a surprisingly hard time with it.

b) Elucidation of terms

Rules 4-7, labeled collectively as klalim uphratim, seem to concern class logic, to a large extent, as they involve the expressions klal (general) and prat (particular) in various combinations. Many arguments of this kind may be viewed as effectively proceeding from definable linguistic conventions – in the non-pejorative sense that they reflect certain uniformities of intent, in the style of Hebrew expression used by the Torah. For instances: the combination of a general term followed by a particular term, in close Torah verses or parts of a verse, yields a particular result (klal uphrat); whereas the reverse combination, of a particular term followed by a general term, yields a general result (prat ukhlal). As every writer or speaker knows, a maximum of information can be communicated in a minimum of words, through certain turns of phraseology. This seems to be the motive, here.

Well and good, thus far – in theory. But in actual practice the expressions klal and prat cannot always be taken at their face value. Closer acquaintance with practical applications of the klalim uphratim rules reveals that their logic is not quite identical with that of Aristotle. In Western logic theory, inclusions or exclusions between broader concepts (genera, overclasses) and narrower ones (species, subclasses), or classes and their singular instances (individuals), are purely mechanical procedures, which presuppose clearly defined terms. Such subsumptive arguments can be readily represented pictorially by circles within or intersecting or outside other circles, known as Euler Diagrams, and are the domain of Aristotle’s syllogistic processes. But in the more Oriental logic of the Talmud, things are not so simple; terms are vaguer and may be taken to “imply” formally unrelated ones.

The truth is that in practice, even in Western thought, terms are not always at the outset clearly defined; rather, usually, the definition of a term is arrived at through a gradual, inductive process, as we focus on the subject matter more and more, and acquire a deeper knowledge of it. Sometimes we do decide by convention to name a phenomenon whose description we have already; but more often, we name a phenomenon before we are able to express its essence in words, and then work our way by trial and error to a satisfactory definition of it. This developmental aspect is not yet well accounted for in the classical theory of class-logic.

Certain efforts at exegesis are rather contorted, and a great deal of fantasy and credulity are needed to accept them. R. Akiba’s methodology, where the terms used for the purposes of inclusion or exclusion are ribui (broad) and miut (narrow), seems especially weird to our minds. For instance, “sheep” may imply “birds” or even “garments”, without apparent rhyme or reason[12]. This is why Maimonides regarded such arguments as having a mere mnemonic purpose[13]. Their conclusions were foregone[14], received in the chain of oral tradition; nevertheless, the Rabbis made a determined effort to anchor them, however flimsily, in the written Torah.

The best we can do to formalize such logic, then, would be to say that, given the tradition that the laws concerning a certain topic are X, Y, and Z; and that these laws are to be derived from a specified passage of the Torah, distinguished by the terms or phrases A, B and C; then, if X is related to A, and Y is related to B, it follows that Z is to be paired-off with C[15]. The formal logic involved is therefore conjunctive and hypothetical:

If A and B and C, then X and Y and Z;

and if A then X and if B then Y;

therefore, if C then Z.

However, apart from this aspect, it is frequently difficult to honestly find formal justification for such argument; that is, how the connective relations of the major and minor premises were in the first place established. When in such contexts the Rabbis are found to argue between themselves at length, the discussion often does not revolve around such basic issues of proof, but is merely a controversy as to which of X, Y, Z is to be paired-off (seemingly arbitrarily) with which of A, B, C. The only way then left to us, to explain the unexplained, is to appeal to ‘tradition’.

c) Harmonization

Rules 8-10, which start with the words kol davar shehayah bikhlal veyatsa (lit. whatever was in a general principle and came out), deal with sets of statements whose subjects are in a genus-species relation. Rule 8, although perhaps originally intended as one rule, has become traditionally viewed as having two variants, which we are calling lelamed oto hadavar and lelamed hefekh hadavar; these concerns cases where the predicates are also in a genus-species relation of sorts. Rule 9, liton toan acher shehu kheinyano, concerns predicates which are otherwise compatible; and rule 10, liton toan acher shelo kheinyano concerns incompatible predicates.

Rule 11, which also starts with the words kol davar shehayah bikhlal veyatsa, and continues with the words lidon badavar hechadash, deals with situations where an individual changes classes and then returns to its original class. Rule 13, the last in R. Ishmael’s list, shnei ketuvim hamakhechishim, concerns other reconciliations of conflicting theses; note that this principle is to some extent reflected earlier in the present volume, in the section on kushya and terutz (6.3).

All these dialectical principles are quite capable of formal expression, and (as we shall see) are mainly inductive in nature, involving generalizations and particularizations. There are some deductive, logically necessary, aspects to them; but on the whole, as complexes of intellectual responses to given textual situations, they favour one course over another, which is logically equally possible, if not equally probable, and therefore they constitute inductive mental acts.

One might well ask why God, the ultimate author of the Torah, expressed Himself in so tortuous and confusing a manner, that necessitated such complicated interpretative principles, instead of speaking plainly and straightly. The answer I received from teachers when I asked that question was that His purpose must have been to conceal the truth somewhat, so as to stimulate Torah study. Also, if everything was made clear in a systematic and explicit manner, the Torah could be studied fully in isolation; whereas, God wished it to be studied in a more social manner.

Some also suggest as an answer, on the basis of qabalistic ideas, that if the Torah was perfectly explicit and unambiguous, then there would be no room for doubt in the world, and skeptics would have no opportunity to make the redemptive leap of faith, which is needed to safeguard human freedom of choice. If God was totally revealed, then humans would be forced, in fear and trembling, and out of infinite love, to surrender all personal will and identity. The diversity of the world was created and is maintained precisely through a concealment of some of the truth (for if the world is ultimately, in truth, unitary, then all appearance of plurality must be a sort of untruth).

