Logic in the Torah

A Thematic Compilation by Avi Sion

7. Louis Jacobs’ Contribution


Rabbinic Thought in the Talmud (2005), by Louis Jacobs, contains an essay devoted to “The Qal Va-Homer Argument in the Old Testament”[1]. We shall here analyze the contributions made in this late essay of his (Jacobs z”l passed away in 2006). Having [before I came across this essay in 2013] read many of his works, and developed a true admiration for this scholar, I was very pleased to see more input from him. One thing that saddened me about it, though, was that Jacobs makes no mention in it of my contributions to the same subject in my Judaic Logic (1995), even though it was published about ten years before his essay. I am sure he would have been stimulated by it, had he read that work.


1.   Comparing enumerations

We shall start by comparing the list of Biblical qal vachomer drawn up by Jacobs in his latest essay with the list in my Judaic Logic and later findings[2]. I feel obliged to engage in this accounting, so as to give everyone his due. If we merge the two lists together, we obtain a grand total of at least 46 instances [all listed and analyzed in chapter 7 of the present volume]. Jacobs’ list is apparently based, largely if not entirely, on an early 19th century work by Wolf Einhorn of Grodno[3], which I have not seen, but which reportedly contains 40 instances[4]. Jacobs presumably rejected some of the latter, since he only lists a total of 35 instances; but he does not say which instances he rejected or even just why he did so[5]. Nor does Jacobs tell us whether any of the instances he lists are his own findings, or all are included in Einhorn’s list.[6]


We both have


I have, he lacks


He has, I lack



Jacobs and I have 24 instances in common. These of course include the famous ten instances given in Genesis Rabbah 92:7; namely, Genesis 44:8, Exodus 6:12, Numbers 12:14-15, Deuteronomy 31:27, 1 Samuel 23:3, Jeremiah 12:5 (2 cases), Ezekiel 15:5, Proverbs 11:31, and Esther, 9:12. Interestingly, probably because the Genesis 44:8 instance is spelled out first and then R. Ishmael says: “This is one of the ten instances of qal va-homer in the Torah,” Jacobs suggests that only the first of these ten instances was originally in the Midrash, saying: “In what is in all probability an editorial, or even later, gloss, the Midrash gives the other nine” after R. Ishmael’s remark[7].

Jacobs uncovers another two instances mentioned in the same Midrash but not listed among the ten, namely: Genesis 4:24 (“If Cain shall be avenged sevenfold, truly Lamekh seventy and sevenfold.”), which I already knew of thanks to Rashi; and Genesis 17:20-21, which I did not know about, and so have included under the category of “He has, I lack” further down[8]. It is interesting that the Midrash lists only ten instances of a fortiori argument in a later page, even though the very same volume mentions another two earlier on! Such inconsistency certainly suggests that there was successive editing of the work.[9]

The failure of the Midrash to list its own 12 instances at once is otherwise inexplicable – unless its author used some unspecified selection criteria. Probably, the Gen. 4:24 case was left out as an “evil” case and Gen. 17:20-21 was left out as an “implicit” case[10]; another possible explanation is that there was later addition of these two cases. The question posed here is of course part of a larger one, which I already asked in my Judaic Logic: how is it that the author of the Midrash, who presumably knew the Tanakh by heart and was not half asleep, missed out on the numerous other a fortiori arguments that we have lately found there? This is a mystery. Jacobs acknowledges this mystery, saying: “the commentators to the Midrash and other scholars are puzzled by R. Ishmael’s reference to only ten Scriptural cases.”[11]

Note also in this context that I do not consider Esther 9:12, which the Midrash list includes, as a credible, sufficiently explicit instance of a fortiori argument. This example, which reads: “The Jews have slain and destroyed five hundred men in Shushan the castle, and the ten sons of Haman; what (meh) then have they done in the rest of the king's provinces!”[12] uses language that is to my knowledge nowhere else connected with a fortiori argument. The interpretation of the word meh as meaning “how much more” therefore seems a bit forced to me. I would at best consider this as an “implicit” a fortiori argument, in the sense of one read into the text (more on such arguments later), since no number greater than 500 is actually specified in the conclusion (which has the form of a question). Nevertheless, because this argument is so universally accepted as a fortiori, just because it is one of the main ten listed in the Midrash, I do exceptionally count it as an explicit a fortiori.

