Logic in the Torah

A Thematic Compilation by Avi Sion

5. The Language of Biblical A Fortiori


In this essay, my purpose is to analyze the language actually used in Biblical a fortiori statements. An empirical study, without preconceptions.



A Biblical a fortiori argument, as we saw, usually consists of two more or less explicit sentences, one of which is the minor premise and the other the conclusion; the major premise is always more or less tacit. The said premise and the conclusion may be, one or both of them, categorical or conditional in form, and may be expressed in full or be in part merely implied.

The premise and conclusion are usually, though not always, signaled by words which serve as “if” and “then” operators, respectively. However, such keywords sometimes concern, not the argument as such, as a whole, but instead belong within clauses subsidiary to the argument. Our job here, therefore, is to distinguish and avoid confusion between the if/then operators (if any) which frame the argument’s antecedent (premise) and consequent (conclusion), from the operators (if any) which play a role as part of these sentences. [1]


2.In Torah books


Genesis 4:24. Lemekh ben Methushael:

“If (ki): Cain shall be avenged sevenfold,

then (ve): Lemekh [shall be avenged] seventy and seven-fold.”

Rashi’s reading: If the punishment on Cain, who willfully murdered, was delayed seven generations, surely my [Lemekh’s] punishment will be deferred for many times seven, seeing that I slew unintentionally.

The if/then operators of this argument are ki/ve. I must say that without Rashi’s commentary, this verse would seem pretty obscure, to me at least. This perhaps attests to its true antiquity. In any case, we may accept Rashi’s interpretation of the sentence as an a fortiori argument. The story-context he adduces from tradition is that Lemekh slew Cain accidentally while hunting for deer.

Note that this a fortiori argument is not perfectly constructed; although the movement from willful to unintentional (the tacit major premise) is indeed a fortiori, the transition from seven (in the minor premise) to seventy-seven (in the conclusion) does not obey the “dayo” (sufficiency) rule: there is an extrapolation involved, which may have an inductive justification, but which is weak from the deductive point of view. However, although this is a Biblical passage, it has no Halakhic authority which might support non-dayo reasoning, being the private pronouncement of Lemekh, and not a statement of Divine or prophetic origin.


Genesis 44:8. Joseph’s Brothers:

“Behold (hen): the money, which we found in our sacks’ mouths, we brought back unto thee out of the land of Canaan;

then (ve): how (ekh) should we steal out of thy lord’s house silver or gold?”

Here, the if/then operators are hen/ve. Hen (behold) signals a presentation of evidence; while ve (and) presents the inference to be drawn from it. The expression ekh (how) is part of the conclusion, serving rhetorically to deny the brothers’ ability to steal; it literally means: given the evidence, ‘how could anyone logically uphold’ such a claim (that the brothers would steal). Thus, ekh signifies necessity of the denial of a claim: it has a modal function; and so we could regard it as qualifying the overall relation between premise(s) and conclusion, instead of as merely an internal qualifier of the conclusion.


Exodus 6:12. Moses:

“Behold (hen): the Children of Israel have not hearkened unto me;

then (ve): how (ekh) shall Pharaoh hear me?”

Same language as in the previous case.




Numbers 12:14. God:

“[Granting that:] if (ve) her father had but spit in her face, should she not (halo) hide in shame seven days?

[Similarly, since God is angry with her,] let her be shut up without the camp seven days.”

In this case, the argument as a whole, although clearly a fortiori in intent, is expressed without explicit if/then operators (this is not disturbing, but a common manner of speaking in all languages). The stated premise is a conditional proposition, with ve as its if-operator but without explicit then-operator; the expression halo serves a rhetorical purpose within the consequent. The conclusion (as seen in our earlier technical analysis), though stated as a categorical proposition, should be read as a conditional one devoid of explicit operators; its tacit antecedent clause being the fact of Divine disapproval, while its consequent is similar to the premise’s.