So much for the content, in brief, of R. Ishmael’s list of rules. Our analysis (above and below) somewhat justifies the order in which the rules appear in this list (except, as already stated, for rule 12). However, some of the groupings implied by this list are open to discussion. I would suggest that all inferences from context, including heqesh and semukhim (traditionally considered as subcategories of gezerah shavah) and meinyano and misofo, should have been grouped together under one heading (just as, for instance, gezerah shavah constitutes one heading with subdivisions). Especially, the klalim uphratim should, in my view, be reorganized, and counted as one heading, or as at most two (classifying each process according as its result is a klal or a prat)[16], instead of four. Finally, in my opinion, the two variants of lelamed ought to be regarded as separate rules, comparable to the two rules liton toan acher.

A comment worth making is that the arrangement and numbering of the midot may not be stipulations of R. Ishmael, but may be proposals of the compiler R. Yehudah. To my knowledge (without having researched the matter greatly), R. Ishmael did not systematically group and list his midot, but merely formulated them and referred to them individually in various contexts as the need arose; it is probably R. Yehudah who later brought them together in a list, and organized them into 13 sentences in the given order. But the number 13 is not sacrosanct. According to Bergman, the Raavad noted the possibility of a count of 16 (counting rules Nos. 3, 7, 12 as two each); while others suggested counting rules 8-11 as one[17] and thus supposedly arrived at a count of 10. My preferred manner of counting yields the number 13-2+1=12.

It must be noted that, judging by actual Talmudic and Rabbinic discourse, the inventory is incomplete[18]. Orthodox commentators would not accept this last remark, and try to explain away every silence or disagreement of R. Ishmael (or R. Yehudah) concerning some rule or some detail of a rule mentioned by other authorities, earlier, contemporary or later. Since they regard the 13 rules as (an oral) part of the Revelation at Sinai, they must explain why Hillel listed only 7 rules, or R. Eliezer listed as many as 32. For this reason we find Bergman making statements like “Hillel certainly did not intend to dispute the teaching of R’ Yishmael,” even though Hillel lived a couple of centuries before R. Ishmael![19]

Hillel’s rules (which we shall label (a) through (g), to distinguish them from R. Ishmael’s labelled numerically) are given in the Jewish Encyclopedia as follows:



R. Ishmael’s


qal vachomer



gezerah shavah


c, d

binyan av



klal uphrat and prat ukhlal

4, 5


kayotse bo mimakom acher




part of 12



Now, I have put in the last column my initial impressions as to correspondences; from which it appears that Hillel did not know (or use or list) at least seven of R. Ishmael’s rules, namely 6-11, 12 (the misofo part), and 13, while he adds (or has another name for) one, namely (f). We might stretch our equations, and include rules 6 or 7 under (e); regard R. Ishmael’s misofo as a special case of Hillel’s meinyano; and maybe even assimilate eventual cases of (f) under rules 2, 3, and 12. But it seems very unlikely to me that Hillel intended any of R. Ishmael’s harmonization rules (8-11, 13).

It could well be, as J.E. suggests, that R. Ishmael gradually developed the latter additional rules[22] as “special applications” (I would prefer to say extensions) of Hillel’s (e), since they concern subjects in a genus-species relation. But we must in any case admit that R. Ishmael’s list of 13 was more than a mere rearrangement of Hillel’s list of 7; there were clearly novel elements in it[23]. Similar patterns of development, involving subdivisions, collapsing of categories, and new issues, are apparent with regard to R. Eliezer’s list of 32[24], judging by the data given in J.E. Note that if we refer to Shammai and R. Akiba, the problems of comparison and contrast become much more complicated[25]; and it would be very difficult to claim that these various authorities based their work on a common blueprint.

Not only does Talmudic logic have specificities in comparison to generic logic, but there are different logical trends within the Talmud itself. That is already clear in what we have said above, concerning the competition between the schools of Hillel and Shammai, or between R. Ishmael and R. Akiba. But the differences embodied in explicit principles may not reflect all the underlying differences; there seems also to be unstated differences, which were not brought out into the open. This refers to the concept of the shitah: as is well known, there are leitmotifs which run through the legal rulings of individual Rabbis.

Some Rabbis, for instance Hillel, tend to rule leniently; others, like Shammai, are reputed to lean on the side of stringency. The terms lenient and stringent, here, need not be considered as implying a value-judgment on our part. Hillel appears the warmer of the two, because he tends to ease people’s obligations; but Shammai also cares for people, he just wants to make very sure they get to Heaven. (It is interesting to note, in passing, that in the French language the word chamailles to refer to endless quarrels! I have long suspected, though this is not the explanation given in etymological dictionaries, that the word was derived from the proverbial Shammai-Hillel controversy.)

What concerns us, here, is the possibility that different logics underlie these different tendencies. Say, someone utters what seems like a vow; how binding is it legally? One Rabbi might answer generously that the statement is binding only if it has a certain precise wording; it is to be taken at face value, with a minimum of implications, admitting as inference only what strictly necessarily follows according to generic formal logic. Another Rabbi might take the more severe view that, so soon as the utterance is articulated, all sorts of motives and intentions may be taken for granted as implied; little need be said to mean much. The latter Rabbi seems to be referring to a more specific logical framework, in which there are unaccustomed relations among propositions.

To give an idea of the issue, here: in ordinary logic “all X are Y” does not imply “all Y are X”; but one can readily construct a special logical system in which such inference is acceptable. It would be onerous, make difficult the expression of all possible thoughts, but it is not unthinkable (since every form has a contradictory). It may well be such distinct (specific) patterns of formal logic underlie the differences in shitah. This is merely a speculation; but the idea seems worthy of follow-up. To demonstrate it decisively would require analysis of all of any given Rabbi’s pronouncements, in search of uniformities.


