Logic in the Talmud

A Thematic Compilation by Avi Sion

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5. A Fortiori in Certain Lexicons

In the present chapter, we shall investigate the treatment (or non-treatment) of a fortiori argument in general – and of the more specifically Jewish concepts of qal vachomer and dayo – in three standard encyclopedias (more are dealt with in AFL 32). This is not intended to be an exhaustive survey, but should give us a good idea of how this topic is regarded and how far it is understood by the academics, writers and editors, who produce the lexicons concerned.


1.   The Jewish Encyclopedia

The Jewish Encyclopedia (henceforth, JE) is an important English-language resource for information on Judaism and Jews, which was published in 1901-6 in New York. It can nowadays be consulted online[1]. The article in it which interests us here is called “Talmud Hermeneutics” (in vol. 12, pp. 30-33); it was apparently written by Jacob Zallel Lauterbach (1873-1942), with a bibliography by Wilhelm Bacher[2]. This article is wide-ranging, dealing with all sorts of interpretative techniques, as well as the more logical ones enshrined in the seven rules of Hillel and the later thirteen rules of R. Ishmael.[3]

We shall not here, needless to say, review the whole article but only focus on what it says regarding a fortiori argument, i.e. which it refers to as Ḳal wa-ḥomer, the first rule in the lists of Hillel and R. Ishmael. JE tells us that “The completed argument is illustrated in ten examples given in Gen. R. xcii.” – however, this statement is not entirely accurate, because this set of ten examples is claimed in Genesis Rabbah 92:7 to be exhaustive; JE should have pointed out that there are a lot more than ten examples of such argument in the Tanakh (at least 46, according to more recent research).

JE identifies Ḳal wa-ḥomer as “the argument ‘a minori ad majus’ or ‘a majori ad minus’;” and states that “The full name of this rule should be ‘ḳal wa-ḥomer, ḥomer we-ḳal’ (simple and complex, complex and simple), since by it deductions are made from the simple to the complex or vice versa, according to the nature of the conclusion required.” This is of course an important observation regarding the two directions of a fortiori thought; but JE does not clarify when it first appears in Jewish texts. Note also its translation/interpretation of the terms ḳal and ḥomer as respectively “simple” and “complex;” this is not the most accurate rendering of their meanings. For a start, we are not told what is qualified as “simple” or “complex,” let alone what these expressions mean. This is not terminology used by the rabbis.

Note that JE gives no unified definition for a fortiori argument, i.e. it does not attempt to uncover what the two above forms of it have in common. Nor indeed what in fact distinguishes them (namely, that the first is positive whereas the second is negative). Moreover, JE makes no attempt to clarify how and why the a fortiori argument works, i.e. to formally describe and validate it. All it tells us regarding its structure is: “The major premise on which the argument is based is called ‘nadon’, or, at a later period, ‘melammed’ (that which teaches); the conclusion resulting from the argument is termed ‘ba min hadin’, or, later, ‘lamed’ (that which learns).” It is inaccurate to call the nadon the major premise; it is more accurate to refer to it as the minor premise.

Evidently, JE is not aware of the premise that compares the major and minor terms in relation to the middle term, which deserves the name of major premise. As we saw, it does not mention the major and minor terms as such (it mentions ḳal & ḥomer and simple & complex – but it does not say that these items are terms). Also, it does not even hint at the middle term, nor realize that it has to be present (setting a threshold) in the minor premise for the conclusion to be possible. The predication in common to the minor premise and conclusion is not at all mentioned either. Furthermore, JE shows no awareness of the differences between subjectal and predicatal forms of a fortiori argument, let alone of the differences between copulative and implicational forms.

All in all, then, this article provides little information on the nature of a fortiori reasoning. It does mention the distinction, found as rules 5 and 6 in the list of Eliezer ben Jose ha-Gelili, “between a course of reasoning carried to its logical conclusion in the Holy Scriptures themselves (‘ḳal wa-ḥomer meforash’) and one merely suggested there (‘ḳal wa-ḥomer satum’).” But this is a relatively unimportant insight, as it refers to the degree to which the Biblical text is explicit or implicit rather than to the form of a fortiori argument as such.