With regard to halo (is it not that): it expresses in the speaker and causes in the hearer a certain turn of mind, which is not peculiarly Hebrew or oriental, but is equally to be found in western formal logic. Its role is to remind us of the following formality: ‘if X, then Y’ means that X cannot but exist with Y, and not merely that X and Y happen to have occurred together. Thus, halo, like ekh, is a modality, though of opposite polarity; while ekh means ‘must deny’ (=cannot affirm), halo means ‘cannot but affirm’ (=must affirm); and, in the last analysis, such modality may just as well be viewed as concerning the whole antecedent-consequent relation concerned, rather than merely the consequent part of it.




Deuteronomy 31:27. Moses:

“Behold (hen): while (be) I am yet alive with you this day, ye have been rebellious against the Lord;

how much more (af): in the time (ki) after my death, so (ve) [i.e. will ye be rebellious]?”

Here, I suggest, the if/then of the a fortiori argument as such are hen/af. The premise is a conditional proposition with be as its if-operator, and no explicit then-operator. The conclusion is similarly a conditional proposition, with ki as its if-operator, and ve (meaning, so or the-same) as its then-operator tacitly implying ‘ye will be rebellious’. The expression actually used in the text is ve af ki, but the elements of this expression play distinct roles in the statement, which is why I have slightly reshuffled them.


3.In historical books


1 Samuel 14:29-30. Jonathan:

“See (reu): because (ki) I tasted a little of this honey, how (ki) mine eyes are brightened.

How much more (af): if (ki) haply the people had eaten freely today of the spoil of their enemies which they found, then (ki) would there not have been a much greater slaughter among the Philistines?”

Here, the qal vachomer is a larger if/then statement, signaled by reu/af, within which are contained two smaller if/then statements, signaled by ki/ki, which are respectively the minor premise and the conclusion of the argument. (Note the reshuffle of antecedent and consequent in the premise for the sake of logical clarity. The original, opposite, order serves merely a rhetorical purpose: from phenomenon to its explanation, from effect to cause -  it is a didactic presentation.) The dayo (sufficiency) principle is ignored.


1 Samuel 21:6. David:

“Of a truth (ki): when (be) I came out, though (ve) it was but a common journey, yet (im) women have been kept from us about these three days, and (ve) the vessels of the young men were holy;

how much more (af): when (ki) today there shall be holy bread in the vessels, so (ve) [i.e. have we avoided women and kept the young men’s vessels holy].”

In this case, the qal vachomer proper is formed with the operators ki/af. It has a conditional proposition, with a compound antecedent and a compound consequent, as premise (here re-ordered for clarity); and another, with a simple antecedent and a tacit but obvious enough compound consequent, as conclusion. The operators (be/im) and conjunctives (ve) within the premise, and those within the conclusion (ki/ve), are not to be counted among the operators of the argument as such.


1 Samuel 23:3. David’s men:

“Behold (hine): here in (be) Judah [=our own territory], we are afraid;

how much more (af): if (ki) we go to Keilah [=enemy territory], so (ve) [i.e. will we be afraid]?”

Here, the operators of the a fortiori as such are hine/af. The premise is in conditional form, its antecedent being signaled by be, but its consequent having no signal (as is common in all languages). The conclusion is announced by the phrase ve af ki: the af of this phrase belongs, as we said, to the qal vachomer construction, while the ve of ve af ki serves to imply the consequent of the conclusion, equating it to the consequent of the premise (and it is for this reason left tacit in the text, to avoid repetition), and the ki of ve af ki refers to the antecedent of the conclusion.


2 Samuel 4:10-11. David:

“If (ki): [when] one told me saying, ‘behold, Saul is dead’ and (ve) he was in his own eyes as though he had brought good tidings, then (ve) I took hold of him and (ve) slew him in Ziklag in the way of reward.

How much more (af): when (ki) wicked men have slain a righteous man in his own house upon his bed, then (ve) now shall I not (halo) require his blood of your hand and (ve) take you away from the earth?”