2.   Heuristics

The hermeneutic principles were intended, as discussed in the previous section, to explain and justify the development of Jewish law from its Torah source. They were the methodological bridge between the Torah and the Mishnah and Gemara; the more or less logical techniques by means of which (to the extent that they are accurate renditions and exhaustively listed) the written foundation-document, together with the oral tradition, were transmuted into the Talmud.

However, a further set of principles is traditionally transmitted in Judaism, which reflects more broadly the transition from Mishnah to Gemara, and then from Talmud to subsequent Rabbinic Law, and finally the way Halakhah is actually taught and studied. These additional principles may be characterized as heuristic (practical rules of thumb), rather than hermeneutic (a priori methodologies), in that most of them constitute ex post facto summaries of certain uniformities in terminology[26], textual presentation and personal authority found in the Talmud. I say ‘most’, because some of them though listed together with relatively incidental rules of thumb, are more or less objective logical forms and would have been more appropriately listed together with interpretative techniques[27].

Many of the heuristic principles were already made explicit in the Talmud itself, reflecting the intelligence, self-consciousness and unity of purpose of its protagonists, recorders and redactors[28]; but some were evidently formulated in succeeding centuries, by Savoraim, Geonim, Rishonim and Acharonim. Among the current works in English which describe such principles, often in tandem with hermeneutics, we may mention again Steinsaltz’s Reference Guide, Bergman’s Gateway to the Talmud, as well as Rabinowich’s Talmudic Terminology[29] (whose introduction includes an excellent bibliography on the subject[30]) and Feigenbaum’s Understanding the Talmud. The last two of these books are summarized in Appendix 4 of JL for the reader’s edification.

The primary function of traditional teachings is simply to enable the student to understand what the dense Talmudic text is all about. This presupposes, for a start, a knowledge of Hebrew[31], to follow the Mishnah, and of Aramaic, to follow the Gemara, including the ability to read and a certain amount of vocabulary and grammar. Practice is, of course, crucial, but theoretical accessories are also essential, both to begin with and as one proceeds. Such tools are provided to some extent within the text itself; but studying with a teacher, at least at first, is necessary for most people, and a relatively easy way to gather information and skill; additionally, there are quite a few written aids to Talmud study.

The phrases used in the Talmud, as well as their meanings and the significances of their sequences, are not absolutely uniform and permanent, but do vary subtly from context to context, as well as (to a larger extent) from one geographical location to another and from historical period to historical period (in the different generations of Tanaim, of Amoraim, and of later Rabbis)[32]. The uniformities in vocabulary and semantics no doubt developed largely spontaneously, reflecting the idiom of time and place, although the Talmudic disputants and the compilers of the Talmud must have made some arbitrary conventions, too. As for the patterns of exposition, e.g. the rule that “if an anonymous Mishnah [containing only one opinion] precedes one containing a dispute, the Halakhah does not follow the anonymous Mishnah”[33], they must have been ab initio conscious conventions or at least ex post facto decisions supposedly based on research findings.

With regard to the rules of thumb, and their exceptions, concerning the relative reliability of deciders of the law, e.g. that “the Halakhah generally follows Beis Hillel over Beis Shammai, except...” for certain cases, they must be understood as after-the-fact summaries of information[34]. They were not prejudices imposed by Divine fiat, but final evaluations of the winners and losers in a multitude of unrelated disputes. In other words, such principles are statistical reports on personal scores, rather than reflections on substance or logical techniques; they cannot be used as proofs.

We have to take into consideration the historical development of this science[35] of Talmudic language, textual order and personal authority. There is an inevitable empirical element involved in the formulation of heuristic principles, since they are not (as it were) inscribed in Nature in the way Logic is, but depend on human factors. We may well wonder how much of the regularity described by the books on the subject is shaky assumption and how much of it is incontrovertibly established: i.e. what constitutes evidence for, and what inference from, the postulate that there is regularity; for if the assumption is an empirical generalization, rather than a before-the-fact convention, then it has to be studied much more carefully (since the law is affected by it).

The Talmud page is laid-out in a standardized way, with portions of Mishnah first, followed by Gemara commentary thereon, the latter being separated by the Hebrew letters גמ (GM); later commentaries, including mainly those of Rashi and Tosafot, are normally included in the page, around the Talmudic text. It should be noted that, Semitic languages being basically consonantal, the text was originally written and published without vowel signs; and until recently this practice has been continued, partly because of uncertainties or different traditions concerning proper vocalization. Since the text is also devoid of punctuation marks, it is first necessary to identify where a sentence begins and ends, and its various clauses; what we include or exclude in a sentence, and how we cut it up into clauses, will obviously generally affect its meaning. Also, many abbreviations are used, which must be assimilated.

As Feigenbaum makes clear, a related issue is the role of the sentence in the wider context: is it a new topic or the continuation of an ongoing discussion; and if the latter, is it a question or an answer, and in relation to what? This implies the need to recognize and appreciate the function of every word, phrase, or sentence in each and every line of argument, and to keep track of who said what and why. Facilitating such apprehension and comprehension is the fact that there are recurring schemata; but even having prepared oneself by their theoretical study does not always guarantee one’s ability in practice to correctly match the data and map the course of the discussion.

Talmud heuristics, judging by Rabinowich’s excellent effort, consists of an ordered lexicon of terms, including, at a first level, terms found in the Mishnah, then terms the Gemara uses to clarify its Mishnah antecedents, and finally terms instituted by the Gemara for its own development. Some terms can be characterized as analytical, as they help to define the subject-matter, referring to various aspects of its classification; this division mainly concerns the form and content of propositions, their terms, quantity, polarity, eventually also modality or conditions; and (to some degree) awareness of what is implicit in them. Some terms are synthetical, describing the logical or discursive procedures through which a formulated proposition has come to be considered and eventually become established or rejected.