The remaining 13 instances we have in common are: 1 Samuel 14:29-30, 2 Samuel 12:18, 2 Samuel 16:11, 1 Kings 8:27, 2 Kings 10:4, Jonah 4:10-11, Proverbs 15:11, Proverbs 19:7, Proverbs 19:10, Proverbs 21:27, Job 4:18-19, Job 15:15-16, Job 25:5-6. That these instances were found independently by two or more parties is of course no surprise. Anyone looking out for arguments of a certain kind, who has some idea as to how they go about, will notice them as he reads through the Bible. In my case, the research was more systematic. I looked at the wording of known instances of a fortiori discourse, and then sought other Biblical passages with the same wording using a concordance.

As regards Jonah 4:10-11, where God says: “Thou hast had pity on the gourd, for which thou hast not laboured, neither madest it grow, which came up in a night, and perished in a night; and should not I (vaani lo) have pity on Nineveh, that great city, wherein are more than sixscore thousand persons that cannot discern between their right hand and their left hand, and also much cattle?” Although this case lacks distinctive a fortiori language, it clearly has a fortiori intent. I did not have this case in the early editions of my Judaic Logic, but after finding it by chance added it on (as a final footnote to chapter 6) as of June 1998.

Because of my use of a concordance, no doubt, I found numerous cases apparently previously unknown. The 14 instances I have but Jacobs lacks are: 1 Samuel 17:37, 1 Samuel 21:6, 2 Samuel 4:10-11, 2 Kings 5:13, 2 Kings 18:23-24 and its repetition in Isaiah 36:8-9, Ezekiel 14:13-21, Psalms 78:20, Psalms 94:9-10 (3 instances), Daniel 2:9[13], 2 Chronicles 6:18[14], 2 Chronicles 32:15. Note that since Jacobs only mentions 35 cases and Einhorn enumerates 40, it may well be for all I know that some of these 14 cases were known to the latter and rejected by the former. But it seems unlikely – why would Jacobs reject any of these cases, which are all pretty clear and explicit?

Note that 1 Samuel 17:37 was publicized and analyzed in Addendum 4 of my Judaic Logic (as of 2001); I did not myself discover it, but had my attention drawn to it by a reader named Mark Leroux (from South Africa). Ezekiel 14:13-21 was not mentioned in my Judaic Logic: I only recently discovered it (in 2012). It may be paraphrased as saying: “More spiritual credit is required to stop more numerous negative Divine decrees than fewer ones; therefore, if holy men, like Noah, Daniel or Job, lack sufficient spiritual credit to prevent the execution of the four separate decrees of the sword, famine, evil beasts, and pestilence, then they lack enough credit to stop all four of these decrees together”[15]. The latter case was not easy to spot, because it is spread out over several verses; what helped me find it was the key phrase “How much more” (af ki, in Heb.) used in it.

As regards 2 Kings 18:23-24 and its word-for-word repetition in Isaiah 36:8-9[16], they are mentioned in my Judaic Logic, but I had considerable skepticism concerning them and so did not at the time count them as sure cases[17]. However, reviewing the argument involved at a later date, its a fortiori intent became clearer to me. Rab-shakeh (emissary of the king of Assyria) says: “Now therefore, I pray thee, make a wager with my master the king of Assyria, and I will give thee two thousand horses, if thou be able on thy part to set riders upon them. How then (ve-ekh) canst thou turn away the face of one captain, even of the least of my masters servants? and yet thou puttest thy trust on Egypt for chariots and for horsemen!” The Assyrian spokesman thinks that king Hezekiah is hoping for Egyptian chariots and horsemen; so he says to him: ‘even if your force was increased by 2000 horses (which I am willing to give to you), you could not find warriors to ride them and therefore could not hope to defeat the invaders; all the more so, without such additional force, you cannot hope to defeat the invading force, even the least fraction of it’. I do, therefore, henceforth class these two identical cases as surely a fortiori.


2.   Cases new to me

Let us now look at the cases Jacobs has but I lack. Since I have never before analyzed these, I will do so now. I will first list the 8 instances I accept as explicit a fortiori argument, and thereafter deal with the instances he mentions that I consider as only at best implicit.

Judges 14:16. “And he (Samson) said unto her (his wife): Behold (hine), I have not told it my father nor my mother, and (ve) shall I tell thee?” This is a clear case of qal vachomer, using keywords (hine/ve) found elsewhere. So much so that I am surprised I missed it! The reason I did so was probably that the word hine is very often used in contexts where there is no a fortiori intent, so I did not closely examine every occurrence of it.