In this case, the argument’s if/then operators are ki/af. The minor premise consists of a conditional, with both theses compound, without explicit if-operator (unless the initial ki is intended to serve a dual purpose, to avoid saying ki ki) and with ve as then-operator. The conclusion is also a conditional proposition, with a compound consequent, with ki/ve as operators. The extra occurrences of ve serve to signal compound antecedences or consequences. Dayo principle obeyed.


2 Samuel 12:18. David’s servants:

“Behold (hine): while (be) the child was yet alive, [David’s sorrow was so great that] we spoke unto him, and (ve) he hearkened not unto our voice;

then (ve): how (ekh) shall we tell him that the child is dead, so that (ve) he do himself some harm?”

In this case, the operators of the qal vachomer as a whole are hine/ve, and these frame two conditional propositions. One, the premise, has be as if-operator, but no visible then-operator (and indeed part of its compound consequent is also tacit); the other, the conclusion, has no visible if-operator, though it has ve as its then-operator (ekh serves an internal rhetorical purpose in the conclusion: without ekh the conclusion would be merely hypothetical ‘if we tell him, he will harm himself’, ekh signals a pursuit of the reasoning by apodosis ‘we do not want him to harm himself, therefore we cannot tell him’).

Note that the whole a fortiori argument is itself enclosed in a wider antecedent/consequent (not shown above), expressed by ki (because they thought thus), ve (therefore they feared to tell him). All these sentences within sentences can lead to confusion; that is why it is important to analyze their logical hierarchy carefully, if we want to be clear as to the identity of a fortiori argument per se. Dayo principle ignored.


2 Samuel 16:11. David:

“Behold (hine): my son, who came forth from my body, seeketh my life [still, I do not react];

how much more (af): in the case of (ki) this Benjamite now [who is less close], and curseth [me], then (ve) should I let him alone; for the Lord has bidden him.”

Here, the argument is signaled by hine/af. The premise is a conditional proposition without any explicit operator, and with a tacit consequent implied by the conclusion. The conclusion takes the ki of the expression ve af ki as if-operator and, we might say, its ve as then-operator. But more precisely, the conclusion, having an explicit consequent, can do without the ve conjunction, which rather serves to imply the tacit consequent of the premise.

As for the phrase ‘for the Lord has bidden him,’ its function is to strengthen the bonds between antecedent and consequent in the premise and the conclusion; for neither of these bonds is naturally automatic, but they proceed from a volitional choice by David. One might well object that the leeway a king’s son may be granted is not applicable to a mere subject like Shimei (the Benjamite in question); in that case, David’s argument seems weak: at worst concealing passivity or fatalism, at best mercifulness in time of trouble. For this reason, David has to explain himself, clarify his motivation, and point to his general attitude of acceptance of God’s will. Once the if/then bonds are thus firmed, the qal vachomer as such can proceed more credibly.


1 Kings 8:27 and 2 Chronicles 6:18. Solomon:

“Behold (hine), heaven and the heaven of heavens cannot contain thee;

how much less (af): in the case of (ki) this house that I have builded, will (ki) God in very truth dwell on the earth [i.e. be contained in this house]?”

Here, the a fortiori is expressed through hine/af. The premise is categorical in form, needing no operators; and the conclusion uses the operator ki for both its antecedent and consequent, the former deriving from the expression af ki, and the latter being stated in the original text even before the premise, together with the consequent of the conclusion (which is here properly moved to last place).


2 Kings 5:13. Naaman’s servants:

“Granting (ki): had the prophet bid thee do some great thing, wouldest thou not (halo) have done it?

how much rather (af): he [merely] saith to thee: wash and be clean? then (ve) [you should do it]”

In this argument, ki and af might be taken from the key phrase ve af ki as the if- and then- operators of the a fortiori argument as a whole. The premise is a conditional proposition, bare of any explicit operators (though containing the rhetorical expression halo). The conclusion consists of an explicit antecedent with a tacit if-operator, and a tacit consequent implied by the explicit ve in the key phrase. (This interpretation is open to debate: one might equally have regarded the ki as if-operator of the conclusion, or of the premise; or it might be viewed as playing a triple role. See also Prov. 15:11 below.)