The divisions and subdivisions of words and phrases appropriate to each context, differ considerably in Mishnah and Gemara, because of differences in the development of these two documents. The Mishnah is essentially a document intended to lay down predetermined laws; a relatively static picture of the law at a given time, an end-product. Whereas the Gemara is engaged, to begin with, in a studying and digesting process, and eventually, having acquired momentum, it develops the law further in the presence of the reader.[36]

So much, here, for the content of Talmud heuristics; we need not go into detail, duplicating the work of others. However, some broad critical comments on the subject are necessary. First, let us point out that if we wish to elicit from heuristic teachings some items of epistemological significance, we must look especially at all little notes their authors make concerning deviations from the norm: terms used with variant meanings in certain contexts; different terms used for seemingly the same thing; unusual terms sometimes used by certain players instead of the standard terms used predominantly; Gemara contradicting or emending Mishnah, Savoraim doing same to Gemara; and so forth. It is precisely such limiting cases, which fall outside the traditionally stressed major norms, which should be carefully considered by us.

We may refer to some examples of abnormal heuristics given in Rabinowich’s treatise. The Gemara may indicate cases “not provided for in the Mishnah” (p. 62). This suggests that the Amoraim did not consider the Tanaim as omniscient, or at least as having foreseen all possibilities. The Gemara sometimes rejects a Mishnah, for one reason or another: “In one instance (Niddah 13b) the Mishnah is not accepted since the law it states is considered illogical!” and the Gemara will often consequently “make slight emendations in the text” of the Mishnah (p. 21); “in one instance (Yevamos 43a)”, due to differences in decision for seemingly like cases, the Gemara states “this Mishnah is not authoritative” (p. 26). These examples suggest that the Gemara sages considered themselves fit to question the judgment of the Mishnah sages, rejecting material which in time becomes contrary to reason.

This is also suggested by the following example: “In fact, in one case (Yevamos 27b)” the Gemara “pushes aside a Mishnah in deference to a Memra of R. Yochanan!!” (who was an Amora) (p. 28). There are also suggestions that the Mishnah text had been adulterated by the time the Gemara reviewed it: “In, at least, two instances (Chullin 82a),” the Gemara cannot resolve a conflict between authoritative passages, “and must claim that a certain law is not really part of the Mishnah!” (p. 28); a Mishnah may also be corrected (p. 32). Baraitot were also occasionally ignored (p. 37) or corrected (p. 32), though that is less significant, since by definition, though of the same period as the Mishnah, they may have been intentionally excluded from it because not authoritative. The expressions “perhaps it is mistaken”, “it should not be taught”, and “it is not to be taken seriously” reflect this greater possibility of rejection in regard to Baraitot (p. 60).

Further on in time, we find cases of Savoraim making additions to the Talmud, for instance in Yoma 30b (p. 56), or again, according to one opinion, in Pesachim 102a-b (p. 45). This suggests that the Talmud was doctored after being sealed. More broadly, we should also consider discordances between sages of the same epoch: the Sages finding an argument of one of their colleagues strained (p. 59) or arbitrary (p. 69) or unconvincing; or finding his approach to an issue too vague or too fantastic or trivial (p. 64); or Sages being frankly stumped by a problem, unable to solve it (teku) (p. 63). Such events tell us something about the sages as individuals: their knowledge and reasoning powers were not necessarily perfect.

All the above applies to successive later generations of poskim, too. It all demonstrates the inductive nature of the development of Jewish law – and it cannot but be so, since human knowledge develops in response to phenomena. It is well known, also, that, as a consequence of being transcribed by hand over and over again, from copies on which readers had put their own handwritten commentaries, and sometimes as a consequence of censorship of parts of it by non-Jewish authorities, by the time of the Rishonim, many versions of the Talmud were circulating; and scholars had to labor mightily to detect the correct, or most likely, version[37]. That, too, is induction: observation and reasoning, hypothesis and confirmation or infirmation.

We need not, here, belabor these matters further, though many more examples can be brought to bear from throughout the history of Jewish jurisprudence. In my view, such footnotes to Talmudic study cannot be taken lightly and dismissed as insignificant; they prove several things beyond shadow of doubt, such as: that later sages did not always defer unconditionally to earlier ones, but were willing to use their heads; that texts were often enough doubtful, so that there were breaks in the continuity of the transmission of Jewish law; and more broadly, that the law underwent a development, with growth and decay, changes and reversals.

It is interesting that even an author like Feigenbaum, who may be classed as very orthodox, acknowledges a development in the method and language of the Oral Law: “The Tannaim... began to organize it into a network of precise laws arranged by topics” – and eventually “the material, methods of analysis, and modes of expression expanded greatly” (p. 3, my italics). The fact is that the orthodox are usually loathe to admit that the law, and indeed its methodology, have undergone any significant change since Moses’ time. Changes have to be glossed over as ‘minor’, for the simple reason that the Law would otherwise not be purely Sinaitic and therefore entirely Divine in origin.

However, the reader has only to examine a work like Lewittes’ Principles and Development of Jewish Law[38] to see that there has undeniably been change over time, most often in the way of expansion and increased density, and often enough in the way of contraction or simplification. Practices may be added or abandoned, specified in increasing detail or become less demanding. How such changes, viewed collectively, are to be frankly reconciled with the Biblical injunction not to add to or subtract from the Law (Deut. 4:2; 13:1) is unclear – and that is the reason why the matter has to be glossed over. Similarly, study of works on hermeneutics and heuristics clearly shows that there have been variations in Judaic logic[39].