As regards the dayo principle, JE describes it as follows:


“The process of deduction in the ḳal wa-ḥomer is limited by the rule that the conclusion may contain nothing more than is found in the premise. This is the so-called ‘dayyo’ law, which many teachers, however, ignored. It is formulated thus: dayo lavo min hadin lihiot kanidon (‘The conclusion of an argument is satisfied when it is like the major premise’).”


This description, too, is inaccurate, in that it confuses the dayo principle with what I have called the principle of deduction, i.e. the logical rule applicable to all deductive argument that “the conclusion may contain nothing more than is found in the premise.” As I have shown, the dayo principle is something else entirely: it is an ethical limitation on the inference of greater penalties for greater crimes, or relatively stringent laws, from information given in the Torah regarding lesser penalties for lesser crimes, or relatively lenient laws. It constitutes self-restraint on the part of rabbis, so as to avoid the risk of excessive punishment, or severity of duties, through erroneous human interpretation of Divine law.

JE should have realized that the reason why “the ‘dayyo’ law” could be “ignored” by “many teachers” is precisely that it is not a principle of deduction, but more like one of induction. JE also shows unawareness of the difference between inductive and deductive inference when it informs us that: “The discovery of a fallacy in the process of deduction is called ‘teshubah’ (objection), or, in the terminology of the Amoraim, ‘pirka’. The possibility of such an objection is never wholly excluded, hence the deduction of the ḳal wa-ḥomer has no absolute certainty.”

In truth, most such objections in practice refer to the content, rather than to the form, of the a fortiori argument. The deduction involved in the argument, if properly formulated, is quite certain – that is what the term “deduction” (when applicable) means. The questions raised in objections are occasionally whether the argument has indeed been correctly formulated, but more commonly whether the information or perspective it relied on is indeed reliable. Thus, we see, here again, that the author of the JE article was not too clear about many issues concerning general logic, as well as some issues relating to Talmud.

Nevertheless, the article as a whole remains very interesting historically and doctrinally. It certainly, albeit brief, contains a lot of valuable information on the topics it treats.


2.   Encyclopaedia Judaica

The Encyclopaedia Judaica (henceforth, EJ) is a more recent English-language resource for information on Judaism and Jews, which was published in 1971-2 in Jerusalem and New York; over time, this was supplemented with several yearbooks and decennial volumes; a second edition, including many major revisions and updates, was published in 2006-7[4]. The article we shall take a look at here is called “Hermeneutics,” and is found in the first edition (pp. 367-372). It is signed by Louis Jacobs (Britain, 1920-2006). This article was retained in the second edition, perhaps with some minor modifications (since it is there cosigned by David Derovan)[5].

Although the EJ article expounds the thirteen rules of R. Ishmael and other interpretative techniques in some detail, we shall only here be concerned with its exposition of Kal va-ḥomer, i.e. of the first of the thirteen rules. Since, in AFL, we have already devoted a whole chapter (16) to the views of Louis Jacobs regarding a fortiori argument, we need not go into great detail in the present context. It will suffice for us to briefly comment on a number of points.

To begin with, EJ defines “Kal va-ḥomer” as “an argument from the minor premise (kal) to the major (ḥomer).” This is, of course, wrong – kal and ḥomer refer not to premises but to terms within the premises and conclusion! It is true that in the a minori ad majus form of the argument the kal (minor) term is in the minor premise; but the ḥomer (major) term here intended is, not in the major premise as EJ implies, but in the conclusion. It is also to be found in the major premise, which compares the two terms, but this is not the proposition that EJ is referring to here. So, this is an error, if only of inattention[6].