2 Kings 10:4. The rulers of Jezreel in Samaria:

“Behold (hine): the two kings [Joram and Ahaziah, who were powerful men], stood not before him [Jehu];

then (ve): [we, who are relatively weak,] how (ekh) shall we stand [before him]?”

In this case, the a fortiori is signaled by hine/ve. The premise and conclusion have no explicit operators, because, though explicitly categorical, they are implicitly of conditional form. Dayo principle obeyed.


4.In other books


Job 4:18-19. Eliphaz the Temanite:

“Behold (hen): He puts no trust in His servants, and (u) His angels he charges with folly;

how much more (af): those who dwell in houses of clay, whose foundation is in the dust [does He distrust and charge with folly]?”



Job 15:15-16. Eliphaz the Temanite:

“Behold (hen): He puts no trust in His holy ones; and (ve) the heavens are not clean in His sight.

How much less (af): one who (ki) is abominable and filthy, man, who drinks iniquity like water [does He trust or consider clean]!”

Job 25:5-6. Bildad the Shuhite:

“Behold (hen): even the moon has no brightness, and (ve) the stars are not pure in His sight;

how much less (af): man, that (ki) is a worm [is bright and pure in His sight]?”

In Job, we find three a fortiori arguments with very similar wording and significance, namely that man cannot judge God, being infinitely morally inferior to Him. In each case, the operators of the argument are hen/af. The latter two cases involve the expression af ki; whereas the first case has af without ki, which proves incidentally that the word af can be used independently of ki.


Psalms 78:20. Asaph:

“Behold (hen): He struck a rock, then (ve) waters flowed and (u) streams burst forth.

In that case (gam): bread He can give; is there any doubt that (im): He will prepare meat for His people?”

The if-operator of argument is hen, and gam and im seem to be its then-operators. The premise is a conditional proposition, without if-operator, though with ve as then-operator to a compound consequent. The conclusion is double, a compound of categoricals. The implicit major premise has to be, for a fortiori purposes, that it is just as hard (or harder) to get water from a rock as (or than) to provide bread and meat. Incidentally, ‘Asaph’ probably refers to the Levite serving in the Temple during David’s reign, mentioned in 1 Chron. 16:7.


Psalms 94:9-10. Moshe:

“He who implanted the ear, does He not (halo) hear?”

“If (im) He formed the eye, does He not (halo) see?”

“He who chastises nations, does He not (halo) reprove [the individual]?”

Here, we have three distinct qal vachomer arguments, with the same thrust (in each case, the conclusion is something easier to do than the premise[2]). One of them has im as if-operator, but two of them have no if-operator; and none of them has a then-operator, though all three use instead the rhetorical expression halo.


Proverbs 11:31. Solomon:

“Behold (hen): the just man shall be recompensed on earth:

how much more (af): the wicked and the sinner, so (ki) [i.e. shall be recompensed on earth].”

This statement is a fortiori only if ‘recompense’ is interpreted negatively as in “if the just man (who has few sins) will be punished here on earth, all the more will the wicked and the sinner (who has many sins) be so punished” (this being ‘minor to major’ positive subjectal, valid). If ‘recompense’ were interpreted positively, the statement would not constitute a valid a fortiori (being ‘major to minor’ positive subjectal); but would needs be read as a mere conjunctive statement “the righteous (who has much credit) will be rewarded here on earth, and even the wicked and the sinner (who has little credit) will be so rewarded.”

Judging by its use elsewhere, the language (hen/af) favors the former alternative, namely the statement’s interpretation as an a fortiori. The word ki here serves to signal the tacit predicate of the conclusion (added in brackets), equating it to that of the premise.