Isaiah 66:1. “The heaven is My throne, and the earth is My footstool; where (eizeh) is the house that ye may build unto Me? And where (eizeh) is the place that may be My resting-place?” This passage obviously echoes the message of 1 Kings 8:27 and 2 Chronicles 6:18, though the wording differs somewhat; viz. that God is too great to be housed in an earthly abode. I perhaps missed it because the Hebrew operator used in it, eizeh (זֶה-אֵי), meaning what? (or which? rather than where? as this JPS translation has it) does not to my knowledge occur in other a fortiori contexts. Nevertheless, it is quite credible as a case of a fortiori discourse.

Jeremiah 25:29. “For, lo (hine), I begin to bring evil on the city whereupon My name is called, and (ve) should ye be utterly unpunished? Ye shall not be unpunished; for I will call for a sword upon all the inhabitants of the earth.” Here again, we have the keywords hine/ve, sometimes indicative of qal vachomer intent. The a fortiori argument is that if God is willing to bring evil on the city whereupon His name is called, he is certainly willing to utterly punish less important kingdoms.

Jeremiah 45:4-5. “Behold (hine), that which I have built will I break down, and that which I have planted I will pluck up; and this in the whole land. And (ve) seekest thou great things for thyself? seek them not; for, behold, I will bring evil upon all flesh.” Here again, we find the keywords hine/ve used. The a fortiori argument is that if God is willing to break down what He has built, etc., he is certainly willing to prevent the success of endeavors by Baruch ben Neriah.

Jeremiah 49:12. “Behold (hine), they to whom it pertained not to drink of the cup shall assuredly drink; and (ve) art thou he that shall altogether go unpunished? thou shalt not go unpunished, but thou shalt surely drink.” Here again, note use of the keywords hine/ve. The a fortiori argument is that if God is willing to punish those who do not deserve it, he is certainly willing to punish those who do. Note the similar form of the three a fortiori arguments of Jeremiah mentioned here – it is indicative of their common authorship.

Ezekiel 33:24. “They that inhabit those waste places in the land of Israel speak, saying: Abraham was one, and he inherited the land; but (ve) we are many; the land is given us for inheritance.” In this case, there is no keyword indicative of a fortiori intent; but that happens. There clearly is an a fortiori intent, even if the argument is logically rather weak. Why should ‘many’ be more assured of inheritance than just ‘one’? Indeed, this is precisely what the next two verses (25-26), which are spoken by God, contend – that it is not quantity but moral quality that determines ownership of that land:

“Ye eat with the blood, and lift up your eyes unto your idols, and shed blood; and (ve) shall ye possess the land? Ye stand upon your sword, ye work abomination, and ye defile every one his neighbour's wife; and (ve) shall ye possess the land?”

This case is very interesting, because it provides a Biblical example of rebuttal of a weak a fortiori argument by attacking the major premise. Note well that God’s reply is not itself an a fortiori argument, but an objection to such argument. This form of counter-argument is later practiced routinely by the rabbis of the Talmud, under the heading of pirka (in Aramaic) or teshuvah (in Hebrew). No doubt there are many such counter-arguments in the Bible, which we should henceforth lookout for and register. I have not looked for or noticed such rebuttals in the past.

Job 9:13-14. “God will not withdraw His anger; the helpers of Rahab did stoop under Him. How much less (af ki) shall I answer Him, and choose out my arguments with Him?” Job considers himself as less worthy than “the helpers of Rahab,” therefore he is more than them bound to incline before God’s judgment. This is a clear case of qal vachomer, using keywords (af ki) found elsewhere. I am very surprised I did not spot it!

Nehemiah 13:26-27. “Did not Solomon king of Israel sin by these things? yet among many nations was there no king like him, and he was beloved of his God, and God made him king over all Israel; nevertheless even (gam) him did the foreign women cause to sin. Shall we then (ve) hearken unto you to do all this great evil, to break faith with our God in marrying foreign women?” The gist of the argument is: If even Solomon could be caused to sin by foreign women, will not the lesser men of today be likewise caused to sin? This is clearly a fortiori argument, even if the operators (gam, ve) are rarely used.

We have thus drawn eight new, credible and pretty explicit, a fortiori arguments from Jacobs’ (or Einhorn’s) list. Six use known operators: four use hine/ve, one uses af ki, one uses gam/ve; one involves only the ubiquitous conjunction ve; and one involves the previously unheard of operator eizeh.