One suggestion I can make here, to resolve the inherent ideological problem, is that we distinguish between ‘a general delegation of authority’ and ‘an endorsement of all the particular expressions of the authority’. That is to say, God may well say to us: your wise men of each generation and locality have My sanction to enact and enforce laws, without thereby implying that these laws must be the same everywhere and for all time. Just as, in the secular realm, the king (in a kingdom) or ‘the people’ (in a democracy) grants its chosen government (the executive, the legislative and the judiciary) the power to make laws, without implying that it cannot later revise these laws, as it may reasonably need to as circumstances change, within limits defined by some Constitution – so in the religious realm may God do so.

The mere fact of delegation of authority does not make immutability imperative and adaptation forbidden. Indeed, the Torah passage in question specifies the judges “in those days” (Deut. 17:8-13), reflecting an awareness that man-made laws, even those with general Divine sanction, may well need to be modified, as knowledge and social conditions evolve[40]. In no way does such delegation of authority logically necessitate that earlier judges be regarded by later ones as perpetually right, as having divine powers of omniscience and infallibility, but it is only suggested that they are likely to be the wisest for their time and place. If, say, today, our judges, reviewing the status of women, perceive them differently than previous generations did, in the light of a more open intellectual and societal atmosphere, they may well revise certain laws relating to women, without thereby insulting past sages, or denying the sages in general Divine sanction and invalidating their work.

Nowhere is it demonstrated formally that later sages need rigidly comply with all rulings of the earlier. Such a principle of compliance is taken for granted by current orthodoxy, as an established tradition, but there is no real textual basis for it. A circular argument is required of us: we have to believe in the tradition because the tradition tells us to believe in it. But, I say, there has to first be some kind of more authoritative justification, standing outside the tradition. For example, women cannot be called to the weekly Torah reading, not because the Law originally forbade it, but because of ‘the community’s honour’. Perhaps in those days communities generally had such reactions; but what if today, in many communities, that is not the case anymore?[41]. The reason proposed by the ancients reinforces itself, instituting social habits, but it has not been considered at a sufficiently radical level.


3.   A methodical approach

Although logic is ever-present in Jewish thinking, it is not as explicitly referred to as it ought to be, in my view. Talmud Torah, i.e. Biblical and Talmudic studies, constitute a powerful logical training, and the extraordinary success of Jews in all other fields is in large part, directly or indirectly, attributable to this training. Nevertheless, we could do better – much better.

Biblical exegesis could be improved by a more conscious application of logic. What precisely has been, or can be, logically inferred from each and every sentence and wording of the Torah, and by means of which specific form(s) of argument? Commentators give explanations, but they rarely specify their precise sources, whether they are purely traditional or whether they are based on reasoning. I imagine a book which would collect next to every verse all the lessons to be learned from it, and just how. Judaism constitutes a mass of beliefs, most of which are implicit if not explicit in the Torah. For instance, the belief in Providence is not only based on abstract statements (like, say, that in the second paragraph of the Shema), but is also suggested by various concrete stories.

But especially in Talmud studies, I believe a great improvement to be called for. A section of the Talmud which describes all the complex arguments and counter-arguments concerning a specific issue, is known as a sugya. The Talmud is naturally subdivided into a large number of sections; some are brief, some are very long. The Mishnah makes a statement; the Gemara finds some difficulty in it, in relation to some other Mishnah or to a Baraita, and debates the issue; later commentators enter the discussion: Chai Gaon, Rashi, Tosafot, Moshe Feinstein. More and more subtle questions are raised, finer and finer distinctions are made, until everyone is satisfied, or silenced.

It appears, and I do not deny it, that experts in the field are able to follow these complex arguments, without even the need for pen and paper; their minds are quick and in perfect working order, and their intelligence is great. But for a dull wit like mine, and I do not think that I am far below average, all this is hard to follow without a more point by point approach. I personally know only too well, from repeated experience, how an argument may seem very convincing on the surface, and then be found by applying the methods of formal logic to be erroneous, or at least in need of revision.

I would like to see each sugya patiently analyzed, in such a way that all its arguments are rendered entirely explicit, line by line, and it is demonstrated that all possibilities have been taken into consideration, and no other conclusions than those traditionally proposed are drawable. If there was an area of doubt, and a psak din, a ruling by the authorities, was made, so well and good; the law need not be based exclusively on logic. But the logic involved must in any case be made clear, to be fully justified. A whole book might be written about each sugya, if necessary. There is great scope for scholarly study in such an approach, and it would surely highly revive and stimulate interest in the Talmud.

Our proposal may seem to go against the tradition that the Oral Law be kept as oral as possible. But the truth is that this tradition has been virtually ignored since the redaction of the Mishnah and of the Gemara: look at all the written commentaries which have made their appearance since then. All I am advocating is the collection of all the authoritative writings, concerning any given sugya, and their exact ordering with formal logic in mind. That is only a kind of supercommentary, one might say. In any case, there is nothing to hide from non-Jews; their scholars know the languages involved, and can study the original texts, anyway, if they care to. On the other hand, the Talmud might in this way be made more accessible to the modern Jew; and surely that is what counts the most.

The following is a succinct illustration of what I mean; how I would like to see the Talmud studied and taught. The example is partial, but it suffices (in any case, these are the only notes I took!). It is drawn from tractate Berachot, p. 14. The sugya arises out of a difference of opinion (machloqet), between Sheshet on the one hand, and Rav and Shmuel on the other, about whether or not it is permitted to “verbally salute” someone “before prayer”; further complicating the matter, the terms involved have alternative interpretations. Note the symbols I insert, to abbreviate the discussion.