People prone to theodicy (like Jeremiah: ‘wherefore doth the way of the wicked prosper?’ etc.) would tend to doubt the empirical veracity of this statement, however interpreted; but one can always argue back that only God really knows men’s deepest motives (as the next argument indeed affirms) and the relative values of all their deeds, and therefore His empirically apparent judgments might well be fully justified, however contrary to our expectations. The rebuttal is perhaps too simplistic, which is why appeal by theologians to a fuller accounting including life after death (and for some, previous lives) is usual.

Indeed, we find the Malbim (R. Meir Leibush ben Yechiel Michael, Rumania, 19th Cent. CE), with reference to this verse, commenting that while the righteous man tends to be made to pay for his sins in this world and to be paid for his good deeds in the next, the wicked man reaps his rewards in this world and is deprived in the next[3]. However, while this may well be true, I wonder whether it is logically implicit in the proverb under scrutiny. For, note well, the minor premise specifies recompense on earth, in which case by the dayo (sufficiency) principle the conclusion must similarly be limited. As far as I can see, we cannot strictly, without illicit process, extrapolate further, to a world beyond.

I want to add, here, that I have all too often noticed similar breaches of the sufficiency principle in other Talmudic and Rabbinic commentaries.


Proverbs 15:11. Solomon:

“If (ki): hell and destruction are before the Lord;

how much more (af): the hearts of the children of men [are before the Lord]?”

Here, the premise is apparently not signaled by an if-operator, while the conclusion is signaled by the word af; but since both propositions are categorical (the latter with an explicit subject and an implicit predicate), the word ki, which is normally an operator, would be redundant if viewed as part of the conclusion: it must therefore be viewed as the missing if-operator of the argument, more rightfully placed before the premise. (Alternatively, the argument might have been viewed as lacking an explicit if-operator, and ki as referring us to the absent predicate of the conclusion; or ki might have both functions. But see the next case.)

Malbim correctly construes this a fortiori argument’s implicit major premise, when he states: “The netherworld is far deeper, far more beyond sight and ken, than the human heart...”[4]. The inductive proof of this statement would be that most of us know a bit about the human heart and nothing at all for sure about the netherworld. Still, I want to make a general comment in this context, which I think is important.

While the logical form in which the verse under consideration is cast is indubitably a fortiori, it cannot really be viewed as instructing a deductive process. Deduction, viewed very strictly, is inference from more-known contents to the less-known. In the case of our verse, the minor premise cannot be said to be known by us; rather, it, as well as the conclusion, are being simultaneously taught to us, presumably as Divinely-inspired. None of us non-prophets can claim to know what it is that God knows; at best, we have a general assumption that God knows everything, under which all particular statements made (whether or not logically ordered, relatively to each other, as premises or conclusions) are equally subsumed, in which case the inference involved is essentially syllogistic.

We must thus view the whole verse as simply (from a logical point of view) a statement - that God will judge us, with full knowledge of our most inner thoughts, and may well send us to hell and perdition. The purpose of this statement is not maieutic, though outwardly cast in such form, but more practically homiletic, a warning to the unconverted or a reminder and encouragement to the converted: namely, that there will be a final judgment, etc. Religious literature, Jewish or otherwise, often indulges in such rhetorical techniques, giving preachments a maieutic appearance.


Proverbs 19:7. Solomon:

“If (ki): all the brethren of the poor do hate him,

how much more (af): do his friends go far from him?”

Same operators ki/af as in the previous case, for the same reasons. Note, however, that here the word ki has no other possible role to play, than the one we have here assigned to it, since the propositions are not only categorical, but wholly explicit; this justifies the similar position we took in previous such cases.

With regard to the content: one might point out that sometimes friends or even strangers will stand by you more than family. At least outwardly - in truth, their motive may not always be disinterested love for you, but for instances a desire to bind you to them out of gratitude, so they may use you in the future, or simply a role-play to satisfy their ego or to impress their peers with their charity or to effect a commercial transaction with God.