Jacobs lists in his paper another three Biblical passages that in his opinion involve a fortiori arguments. The first of these, which he has found mentioned in Genesis Rabbah, is:

Genesis 17:20-21. “And as for Ishmael, I have heard thee; behold, I have blessed him, and will make him fruitful, and will multiply him exceedingly; twelve princes shall he beget, and I will make him a great nation. But (ve) My covenant will I establish with Isaac, whom Sarah shall bear unto thee at this set time in the next year.” Jacobs casts this in a fortiori form as follows: “If Ishmael, the son of the handmaiden will be blessed in this way then all the more will Isaac, the son of Sarah, be blessed.”

Although I can see that such an a fortiori argument can certainly be read into the text, I do not agree that it is the only way the passage can be read. God may simply be saying to Abraham: I have blessed Ishmael thus and thus, but My covenant I will not establish with Ishmael but only with Isaac. The emphasis in this alternative reading is clearly different, and not a fortiori. Note moreover, that whereas Jacobs’ a fortiori interpretation makes no mention of the covenant, it is central to my reading. For this reason, I would say that the proposed a fortiori argument qualifies as implicit rather than explicit. This is using the word “implicit” in the sense Jacobs uses it when presenting the next two cases. These instances are mentioned in the so-called Baraita of R. Eliezer b. R. Jose the Galilean:

Psalms 15:4. “He that sweareth to his own hurt, and changeth not.” This verse could be read, as Jacobs has it, as saying that if he (i.e. the good man that the psalmist is describing) doesn’t go back on his word when it is hurtful not to, then he certainly won’t do so when it is for his good. But we could simply read this as saying that when the good man utters an oath, he sticks to it no matter how strong the pressure to break it increases. There is no necessity for the a fortiori interpretation; it is read into the text, rather than drawn from it. There is no call for it, because if the man utters an oath which causes him pleasure rather than pain, he obviously will be under no pressure to break it. This is not a conclusion obtained by a fortiori inference, but something everyone can confirm by introspection. So, really, this a fortiori reading is rather artificial. No doubt, it was concocted simply because its author needed some examples for teaching purposes.

Psalms 15:5. “Nor taketh a bribe concerning (al) the innocent.” Two translations of this verse are possible, the Hebrew word al (meaning: on) being a bit equivocal (even in English).

Let us first consider the translation used by Jacobs: “Nor taketh a bribe to side with (al) the innocent.” This verse can be read, as Jacobs has it, as saying that if he (i.e. the good man) won’t take bribe to rule in favor of an innocent person, then he certainly won’t do so regarding a guilty party. But we could simply read this as saying that the good man would not take a bribe even if he was being bribed to judge a matter as he would without being bribed, i.e. in favor of the innocent. It is true that, in this case (in contrast to the previous one), the a fortiori argument just indicated can additionally be constructed, and it makes a valuable prediction. So, here we are justified in referring to an “implicit” a fortiori argument. It is not explicit, because the text can be read in a first phase without an a fortiori thought. But it is implicit, in that, if we dig deeper into it, we can indeed use it to make a useful a fortiori inference.

Let us now consider the alternative translation of the same verse given in the JPS 1917 edition: “Nor taketh a bribe against (al) the innocent.” We can interpret this translation like the previous one, albeit with an interpolation: if he (i.e. the good man) won’t take a bribe not to rule against an innocent person, then he certainly won’t do so regarding a guilty party; and we can say more about it as before. However, a quite different, more literal approach to this translation is also possible: we could simply read it as saying that the good man would not take a bribe against an innocent person, i.e. in favor of a guilty one. We might now attempt the following a fortiori argument: if he (i.e. the good man) won’t take a bribe to rule against an innocent person, then he certainly won’t do so regarding a guilty party. But this argument is a non sequitur, since someone might well refuse to rule against the innocent for a bribe, but accept to rule against the guilty for a bribe, thinking that since he intended to rule against the guilty anyway, no harm is done by taking a bribe for it. Therefore, in this translation and reading there is no a fortiori adjunct, whether explicit or implicit.

Thus, if we qualify as “explicitly” and “implicitly” a fortiori argument, respectively, “a text that can only be read as a fortiori” and “a text that can be read as a fortiori but can also readily be read otherwise (i.e. more simply)” – we would have to say that Gen. 17:20-21 is implicit, that Ps. 15:4 is not a fortiori at all, and that Ps. 15:5 is implicit if read one way and not a fortiori at all if read another way. This is contrary to Jacobs, or rather to the rabbinic sources he refers to, who read these arguments as respectively explicit, implicit and implicit. As for the two examples of explicit a fortiori, which Jacobs mentions as given in the said Baraita, namely Jeremiah 12:5 and Esther 9:12 – we would for our part agree that the Jeremiah instances are explicit, but insist (for reasons already put forward) that the Esther example is (if at all a fortiori) at best implicit[18].