Furthermore, EJ does not mention the major premise, nor therefore the presence in it of a middle term that performs the comparison that determines which term is the major and which is the minor. Nor does EJ here mention the presence of the middle term in the minor premise and conclusion, and its crucial role in them in establishing the quantitative threshold as of which predication is possible. The subsidiary term (the predication) is likewise not highlighted. Note also that, whereas JE explicitly acknowledges both the a minori ad majus or a majori ad minus moods of a fortiori argument, EJ only considers the former (implicitly, without naming it) and ignores the latter.

So, what we find in the EJ article on the whole is a very limited understanding of the nature and scope of a fortiori reasoning. All it gives us is a very rough sketch of the paradigmatic form of such argument. Not surprisingly, it fails to distinguish between positive and negative arguments, between subjectal and predicatal ones, and between copulative and implicational ones.

However, further on, when EJ rightly strongly rejects the identification by Schwarz between a fortiori argument and Aristotelian syllogism, it offers a somewhat better definition inspired by Kunst: “in the kal va-ḥomer it is not suggested that the ‘major’ belongs in the class of the ‘minor’ but that what is true of the ‘minor’ must be true of the ‘major’”. In this statement, the “major” and “minor” more clearly refer to subjects (or even antecedents), since the phrase “what is true of” them obviously refers to a predicate (or even a consequent). Thus, EJ here may be said to point to three of the four items of a fortiori argument. But the middle term (or eventually, thesis) is still missing, and this is of course a serious lacuna.

As regards use of a fortiori argument in Judaism, EJ lists the ten examples of it found in the Bible according to the Midrash (Gen. R. 92:7), and two more examples drawn from the Mishna (Sanh. 6:5) and Gemara (Ḥul. 24a). The article then proposes Jacobs’ own theoretical distinction between “simple” and “complex” qal vachomer (which the preceding two Talmudic examples are taken to illustrate, respectively). In the “simple” type, “the ‘major’ and ‘minor’ are readily apparent,” whereas in the “complex” type, “an extraneous element… has to be adduced to indicate which is the ‘minor’ and which is the ‘major’.”

The two types are symbolically represented as follows: “Simple: If A has x, then B certainly has x;” and “Complex: If A, which lacks y, has x, then B, which has y, certainly has x.” As I have argued at length in the chapter devoted to Louis Jacobs (AFL 16), the symbolic formulae used to define the proposed distinction are very superficial, since they fail to clarify why or how the consequents should logically follow from the antecedents. In truth, a major premise is required in either case, whether it is readily apparent or takes an effort of reflection to formulate. This means that the simple type is tacitly complex, since its terms A and B are known to differ in some respect (say, in degrees of y). Thus, the distinction is formally inadequate.

Nevertheless, the “complex” form proposed by EJ does have considerable value, in that it does effectively allude to the middle term and the major premise of a fortiori argument. Here, “y” plays this mediating role, although this is just a special case of a more general form. A more general statement would have been: ‘If A, which has less y, has x, then B, which has more y, certainly has x’. In that expanded formula, the major premise that ‘B has more y than A does’ is clearly implied. The case referred to by EJ is the special case where ‘less y’ is specifically ‘no y’, and ‘more y’ is specifically ‘some y’. We do often in practice come across a fortiori statements both of the general kind (with ‘less y’ and ‘more y’) and of the special kind (with ‘zero y’ and ‘more than zero y’). Thus, EJ cannot be said to have totally ignored the middle term and the major premise – it just did not clearly acknowledge them.

As regards “the principle of dayyo (‘it is sufficient’),” EJ presents it as “a qualification of the kal va-ḥomer,” according to which “the conclusion [can] advance only as far as the premise and not beyond it.” In symbolic terms, this means: “It must not be argued that if A has x, then B has x + y. The kal va-ḥomer suffices only to prove that B has x, and it is to go beyond the evidence to conclude that it also has y.” This definition, though nice and clear, is partly inaccurate. It is a good statement of the principle of deduction for purely a fortiori argument – but that it not what the dayo principle is really about.