P: One can say hello before prayer (Sheshet).

Q: One cannot say hello before prayer (Rav & Shmuel).

(Note in passing that these propositions are modal; the type of modality involved is ethical: “can” here refers to permission, and “cannot” to prohibition.)

At first sight, P and Q are contradictory; however, it turns out that:

Say hello” may mean:

a) seek out to say hello, or

b) chance to meet and say hello.

(Note that “seeking out” may be viewed as a special case of “chancing to meet”; so that P(a) implies P(b), and contrapositely Q(b) implies Q(a), for any given value of the other term (c or d).) Also:

Before prayer” may mean:

c) before starting to pray, or

d) before completing prayers.

(Note that “before completing prayers” is understood as covering all the time before, including that “before starting to pray”; so that P(c) implies P(d), and contrapositely Q(d) implies Q(c), for any given value of the other term (a or b).)

Each of the given theses may thus, according to the terms involved, have four meanings. Thus, P may mean P(a,c) or P(a,d) or P(b,c) or P(b,d); and similarly for Q. Our goal is now to determine which combinations of P and Q, in their various senses, are formally consistent, implying a possible marriage of the two positions. The method used is one of elimination.

If P and Q have precisely the same subscripts, they are formally mutually exclusive, since one says “can” and the other “cannot”. Thus, the four conjunctions like “P(a,c) and Q(a,c)” are self-contradictory and can be eliminated from further consideration. What, however, the remaining twelve conjunctions? We can eliminate a few more of them, by using a fortiori arguments.

First, if one cannot chance to meet and say hello, then one cannot seek out to say hello. That is, P(a) and Q(b) are contraries, for a given value of the other term (c or d).

Second, if one cannot say hello before completing prayers, then one cannot say hello before starting to pray. That is, P(c) and Q(d) are contraries, for a given value of the other term (a or b).

These a fortiori arguments enable us to eliminate five more combinations of P and Q, namely: for the first reason, “P(a,c) and Q(b,c)”, “P(a,d) and Q(b,d)”; for the second reason, “P(a,c) and Q(a,d)”, “P(b,c) and Q(b,d)”; and, for either or both reasons, “P(a,c) and Q(b,d)”. Which leaves us, so far as I can see, with seven internally consistent conjunctions of the two theses:

1.         P(a,d) + Q(a,c) = one can seek out to say hello before completing prayers, but one cannot seek out to say hello before starting to pray.

2.         P(b,c) + Q(a,c) = one can chance to meet and say hello before starting to pray, but one cannot seek out to say hello before starting to pray.

3.         P(b,d) + Q(a,c) = one can chance to meet and say hello before completing prayers, but one cannot seek out to say hello before starting to pray.

4.         P(b,c) + Q(a,d) = one can chance to meet and say hello before starting to pray, but one cannot seek out to say hello before completing prayers.

5.         P(b,d) + Q(a,d) = one can chance to meet and say hello before completing prayers, but one cannot seek out to say hello before completing prayers.

6.         P(a,d) + Q(b,c) = one can seek out to say hello before completing prayers, but one cannot chance to meet and say hello before starting to pray.

7.         P(b,d) + Q(b,c) = one can chance to meet and say hello before completing prayers, but one cannot chance to meet and say hello before starting to pray.

This listing does not terminate the analysis. The next step would be to determine the interrelationships between these combinations. Some are incompatible, because the P part of one has the same terms as the Q part of the other; for instances, Nos. 1 and 6 are contrary to Nos. 4 and 5. Some imply others, in view of the relationship (above mentioned) between the terms a and b, or c and d. Thus, for instances, No. 2 implies No. 3; No. 4 implies No. 2, and therefore also implies No. 3; No. 5 implies No. 3. Some combinations may be neither contrary, nor involve implications, and would in that case be taken as merely compatible. We may also want to linger on each statement and consider just what it means; for instance, No. 1 seems to imply a permission to seek out to say hello in the middle of prayer.

I will not pursue these details further, but will only add: it is only after all such preparatory formalities, that we may begin to wonder about the positions of different Rabbis. Granting that the purpose of the whole sugya is to reconcile the apparently divergent opinions of Sheshet and Rav/Shmuel, logic leaves us with seven possible harmonizations; it is thereafter up to us to find ways to narrow the list yet further. What the Gemara decided, how the various Rishonim leaned, what the Acharonim say, and what precise arguments were brought in from elsewhere – all that concerns only the seven leftover combinations.

If the reader is confused by the above labyrinth of reasoning, it would indeed please me! Because, that would prove my point, namely that only the most exceptional minds could possibly go through this process with certainty using only their heads, without material supports. There is no way to be sure that all alternative possibilities have been covered, without some such systematic approach. It would be hard for any normal person to honestly say that they can zip through such complex logical processes, without seeing them black on white. Even if a teacher orally described things step by step, it would be difficult for a student to retain all the details in memory from start to finish, and thus be sincerely convinced. In any case, a good background in logic theory would seem essential.

Incidentally, I have had the unfortunate experience of some Talmud teachers who rush through a sugya, with little concern for communication. They seemed more bent on an ego-trip, to appear of superior intelligence – or to hold by some arbitrarily imposed time-table (which conveniently excused their skimming over difficulties). But the goal of teachers should be, and supposedly it is the goal of most, to address the unique human minds of their students, and effectively transmit convincing information to them, rather than to the surrounding airspace. The value of the face to face encounter is precisely that the teacher answers the questions which bother the student. One student, be it out of naivety or obtuseness or out of greater knowledge or intelligence, may have no problem with a certain point; while another, for whichever of those reasons, has a hard time assimilating the same information in his specific knowledge-context. There is no virtue in glossing over difficulties; good thinking is relentless, it goes all the way.