Clearly, we have here a serious divergence of views. I have to say that I have in the past, until I read Jacobs’ present article, assumed that the distinction made by Eliezer ben Jose, between a fortiori arguments that are meforash (explicit) and those that are satum (implicit), was referring to how much of the argument’s elements are laid out in the text at hand. If the a fortiori premises and conclusions, with all their terms or theses, are all fully laid out in the given text – then that text is a fully explicit a fortiori argument. If one premise or the conclusion are missing, or some of the terms or theses involved are missing – then that text is partly implicit to varying degrees. By that standard, of course, most if not all arguments in Scripture are partly implicit.

But Jacobs’ article suggests that the rabbis’ “explicit” means sufficiently explicit that there can be no interpretation other than an a fortiori one, while their “implicit” means not so explicit that there can be no interpretation other than an a fortiori one. At least, this is how I now understand these expressions. It could be that the rabbis do not draw the lines so clearly, and understand them sometimes this way, sometimes that way. In any case, to conclude this discussion, the three arguments above listed are – as far as I am concerned, in the light of the above analyses – not to be listed among the explicit a fortiori arguments. They are possible interpretations of the texts, or artificially read into the texts, but the texts in themselves allow of readings that are not a fortiori.

Why is this issue important? Because it relates to attribution and dating. When a Biblical text clearly has an a fortiori intent, we may regard it as an explicit instance of Biblical a fortiori argument. If, however, the a fortiori intent of the Biblical text is not so obvious, and has only been brought out later in time by a rabbinical or other commentator, we must count it as only implicitly a fortiori, and attribute the a fortiori argument as such to the historically later commentator. It is not an issue of who discovers the a fortiori argument, note well, but of whether or not the author of that passage of the Bible worded it with a manifest a fortiori intent. If the a fortiori argument has later been read into the text, rather than found in it, then its author is really the person who proposed the interpretation. This is commonsense hermeneutics.

Of course, the rabbis consider that whatever they read into a Biblical text was indeed intended by that text, since God – its ultimate author – is all-knowing. But, even granting their premises, their conclusion does not follow. That is to say, God may well have foreseen the rabbinical interpretation, but that does not make it any the less an interpretation. Such foreknowledge is not indicative of an actual or direct intent, but only at best of a potential or indirect one. The explicit text constitutes the primary message; other information that can eventually be derived from that message is not strictly part of it, but at best an implicit adjunct to it. Sometimes, of course, it is highly debatable that the original text allows for a certain interpretation; and in such case, the interpretation must be characterized as forced rather than implicit[19]. It would be irrational to accept unquestioningly whatever the rabbis claim; they are, after all, just human beings.


3.   Three rejects

Jacobs additionally mentions (in an endnote) three Biblical passages presented as a fortiori arguments by Chaim Hirschensohn[20]. Jacobs rejects these examples as “extremely doubtful,” and I incline to agree with him. To my mind, they are at best implicit a fortiori arguments, but certainly not explicit ones. The first two texts in question are the following:

Genesis 3:22. “Behold (hen), the man is become as one of us, to know good and evil; and now (ve-atah), lest he put forth his hand, and take also of the tree of life, and eat, and live for ever. Therefore (ve), [He] sent him forth from the garden of Eden, to till the ground from whence he was taken.”

Genesis 11:6-7. “Behold (hen), they are one people, and they have all one language; and this is what they begin to do; and now (ve-atah) nothing will be withholden from them, which they purpose to do. Come (habah), let us go down, and there confound their language, that they may not understand one another's speech.”

It is interesting that the two verses, though chapters apart, use the same language (hen/ve-atah) and have similar form. Also note that in both cases, one of the operators used (hen) is sometimes indicative of a fortiori discourse, and the argument is concerned with increasing magnitudes of something. The argument involved can be paraphrased as follows: This event is bad enough, therefore to avoid an even worse event we had better take certain precautions. This is an interesting form of reasoning in itself, but it is clearly causal and ethical, rather than a fortiori as Hirschensohn reportedly claims.