EJ rightly refers the principle to the Mishna Baba Qama 2:5, where it is first formulated, but it wrongly interprets its discussion in the corresponding Gemara Baba Qama 25a. The latter does not exactly or merely teach that “R. Tarfon rejects the dayyo principle in certain instances.” Rather the Gemara, relying on a baraita (known as The Baraita of R. Ishmael), advocates precisely the view that qal vachomer yields a ‘proportional’ conclusion. This is evident from the Biblical example regarded as the prototype of qal vachomer, viz. Numbers 12:14-15.

In this example, according to the Gemara, the correct inference by qal vachomer would be a punishment of fourteen days incarceration (for Miriam, for speaking out of turn concerning her brother Moses), even though only seven days incarceration is mentioned in the Torah. The dayo principle then serves to reduce the concluding penalty from fourteen days to back to seven. Thus, the Gemara’s view is that qal vachomer is essentially a crescendo argument (rather than purely a fortiori argument as EJ implies it), and that the dayo principle diminishes its conclusion ex post facto (rather than denying that the ‘proportional’ conclusion can at all be drawn as EJ implies it). Thus, EJ does not represent the dayo principle as it is actually understood in Talmudic literature.

Evidently, EJ looks upon the dayo principle as a principle of formal logic, whereas it is more precisely put an ethical principle adopted by the rabbis to ensure their deliberations do not end up with excessively severe legal rulings. Moreover, the scope of the dayo principle is clearly not as wide as EJ has it, if we refer to its genesis in the said Mishna. It is not a general principle regarding any sort of conclusion (i.e. any A, B, x and y) – but more specifically a warning against inferring a harsher penalty for a greater crime from a Biblical text that imposes a certain (gentler) penalty for a specific (lesser) crime. Even though this warning might be extended somewhat to duties in general (instead of being applied only to penalties for crimes), it is by no means as general as EJ implies.

In conclusion, while the EJ article on hermeneutics is admittedly full of valuable information, it is seen on closer scrutiny to be open to considerable criticism. As the saying goes, “the devil is in the details.” Qal vachomer and the dayo principle are certainly more intricate topics than EJ makes them out to be. And I suggest, based on my past study of the hermeneutic principles in JL, that EJ treatment of the other hermeneutic rules can similarly be criticized as oversimplified and not entirely accurate. Of course, one should not expect too much from a brief article in an encyclopedia.

Still, to my mind, there was a failure of adequate research by editors of this important encyclopedia. It is shocking that in the first edition (1971-72) there is no mention of the Ramchal’s 1741 contribution to understanding of qal vachomer (he managed to describe the four main moods of the argument) and that in the second edition (2006-7) there is no mention of Avi Sion’s 1995 clarification of qal vachomer (which included full formalization and validation of such reasoning).


There is in EJ, 2nd ed. (vol. 9) an article on “Interpretation” in which, under the heading of “Analogical Interpretation,” can be found a brief explanation of qal vachomer (p. 819). This article was authored by Menachem Elon. The term analogical interpretation (midrash ha-mekish) refers to “the subject matter of the first three of the 13 middot enumerated by R. Ishmael.” The first of these is “kal va-ḥomer,” which refers to “a fortiori inference, a minori ad majus or a majori ad minus.”

“The basis of this middah,” we are told, “is found in Scripture itself (Gen. 44:8; Deut. 31:27) and the scholars enumerated ten pentateuchal kallin va-ḥomarim (Gen. R. 92:7).” This information is not quite correct. Though examples of qal vachomer occur in Scripture, it does not follow that they are its “basis;” a fortiori argument is rationally evident, and does not require revelation. Moreover, the ten examples given by the cited Midrash are not all “pentateuchal,” i.e. in the Five Books of Moses (Torah), but range across the whole Jewish Bible (Tanakh); and besides, there are in fact many more instances of the argument in the latter than the ten mentioned in the Midrash.