Proverbs 19:10. Solomon:

“If (ki): for a fool to have luxury is not seemly;

how much less (af): for a servant to have rule over princes [would be seemly].”

Same language and logical structure as in the previous case. Note, however, that the relation between the premise and conclusion is a bit hard to find here; perhaps it is merely aesthetic: just as the delight of a fool strikes us as distasteful, so the sight of a lowly man having power over his betters disturbs our sense of fitness. Supposedly, anyway, this is not a statement of intellectual arrogance, or worse still of aristocratic prejudice, but of moral concern (the joy of an unintelligent person is not per se ugly; and some ‘princes’ would certainly deserve to be ruled by their ‘servants’).

Looking further into the matter, I found a very interesting comment by Malbim, which convincingly elucidates the premise-conclusion relation. He points out that the fool is one who lets his soul be ruled by his body (in the pursuit of pleasure) - so viewing the minor premise, the reference to princes and servant in the conclusion becomes less of a non-sequitur[5]. However, in that case, premise and conclusion become two metaphors for the same thing, and the verse becomes a mere reformulation of the same statement, rather than an a fortiori argument. Perhaps we should focus on the question, why the reference to one ‘servant’ and many ‘princes’? This would bring us back to the more socio-political interpretation of the conclusion.


Proverbs 21:27. Solomon:

“If (ki): [even brought with a ‘sincere’ intent] the sacrifice of the wicked is an abomination;

how much more (af): brought with a wicked intent [is it abomination]?”

In this case, as before, the key phrase af ki provides us with the if/then operators ki/af. Note in the above statement how the first part of the premise and the second part of the conclusion were both tacit, but could be readily verbalized by imitation of each other’s explicit parts - a sort of ‘mirror effect’. It is obvious that the premise could not be an unqualified generality free of the clause we added to it, because then the conclusion would be included in it and redundant; as for the conclusion, it would clearly be incomplete and inexplicable without the clause we added to it, which also shows up its a fortiori relation to the premise. Thus, though the given propositions seem categorical, they are implicitly conditional, one with a tacit antecedent, the other with a tacit consequent. They are formulated with a maximum economy of words, yet because of their symmetry none of the message is lost.




Jeremiah 12:5. God:

“If (ki): thou hast run with the footmen and (ve) they have wearied thee,

then (ve): how (ekh) canst thou contend with horses [and not be wearied]?

and if (u): in the land of peace, thou dost [hardly] feel secure;

then (ve): in the wild country of the Jordan, how (ekh) wilt thou do [feel secure]?”

These are two a fortiori with the same thrust. The if/then operators of these arguments are respectively ki/ve and u/ve, though in the latter case the u (=ve) conjoins and equates the two arguments and could thus be viewed as standing in for a tacit ki. Note that in the first argument, the premise is a conditional proposition without if-operator, though with ve as then-operator, and the conclusion has similar form though partly tacit. In the second case, the premise and conclusion are likewise conditional, though all their operators are tacit. In both cases, ekh is used rhetorically, as usual, to deny the ironically suggested strength or security.


Ezekiel 15:5. God:

“Behold (hine): when (be) it was whole, it was not meet for any work;

how much less (af): when (ki) the fire hath devoured it and (ve) it is burned, shall it then (ve) yet be meet for any work?”

Here, the operators of the argument as a whole are hine/af. The premise is a conditional with be as if-operator, and no explicit then-operator; and the conclusion is a conditional proposition (with a conjunctive antecedent, accounting for the first ve, incidentally), whose operators are ki/ve.


Daniel 2:9. Nebuchadnezzar:

“Thus (lahen): tell me the dream,

and (ve): I shall know that you can declare its interpretation to me.”