We could admittedly formulate an a fortiori argument from it as follows: P is worse (R) than Q, and Q is bad (R) enough to be combated (S); therefore, P is bad (R) enough to be combated (S). But where in the text does it say that Q was fought against? It only says that P is to be fought against. So, this a fortiori argument, if at all implied, must be characterized as implicit. It is anyway not the essence of the explicit discourse facing us, which has it that a minor problem (the “bad enough” clause) could well eventually develop into a major problem (the “even worse” clause), and for that reason some preemptive action against the latter is called for before it happens. The said a fortiori argument is perhaps implied by the text, but the text evidently tries to communicate considerably more than just that.

The third text is: Genesis 17:17. “Then Abraham fell upon his face, and laughed, and said in his heart: Shall a child be born unto him that is a hundred years old? and shall Sarah, that is ninety years old, bear?” It is difficult to perceive the a fortiori argument Hirschensohn had in mind here. Perhaps his thought was that it is unlikely enough for a hundred year old man to have a child, and therefore even more unlikely for a ninety year old woman to do so. But frankly, was that Abraham’s thought? No, he was simply saying that it is unlikely for both a hundred year old man and a ninety year old woman to have a child. It is a statement, not a process of inference.

Certainly, in this case, the literal reading is not a fortiori, so that if an a fortiori argument be read into the text, it is at best implicit. But moreover, the a fortiori reading seems rather forced. Since we can fully understand the text without it, it serves no purpose other than to inflate the list of Biblical a fortiori arguments. Therefore, I would not even include this case as an example of implicit a fortiori. Thus, while the first two examples could conceivably qualify as involving an a fortiori discourse implicitly, the third is much less credible. In any event, none of these three cases is explicit.


4.   General observations

Let us now take a closer look at various general observations in Jacobs’ essay. To begin with, it is evident that even in 2005 he had not yet grasped the actual form of a fortiori argument, since he here still describes it very superficially as “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.” This is what he has in the past called ‘simple’ a fortiori argument. He still, note also, fails to detect the use of what he has called ‘complex’ a fortiori argument in the Bible. He rightly remarks that the Rabbis learnt this form of inference from its occurrences in the Bible itself, and then used it “as one of their hermeneutical principles by means of which they expand and elaborate on the Biblical teachings.” And this fact stimulates his present research into the actual examples of the argument in the Bible.

However, it is very surprising to see Jacobs assert (in an endnote) that “There does not appear to be, in fact, any real parallel to the qal va-homer in Greek thought.” This is, as demonstrated in the present volume [AFL], quite off the mark – a fortiori argument is quite present, and consciously so, in Greek (and then Roman) literature, even if not as frequently as in rabbinical literature. He is here going further than he has in the past, where he only (and rightly) contended, against the apparent claims of Adolf Schwarz, that the identification of this form of argument with Aristotelian syllogism is “untenable.” That a fortiori argument is not syllogistic does not imply that it was not used by the Greeks! The latter did not only think syllogistically, any more than the rabbis only thought by means of a fortiori argument. Moreover, to admit that the Greeks used a fortiori argument is of course not the same as to claim that the rabbis learnt it from them. So, Jacobs’ position in this matter, even if expressed offhandedly, is very surprising.

It is a pity that Jacobs did not push his analysis of the a fortiori arguments he lists more deeply. While he acknowledges the rabbis’ debt to the Biblical occurrences of qal vachomer, he does not sufficiently examine how they actually interpreted those arguments. Notably, while he reads the qal vachomer in Numbers 12:14 correctly, saying: “if when [Miriam’s] human father showed his disapproval of her actions she would hide herself in shame for seven days then when the Lord shows His disapproval all the more should she be shut away for seven days,” he does not look further into the matter and discover the significantly different interpretation given by the Gemara in Baba Qama 25a, and the Pandora’s Box of interesting problems (and opportunities) that the latter creates.

Nevertheless, Jacobs makes some valuable general observations:

“From all that has been said it is surely well established that the argument from the minor to the major is used frequently throughout the Old Testament. Its use is not limited to any single phase in Israel’s history but, it would appear, was employed in all periods. Neither is the usage confined to any single book of the Old Testament nor to any particular document, stratum, and trend… Moreover, as in many of the examples quoted, its use is generally of a formal nature, beginning with hien or hinneh and concluding with ‘eykh or ‘aph.”