This article defines “the rule of kal va-ḥomer” as “a process of reasoning by analogy whereby an inference is drawn in both directions from one matter to another, when the two have a common premise – i.e., it can be drawn either from the minor to the major in order to apply the stringent aspect of the minor premise also (BM 95a), or from the major to the minor in order to apply the lighter aspect of the major premise to the minor premise (Beẓah 20b).” The two examples here mentioned are not quoted in the article, but I have looked them up (in the Soncino English ed.) so as to examine them.

The example in Baba Metzia 95a reads as follows: “You can reason a minori: if a paid bailee, who is not responsible for injury and death, is nevertheless liable for theft and loss; then a borrower, who is liable for the former, is surely liable for the latter too!” This argument is indeed from minor to major, being positive subjectal in form. Its major, minor, middle and subsidiary terms are, respectively, “a borrower” (P), “a paid bailee” (Q), “responsible for injury and death” (R, ranging from zero upwards), and “liable for theft and loss” (S). Note that what EJ refers to, here, as “the stringent aspect of the minor premise” is the subsidiary term, S; more precisely, this is a stringency applicable to (i.e. predicated of) the minor term, Q (which in this case happens to be located in the minor premise) which is passed on to the major term, P (located in the conclusion).

There are in Beẓah 20b two examples of kal va-ḥomer (they are there discussed and contested, but this need not concern us here). These are indeed arguments from major to minor, being negative subjectal in form. The first example reads: “If, when it is forbidden [to slaughter to provide food] for a layman, it is permitted [to slaughter] for the Most High, then where it is permitted on behalf of a layman, it is surely logical that it is permitted for the Most High.” Its major premise is that “slaughter for a layman (P) is more restricted (R) than slaughter for the Most High (Q),” since the former is forbidden when the latter is permitted (this involves a generalization, note, from certain cases to all cases). The minor premise and conclusion predicate that P and Q, respectively, are “restricted (R) not enough to be forbidden (S).” The second example reads: “If when thy hearth is closed, the hearth of the Master is open, how much the more must the hearth of thy Master be open when thy hearth is open.” It is very similar (and indeed is presented as “the same in another form”), except that here, P is “thy hearth,” Q is “the hearth of the Master,” R is “restricted,” and S is “closed.”

With regard to these arguments, EJ remarks that they go “from the major to the minor in order to apply the lighter aspect of the major premise to the minor premise.” This tells us that the author of this article interprets the expression ‘from major to minor’ as referring not to terms but to premises; i.e. in his perspective, the “major premise” is the proposition containing the major term and the “minor premise” is the one containing the minor term. But obviously this perspective is incorrect – for the proposition containing the minor term here is not a premise but the conclusion! So, this is a misinterpretation of the said expression. This reveals that the author is not very well versed in logic.

As regards the dayo principle, the article states: “Material to this rule is the principle dayo la-ba min ha-din lihyot ka-niddon (Sifra, loc. cit.; BK 25a, etc.), i.e., it suffices when the inference drawn from the argument (ha-ba min ha-din) is equal in stringency to the premise from which it is derived (the niddon), but not more so, not even when it might be argued that logically the inference should be even more stringent than the premise from which it is derived.” This formulation is potentially interesting, in that the dayo restriction is placed in opposition to possible “logical inference.” Unfortunately, the author does not discuss the implications of such opposition. If it disagrees with logical inference, then dayo is not a logical principle; in which case, we have to suppose that it is based on other considerations, perhaps moral ones. Moreover, we must ponder: is the logical inference necessarily, or only contingently, “more stringent”? If the logical inference is necessarily a crescendo, how can it be occasionally ignored by a dayo principle? And if the logical inference is only occasionally a crescendo, under what conditions does this occur, precisely? The author does not ask these questions.

Despite of such mistakes and deficiencies, the EJ article on Interpretation is on the whole, of course, very informative.


3.Encyclopedia Talmudit

The Encyclopedia Talmudit (henceforth, ET) is a Hebrew language encyclopedia whose purpose is to “summarize all the Talmudic halakhic issues and concepts, and all the opinions of halakhic scholars, from the completion of the Talmud to modern times, on every aspect of Jewish law”[7]. This ambitious task began over 60 years ago, and is still far from finished today (though 29 volumes have been published so far, 50 more are on the way). An English translation, called the Encyclopedia Talmudica, is also being published over time.