Even so, while admitting the value of properly assisted learning, my appeal here is still for a thorough, written exposition and elaboration of all Halakhic arguments, sugya by sugya. Only such a review, performed by experts in both logic and Rabbinic decisions, can render the logical undercurrents of the Talmud and its commentaries entirely transparent, and make possible the demonstration of the high standards of logic involved in orthodox reasoning. I believe, out of faith, that it is possible; but in any case, the Halakhah can only gain from such a programme. For if there happen to be areas of weak logic, they will not put everything in doubt, but simply present opportunities for new debates.

More broadly, it would be of great value to methodical researchers and students of the Talmud and its Commentaries to have simply a table of contents, an index, a concordance. I have not seen such a document, but I am told that it already exists; if not, today with computers it should be easy to do (though perhaps expensive). There is a need of transparency, not only at the level of specific arguments, but equally at the level of making the literature as a whole susceptible to organized and systematic inquiry. For instance, assembling together all pronouncements on any topic under investigation – so as to have a true, unbiased, balanced picture of what has been said by all authorities on the subject concerned, and so as to be able to trace precisely the historical evolution of laws and attitudes.


Drawn from Judaic Logic (1995), chapter 9.



[1]              The hermeneutic principles are applicable more broadly to all Scriptural exegesis, including Hagadah; however, in the case of the non-legal aspects some less strictly regulated forms of interpretation are often used, additionally. If the latter are not considered trustworthy enough for Halakhah, I do not see how they may be relied on for Hagadah, which also affects the beliefs and actions of people.

[2]              Vol.  , pp. 30-33.

[3]              Vol. 8, pp. 366-372.

[4]              Specifically, chapter 13.

[5]              Note that Hillel and Shammai are traditionally not given the title Rabbi, or any equivalent.

[6]              A Halakhic commentary to Leviticus, also known as Torat Kohanim, attributed to R. Yehudah b. Ilayi, a disciple of R. Akiba (2nd cent. CE).

[7]              As Scherman has pointed out, these Baraitot were different, in that they were not in themselves statements of law but explanations of how the laws were derived from the Torah source.

[8]              To explain the differences in listing, orthodox commentators go to great lengths. We shall have occasion to discuss some of these explanations as we proceed.

[9]              For examples, klal uphrat, a R. Ishmael principle, is attributed to Nechunia b. Hakaneh (Tosefta Shevuot 1:7); ribui umiut, a R. Akiba principle, is attributed to Nachum Ish Gimzu (Shevuot 26a).

[10]            Still today, in Talmud study, people do not find it odd that a R. Ishmael rule might prevail in one context and a R. Akiba rule in another. Logically, one would have thought that just one of the systems would have to be adopted for the whole Talmud.

[11]            See chapters 8-9 of the present volume.

[12]                In Baba Qama, as I recall, but I did not note the page. However, here is another example used by commentators, which is probably closely related. Consider, for instance, the sentence "For all manner of trespass, whether it be for ox, for ass, for sheep, for a garment, or for any manner of lost thing... he shall pay double to his neighbour" (Exod. 22:8). The question is, why after saying "all" are various specifics (ox, ass, etc.) mentioned? Klal uphrat understands them as having an constructive function, it starts with a minimalist thesis then expands it: "ox" means ox, and so forth. Ribui umiut gives them an eliminative function, starting with a maximalist thesis then successively contracting it: "ox" is mentioned so as to exclude land (which is immovable property, unlike oxen), "ass" and "sheep" to exclude slaves or bills (which differ from the given examples in certain unstated respects), "garment" to exclude the unspecific (such as unspecified quantity).

[13]                According to what I was told by a teacher; I have not looked for the reference.

[14]            To illustrate this, a funny joke is circulated in Yeshivot: "How do you know you have to wear a yarmulke? Because it says Vayetse Yacov.... Would Yacov go out without a kipah?"

[15]            We might cite as an example of such reasoning Rashi's "if it does not apply", which Bergman clarifies as follows: "If the Torah indicates a halachah in a case or category where it is already known, then apply that halachah to another situation" (p. 120, my italics). Obviously, here, Rashi is appealing also to the R. Akiba principle that there is nothing repetitive or superfluous in the Torah. The problem remains, which other situation, and how is the choice to be justified!

[16]            Including, appropriately separated, the two rules distinguished by the word hatsarikh, which are traditionally lumped together under No. 7. As later discussed, the treatment of complementarity as something distinct is an overreaction, in my view.

[17]            In my view, this is wrong. Rule 11 is functionally radically distinct from rules 8-10, albeit the common opening phrase. And rules 8-10 are sufficiently different in their premises and conclusions to justify separate treatment, even though they are obviously a related series. This will become clear further on.

[18]                Other principles worth noting, which are in practice used for hermeneutic purposes, are rov (this statistical principle is usually associated with majority decision by judges, but it may also be applied to matters of judgment, as for instance in Avoda Zara 75b, where Num. 31:22-23 "every thing that may abide the fire" is understood by Rashi as referring to cooking utensils, since they are the metal implements habitually subjected to fire) and perhaps hazakah (which, again, is usually associated with the legal status quo, but in many contexts refers to empirical evidence). Note in passing, with reference to Num. 31:22, the mention of iron – which suggests that the Iron Age had started by 1300 BCE, whereas historians, supposedly on the basis of archeological findings, place it at closer to 1000 BCE, if I am not mistaken [but about this issue, see also JL, Addendum 5]. See also JL, Appendix 3 for comments on Judaic numerology (gematria), and other such exegetic techniques, which count as aspects, however marginal, of Judaic logic.