I came to similar conclusion in my Judaic Logic. But Jacobs takes the reflection further, raising “important questions, hitherto barely considered by Old Testament scholarship, regarding the use of rhetoric in ancient Israel.” He cites O. Eissfeldt[21], who suggested that there were men and women “specially skilled in speech,” using argumentative techniques acquired through “tradition and ‘training’,” resorting to “certain fixed forms for speech” and rhetorical devices such as “first obtaining from the person addressed an admission which does not appear to be relevant to the matter in hand,” which “then compels him to grant the request which is really involved.” Jacobs concurs, in view of the evidence provided by his listing of Biblical qal vachomer.

Such tradition and training is, of course, evident in the rabbinic period, Jacobs adds, when “formal argument was consciously and extensively cultivated” and “there are certain stereotyped rules” of argumentation. He then asks: “Was there anything like this in the Old Testament period?” and replies: “there seems to be no doubt that the answer should be in the affirmative.” He admits, however, that “it is hard to find anything like an explicit reference anywhere in the Old Testament to schools in which rhetoric was taught.” He could have buttressed his case by adducing that the rabbis did and do believe that such schools (yeshivot) existed throughout the past. The patriarch Jacob is said to have studied in the tents of Shem and Eber (Genesis Rabbah 63:10); king David is said to have studied with his counselor Ahithophel (Pirqe Avot 6:2); and so on.

In my view, to be honest, such claims are largely anachronistic, projecting later mores onto earlier times. It is not inconceivable that there were, very early on, educational institutions of sorts that organized common study of and reflection on knowledge inherited from the past. The issue is, as of when such institutions can be credibly claimed, and what it is that was studied in them. While transmission of knowledge and skills by village adults and elders to children and youth can be classified under the heading of education and is as old as mankind, it is less certain as of when in history the formal study of Torah and related argumentative skills began in Israel. I would say it developed apace in the period after the Return from Babylon after the First Exile, i.e. the formative period of the rabbinical doctrine and class. This is suggested, for instance, in the Mishnaic Pirqe Avot, which refers (1:1) to the Knesset Hagedolah (the Great Assembly).

This hypothesis seems most likely, in view of what was happening at the same time in other nations near and far. What is evident when we study world history is that cultural developments tend to be (increasingly over time) worldwide rather than local. Many major developments occurred as of the middle of the first millennium BCE, as if a new phase in human intellectual evolution was taking place. Suddenly, it seems, existing civilizations burst with newfound energy, producing religious and philosophical thoughts more sophisticated (at least on the surface) than ever before. Though scattered, they awoke simultaneously, in various directions, but also somewhat comparably.

In India, the ancient Vedic religion began its transformation into Hinduism, and Buddhism was founded. In China, Confucianism and Taoism emerged. In Greece, philosophy flowered in earnest, with the advent of Socrates, Plato, Aristotle, and many others. In Israel, Judaism came increasingly under the authority of Torah scholars[22]. This ‘rabbinic’ Judaism was apparently planted at the beginning of the Second Temple period and gradually grew and took shape in the following generations, till it fully flowered in the Mishna (which then stimulated the Gemara and subsequent rabbinic works). The intellectual growth in Israel, involving increasingly legalistic thinking, and therefore to some extent logical reflection, was thus rather typical of that epoch, and can only with difficulty be projected backwards into earlier ones.

Be that as it may, Jacobs ends his reflections with an interesting suggestion, also drawn from Eissfeldt, that the Hebrew root dbr, used to refer to ‘speech’, may in fact often be used with the intention to mean ‘argument’. An example he gives is Gen. 44:18, where Judah begins his plea before Joseph by saying: “O my lord, let thy servant, I pray thee, speak a word in my lord’s ears.” Jacobs comments: “Since the expression yedabber dabhar is used, should it be translated as ‘present an argument’?” Similarly, in other passages, ‘speak rightly’ might be taken to mean ‘argue convincingly’, ‘these are the words’ might be taken to mean ‘these are the arguments’, and so forth. This insight seems credible to me. All this goes to show in what directions and how far Jacobs’ research into Biblical use of qal vachomer drove his reflections.


Drawn from.A Fortiori Logic (2013), chapter 16:4.



[1]           See chapter 12, pp. 109-116.

[2]           Namely, 1 Samuel 17:37, the case given in Addendum 4, which was pointed out to me orally by Mark Leroux (from South Africa, a colleague at an office where I worked) in 2001. Before that (in 1998), I found a further case, namely: Jonah 4:10-11, by happenstance. More recently (in Aug. 2012), I found yet another case, Ezekiel 14:13-21, by means of a search for key phrases at Incidentally, the latter search only yielded a total of 19 cases: 13 cases with ‘how much more and 6 cases with ‘how much less’; there were no cases with the key phrases ‘all the more/less’ and ‘(how/so) much the more/less’.