I looked for but nowhere found the Hebrew ET volume containing an article on qal vachomer[8]. I did however find the volume with an article on the dayo principle (vol. 7, 1990)[9]. It is this article that I will here comment on briefly. As would be expected from an encyclopedia devoted to halakhic thought in Judaism, it simply presents the main lines of the traditional view of the dayo principle relative to qal vachomer argument. There is no novel theoretical research in it, or criticism of existing doctrines and methods.

The dayo principle is stated by the Sages in the Mishna as: dayo lavo min hadin lihiot kanidon, which can be translated as: “it is quite sufficient that the law in respect of the thing inferred should be equivalent to that from which it is derived.” ET explains this rule as teaching, with regard to inferences made by means of a fortiori, that “one cannot lay down (lehatil) more in the conclusion (halamad) than there is in the premises (hamelamed).” This is a reasonable explanation, except that it seems here intended too generally; that is to say, it does not specify what is being “laid down,” whereas (in my view) it should say that this rule specifically concerns the inference of penalties or restrictive laws (as is true of the Mishnaic example where the principle is first formulated).

ET goes on to say that “this principle of dayo is from the Torah;” and it presents its source, just as the Gemara (Baba Qama 25a) does, as the episode of Miriam’s punishment (Numbers 12:14-15). According to the Gemara, even though the Torah only mentions seven days incarceration and makes no mention of fourteen days, the penalty of seven days for offending God was not directly inferred (by purely a fortiori argument) from the seven days for offending one’s father, but was inferred indirectly (by a crescendo argument and then by application of the dayo principle) from fourteen days for offending God. After which, ET merely discusses the basis of the “fourteen days” interpolation, rather than any other (e.g. infinitely larger) quantity.

But the truth is that this narrative is a fanciful retroactive projection by the Gemara (based on a baraita). The dayo principle historically first appears in the Mishna (Baba Qama 2:5) which is being commented on by the Gemara. Here, R. Tarfon tries to prove in two different ways that the penalty for damage by an ox on private property is full payment, and his colleagues the Sages reject his two proofs, saying both times: “dayo—it is enough.” The Gemara’s explanation of this dispute is quite contrived and far from credible, as I have shown earlier in the present volume. Moreover, the Gemara only takes into consideration the first argument of R. Tarfon in its narrative. ET does not show any awareness of the logical issues involved, but accepts the traditional treatment quite unthinkingly.

ET does thereafter mention the two arguments of R. Tarfon, but only in order to illustrate the two types of dayo application. This is of course an important distinction[10]. The first type, called “at the beginning of the law” (al techelet hadin), is illustrated by the Sages’ dayo to R. Tarfon’s second argument; while the second type, called “at the end of the law” (al sof hadin), is illustrated by the Sages’ dayo to R. Tarfon’s first argument.

Both of his arguments attempt to prove that damage by horn on private property entails full compensation; and in both instances, the Sages reject his conclusion and limit the penalty to half. R. Tarfon first argues from the facts that damage by tooth & foot in the public domain entails zero compensation, while on private property it entails full compensation, and that damage by horn in the public domain entails half compensation. Then, seeing his argument rejected, he argues from the facts that damage in the public domain by tooth & foot entails zero compensation, while by horn it entails half compensation, and that on private property damage by tooth & foot entails full compensation. Both attempts, though significantly different, are blocked by the Sages using the exact same words: dayo lavo min hadin lihiot kanidon.