[19]            Besides, how can one make conjectures about a past person's "intentions", without written record to support one's case, and say "certainly"?!

[20]            Bergman claims, in Raavad's name, that (c)=3 while (d)=13. But I do not see, judging from J.E.'s wording, how such a position is possible. I suspect a characteristic attempt to force facts to fit the comforting view that Hillel's list is a condensation of R. Ishmael's; it is significant that Bergman occults the actual wording of the rules in question in the original sources.

[21]            This rule is called mah matsinu by Bergman; it is interesting to note that mah matsinu is equated by Scherman to binyan av! The wording "as came out for it from another place" suggests some kind of inference of information, anyway.

[22]            J.E. does not include R. Ishmael's rule 13 in this remark. Concerning rule 13, J.E. says that it is "not found in Hillel".

[23]            Apparently, some orthodox commentators concede this point, since Bergman remarks "Some explain that when he [Hillel] expounded before the elders of Beseira, he required only these seven rules," implying the existence of other rules not expounded by him on that occasion.

[24]            As already mentioned, R. Eliezer's list is distinguished by its mixture of principles of merely Hagadic value with those of Halakhic value; the exegesis of inspirational stories is less strictly regulated than that of legal matters. I do not know first-hand how true these remarks are, but am just passing on information.

[25]            Is it to avoid bringing such problems out into the open that, apparently, no lists are traditionally given for Shammai's and R. Akiba's rules?

[26]            Note in passing that some terms are apparently reserved to Halakhic contexts, while others are reserved for Hagadic contexts (Rabinowich).

[27]            The reason for their inclusion is usually to elucidate the terminology, rather than to deeply study their logical properties.

[28]            Judging by a chart in Aiding Talmud Study, there were a couple of hundred named participants over a period of some 450 years.

[29]            This work is, according to its author and as the full title implies, an adaptation of M. Mielziner's Introduction to the Talmud; New York, 1903.

[30]            The earliest work on terminology mentioned by Rabinowich, is Sefer Keritot by R. Samson of Chinon, ‘one of the last French Tosafists (fourteenth century)’. Then we have the Mevo HaTalmud of R. Shmuel Ibn Nagrela ‘HaNagid’ (so-called, but wrongly according to M. Margolis). And so forth. Thus, according to Rabinowich’s listing, the systematic development of such linguistic analysis is a relatively late phenomenon (Rishonim). More details on this question might be found in the History of the Talmud by Rodkinson (1903), mentioned on p. xiv, which I have not read.

[31]                For some quite incidental comments on the Hebrew language, see JL, Appendix 5.

[32]            The contrast between Mishnaic Hebrew and the Aramaic of the Gemara or between the Aramaic of B.T. and that of J.T. being only the most obvious variations.

[33]            Bergman, p. 92.

[34]            See Bergman, p. 94. Even here, there are differences of opinion. For examples, some say that the law follows Beit Shammai rather than Beit Hillel in 6 cases, while some say in 3 cases; or again, some say that in disputes between R. Yehudah and R. Nehemiah, the latter wins, whereas the Rambam rejects this rule of thumb.

[35]            Talmudic language and organization has a history; and then the study of such history has its own history. To what extent the latter has been traced, and accurately so, I do not know. Evidently, some effort has been done, witness Rabinowich's bibliography; but a more thorough effort may be necessary.

[36]            Baraitot often stir heated debate. Unlike Mishnaiot (which have primary authority), these pronouncements of Tanaim are not necessarily known to all Amoraim, and yet they have considerable authority (after Mishnaiot). For this reason, Baraitot often cause differences of opinion between Amoraim: those in the know having one opinion, and those not in the know having another opinion.

[37]            Notably, Rashi, see Shereshevsky. Incidentally, it is shocking to learn that there have even been variant versions of the Torah! On this matter, Lewittes (pp. 44-47) informs us that the Talmud reports slight emendations in the text by the Soferim (Nedarim 37b – the Soferim appeared after the First Exile); he also tells how, in one instance, three Torah scrolls were found in the Temple which were not identical, and it was decided to adopt the reading common to two of them as valid (Soferim 6:4) – a simply statistical method, note well. Also note his comment: "Shortly after the period of the Talmud critical editions of Scripture were produced by the so-called masoretes, from whom we derive the present-day Masoretic text. They decided which version of the several existing ones should become standard..." though he rightly considers the matter of minor significance – rightly, because such fiddling presupposes a pre-existing document in many versions. But problems of this sort have recurred, judging by a comment in Cohen that Rashbam "apparently reads alecha 'concerning thee,' not lecha as in the editions" (p. 166). More broadly, there are many apparent inconsistencies (in names, spelling, numbers, etc.) in the Tanakh, which could well be ascribed to mistakes of the writers or to scribal errors, though orthodox commentators go to great lengths to explain them away in other ways; for instance, dodanim in Gen. 10:4 is written rodanim in 1-Chron. 1:7 (the Hebrew letters d and r are easily confused). See Mitchell pp. 31-32, and also 101-102.

[38]            See for instance its ch. 6, but the whole book is well worth reading.

[39]            Examples may be found scattered in the present work.

[40]            Logicians have called the tendency to classify objects with reference to their past characteristics, rather than with respect to their eventual new attributes, commission of the "genetic fallacy". This is an inductive fallacy, of course, in that it reflects a mental rigidity, a failure to empirically monitor objects of study for possible changes in their identity. Progress must be allowed for in our perceptions and conceptions.

[41]            Many women today are evidently 'respectable' in any sense of the term understood for men; the Swiss Conseillère Fédérale Ruth Dreyfuss comes to my mind. Another group which seems to me wrongly despised by the Talmud are deaf-mutes; today, we know their true abilities.

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