[3]           Zeev Wolf Einhorn (Maharzav), Grodno, Lithuania, 1813- 1862. Sefer Midrash Tannaim, 1838.

[4]           Jacobs adds that “other commentators [have] come up with similar results” – but he does not say which commentators, nor what these results were nor compare them.

[5]           He does tell us that some of the instances proposed by various researchers “must be rejected as far-fetched and dubious,” but he unfortunately does not perform his triage in public, and all too confidently declares that his list “contains all the definite references.”

[6]           Goltzberg, in his 2010 essay “The A Fortiori Argument In The Talmud” [which I review in AFL], mentions “the forgotten a fortiori arguments,” without however saying how many he thinks there are or listing them. Apparently, he draws this information from Moshe Koppel’s Meta-Halakha. Logic, Intuition And The Unfolding Of Jewish Law (Northvale, NJ, Jason Aronson, 1987). Not having seen the latter work, I cannot say if it is any more informative than that. Note that Jacobs does not mention Koppel’s book, which is earlier than mine, either.

[7]           It is interesting that R. Ishmael does not here rather mention Num. 12:14-15, which plays such important role in the Gemara explication of Mishna Baba Qama 2:5.

[8]           But only, as it turns out as an implicit case; not as an explicit case.

[9]           Jacob’s comment is based on a note by Theodor-Albeck, the editor of the Genesis Rabbah edition that he refers to. In that edition, 92:7 is on pp. 1145-6, and 4:24 and 17:20-21 are on p. 225. Jacobs also informs us (in endnotes, p. 116) that Yalkut, 1 Sam. 132 “refers to ten but lists only nine” (he does not say which one is left out); and that Gen. 4:24 is also mentioned as a qal vachomer in Avot de-Rabbi Nathan (version B) 44 and in JT Sanh. 10:1 (27d).

[10]          Wiseman claims “evil” qal vachomer to be a rabbinical category, pp. 174-6. As regards the “implicit” case, see further on.

[11]          In this context Jacobs mentions (in an endnote) A. Schwarz, Ch. Hirschensohn, Jofe Ashkenazi (in Yephe toar) and H. Strack.

[12]          This quotation, as indeed all those from the Bible in the present section, is taken from the Mechon Mamre website at, which is based on the 1917 edition of the Jewish Publication Society. Note that the word “then” is an interpolation by the translator; it is not found in the original Hebrew. Likewise, the exclamation mark is an addition; a question mark may have been more appropriate. Obviously, the translator was influenced by the tradition that this statement is a fortiori.

[13]          As I explain in my Judaic Logic (6:3), although the given text of Daniel 2:9 is not directly a fortiori argument, since it consists of an order by the king coupled with a reflection as to its utility, the reasoning used by the king is indubitably a fortiori argument, so much so that it can be counted as effectively explicitly so.

[14]          This is a repetition of 1 Kings 8:27, which Jacobs does have.

[15]          The original wording of this argument is given in Appendix 1.

[16]          Such copy-and-paste repetition is surely useful for purposes of “higher criticism.”

[17]          In chapter 6, where I write: “Note also: 2 Kings 18:23-24, and its repetition in Isaiah 36:8-9, might at first glance be construed as a fortiori in style. But try as I might, I have not been able to make a clear a fortiori argument out of it, however artificial and logically improbable.”

[18]          Although, to repeat, I am still counting the Esther example as explicit, so as not to go against this too well-established tradition.

[19]          An important case in point that we have seen is the Gemara (Baba Qama 25a) interpretation of Numbers 12:14-15.

[20]          Israel, 1857 – 1935. The work cited is Berure Ha-Middot (Jerusalem, 1929), pp. 40-45.

[21]          In The Old Testament: An Introduction (Oxford, 1965), pp. 12-15.

[22]          Perhaps starting with “Also we made ordinances for us,” in Nehemiah 10:33. The Hebrew word used is mitsvot, which is usually translated as commandments. The laws gradually enacted by Jewish lawmakers were, it is worth noting, distinctively based on Torah law. They were not arbitrary, but guided and circumscribed by the strong moral standards already instituted by that document. The ‘legalism’ involved here is of a very different sort than that found in the same period of history in, say, China.

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