ET’s explanation of the two terms seems to be as follows. The dayo objection to the second argument is characterized as “at the beginning of the law,” because it is applied to the major premise (which comes first), while the dayo objection to the first argument is characterized as “at the end of the law,” because it is applied to the minor premise (which comes last). The “beginning” type of dayo could not be applied to the first argument, because there the major premise does not mention horn damage; the “end” type of dayo could not be applied to the second argument, because there the minor premise (concerning tooth & foot) and the conclusion (concerning horn) have the same law (viz. full payment). This explanation is essentially correct in my view, though I would say more precisely that as regards the major premise, it is the generalization that precedes its formation which the dayo blocks; and as regards the minor premise, it is rather the formation of the additional premise of ‘proportionality’ that the dayo blocks.

After this, ET develops in some detail the notion, found in the same Gemara, of “nullification” of an a fortiori argument. It presents various views regarding when such nullification is possible or even necessary, and how this affects application of the dayo principle. ET also details various limitations imposed on the dayo principle in later rabbinic discourse. All this is presented with apposite examples. But the logical issues underlying such manipulations of human discourse are never raised. Thus, ET treatment of the subject-matter tends to remain on a rather superficial level, a mere presentation of traditional doctrines without any attempt to question them and dig deeper.

This, as already said, was to be expected from the sort of publication that ET is intended to be. Even so, the article can be faulted for lacking chronological information, i.e. for not tracing the historical development of ideas relating to the qal vachomer argument[11] and the dayo principle. Moreover, it fails to present certain ideas as clearly as it might and should have, preferring to faithfully reproduce the peculiar ways of expression found in rabbinic discourse.


Drawn from A Fortiori Logic (2013), chapter 32:1-3.



[1]              At: For more on this encyclopedia, see:

[2]              See at: The JE articles on Talmud and on Bible Exegesis: are also worth reading in this context.

[3]              Two remarks in this article are worth noting in passing. First, that “neither Hillel, Ishmael, nor Eliezer ben Jose ha-Gelili sought to give a complete enumeration of the rules of interpretation current in his day.” Second, that “The antiquity of the rules can be determined only by the dates of the authorities who quote them; in general, they can not safely be 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. The Talmud itself gives no information concerning the origin of the middot, although the Geonim regarded them as Sinaitic…. This can be correct only if the expression means nothing more than ‘very old’, as is the case in many Talmudic passages. It is decidedly erroneous, however, to take this expression literally and to consider the middot as traditional from the time of Moses on Sinai.”

[4]              More on this encyclopedia at: Note that a CD-rom version of it (presumably of the 1st ed.) exists.

[5]              Online at: The only difference I have spotted in the section about qal vachomer in the 2nd ed. is the added statement: “Not all of the thirteen principles are based on logic as is the kal va-ḥomer. Some are purely literary tools, while the gezerah shavah is only valid if received through the transmission of a rabbinic tradition.” This statement is interesting in that it explicitly characterizes qal vachomer as “based on logic.”

[6]              In a 1972 paper, “The Qal Va-Ḥomer Argument in the Old Testament” (Bulletin of the School of Oriental and African Studies, 35:221-227.  Cambridge University Press), Jacobs writes more accurately: “The argument runs: if A is so then B must surely be so; if the ‘minor’ has this or that property then the ‘major’ must undoubtedly have it.”

[7]              It is published by the Yad HaRav Herzog Torah Institute in Jerusalem. More information on this work is given at:

[8]              Maybe the libraries I looked in did not buy that volume; or maybe it has not been published yet; or maybe it has not been written yet – I do not know.

[9]              I do not know who its author(s) is (or are). I hired someone to translate it for me. Actually, he only translated the main text, and ignored the footnotes. He was a Hebrew speaker, but (to put it mildly) not very good at English.

[10]            To my knowledge ET does not state precisely who first made the distinction; this information is historically important and must be sought. I suspect offhand the discovery was made by some Tosafist, though I have not found out just who and in what commentary precisely.

[11]            Perhaps some of that may appear in the ET article on qal vachomer, if there already is or ever is one. I would be curious to see, in particular, if ET there mentions the important contribution of the Ramchal to the categorization and thence understanding of qal vachomer argument. See my essay on this topic in chapter 4.9 of the present volume.

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