Here, the king’s utterance is not in itself a qal vachomer argument, strictly-speaking (since the first statement is an order, not an item of information), but it testifies to an underlying thought-process which is qal vachomer in form. The argument is obviously ‘if my advisors are capable of telling me what the dream was, then they are skilled enough to tell me what it means.’ For this reason, an if-operator is lacking, though we may take it to be lahen (cognate to the by now familiar hen), since this is the word the king uses to express his precondition; likewise, we may consider ve as the then-operator of the argument, though in the king’s statement it refers to the mental consequence in him of the satisfaction of the precondition he set.



Finally, some comments concerning cases which might superficially be interpreted as a fortiori, but which on closer scrutiny fail to make the grade for one reason or another.


Concerning 2 Chronicles 32:15. Sennacherib, king of Assyria (through his messengers) says:

“For (ki): no god of any nation or kingdom was able to deliver his people out of my hand, and out of the hand of my fathers;

likewise (af): therefore (ki), shall your God not be able to deliver you out of my hand.”

The first statement is based on enumeration of past Assyrian experience; the second statement is an application of the same predicate to a new subject, Judah’s God. The argument is therefore essentially inductive, going from the relatively particular to greater generality, and then back down by subsumption (eduction or syllogism) to the new case. It is not an a fortiori argument; to have this form, the argument would need as major premise a statement that some of the gods of the already defeated nations were superior in power to the God of Judah, and no such statement seems even implied here.

Yet the argument gives an impression of being a fortiori, because it uses the characteristic af ki terminology (actually, this sentence uses the word ki twice, once redundantly, with intent to stress that an inference is involved). Perhaps the speaker wanted to give it more force, to scare his audience into submission. Note that a bit further on, in verse 17, essentially the same statement is repeated using another terminology, ken/lo; but there the style is clearly not a fortiori.


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. If we suppose the speaker is arguing: ‘Even if I give you two thousand horses, you would not be able to set riders upon them; how then (ve-ekh) can you hope to defeat even the least of my master’s captains?’ - we are hard put to explain the rest of the statement about ‘trusting in Egypt for chariots and for horsemen.’ The text is unclear, even viewed simply.




Lastly, with regard to Esther 9:12. Ahasuerus says:

“In (be) Shushan the capital, The Jews have slain and destroyed five hundred men and the ten sons of Haman;

in (be) the rest of the king’s provinces, what (meh) have they done?”

This is one of the ten qal vachomer arguments recognized by Genesis Rabbah. As the Rabbis see it (thus for instance, I read somewhere, does Malbim on the basis of the Talmud), the king was surprised and angry that Esther’s People, the Jews, had been so threatened that at least 500 anti-Semites were found; this viewpoint would help explain why the king next asks Esther what else she requests of him (he was concerned, he evidently felt somewhat responsible).

But frankly I have some doubts as to the sentence’s status as a qal vachomer argument. For a start, its language is sui generis: I have not found another a fortiori signaled by the word meh. This in itself is not proof, of course, for the linguistic habits of that place and time may have been distinctive (and I may well have missed other cases). And indeed, one can easily imagine the statement (perhaps accompanied by an up and down wave of his open hand[6] and an emphasis on the mah) as signifying that the king expected more people to have been killed in the rest of the kingdom. We of course know from verse 16 that in fact as many as 75,000 were killed elsewhere.

But the problem is not the king’s expectations, but whether an argument (and specifically an a fortiori) was at all formulated (let alone, whether or not correctly). Given the premise, one could reasonably equally well expect that less people were killed elsewhere. One can as well conceive that most of the Jews’ enemies were in the capital, as conceive that they were proportionately (or even more) frequent in the rest of the empire, according to our view of the sociological profile of anti-Semites. Thus, the king’s question may well have been no more than an open question; and indeed, there is no indication within the text that his statement was other than a simple statement of amazement and curiosity.[7]


6.Addendum (2005)

One More Example of A-Fortiori in the Tanakh[8]. An acquaintance of mine and reader of Judaic Logic, Mark Leroux, has in 2001 rightly pointed out to me an additional a-fortiori argument in the Bible, in 1 Samuel 17:37. The passage reads[9]:

And David said, “The Lord who saved me from the paw of the lion and the paw of the bear, He will save me from the hand of the Philistine”

Although this statement is not per se an argument, but has an assertoric form (that of a blunt statement of fact), David’s underlying thought-process is indeed kal va-chomer (we encountered a similar situation, with reference to Daniel 2:9). I easily constructed a positive predicatal a-fortiori reflecting this thought-process, by proposing an appropriate middle term (say, favoring by God):

God must favor (R) someone at least as much to deliver him from big wild animals (P) as to deliver him from big seasoned warriors (Q); David (S) was favored by God (R) enough to be delivered from a lion and a bear (P); therefore, David (S) will be favored by God (R) enough to be delivered from Goliath (Q).

Notice that I used the egalitarian form of a-fortiori (major premise with “as much as”), which suffices to make the point without too much assumption. But Mark Leroux suggested a bolder, and finally more convincing, interpretation to me.

He pointed out that the lion and bear were innocent animals, merely attempting to feed themselves, and yet God favored David over them. In contrast, the Philistine was a willful enemy of His people, so God had all the more reason to favor David over him.

In other words, David’s argument could be cast as “If God gave me victory over innocent beasts obeying their natural impulses, he will surely give me victory over a rebellious brute out to upset God’s plans.” The result is the same, but the argument is more forceful.

Finally, looking at the Hebrew version, we note first that it contains no logical operators (such as ki); but this does not detract from its being an argument, as we have seen in many previous cases. Furthermore, it contains no keyword (such as ve-ekh or halo), let alone a novel one which might have helped us to discover yet other, similar cases through a concordance.

I want to underline here that Biblical a fortiori arguments usually require interpretation, in that they involve tacit elements, usually the major premise at least. This can also be illustrated with reference to the following two cases (paraphrased).

In 2 Samuel 4:10-11, David states that if he sentenced to death the man who brought him tidings of Saul’s death (whom the man claimed to have killed at the wounded Saul’s own request), how much more will he so deal with the two men who brought him tidings of Ish-Bosheth’s death (whom they had murdered in his bed). The major premise of the argument being that the latter crime was greater than the former, either because of the circumstances or because of the comparative innocence of the victim.

Similarly, in 2 Samuel 16:11, David states that considering that his own son, Absalom, was seeking his life, how much more could one expect Shimei, a Benjamite supporter of the late Saul, to express opposition to David. Here, the major premise would be that Shimei compared to Absolom either had a better pretext for his actions or that they were less dangerous.


Drawn from Judaic Logic (1995), chapter 6.


[1]          I have referred to various standard translations: for the Pentateuch, Samuel and Kings, mainly to the more classical Soncino Books of the Bible; for the Psalms, to The Metsudah Tehillim, and for the rest to The Jerusalem Bible. In some cases I have had to make small modifications in the choice or order of words, called for by the needs of our analysis. I make an effort to explain the positions I have taken; though if situations are similar, I try to avoid repeating myself. (The mystically inclined may find it interesting to notice, in passing, the content of the Biblical passages this research happens to have brought together; their collective message, as it were.)

[2]           However, the truth of the first two propositions is open to doubt. This is made evident if we apply similar reasoning to humans and say "he who designs an airplane, can he not fly?".

[3]           P. 119.

[4]           Ibid., p. 159.

[5]           Ibid., p. 198.

[6]            This is not just a quaint Israeli gesture, but in my view signifies the act of weighing, whence ‘how much?!’

[7]           I have by chance found (this is June 1998) yet another a fortiori: Jonah 4:10-11, which goes to show, as I asserted earlier, that there are probably still more cases than those indicated thus far. This argument is uttered by the Lord, who says: "Thou art concerned about the castor oil plant, for which thou hast not laboured..., and should I not be concerned for Nineve, ...." The expression vaani lo (and should I not) is obviously similar in function to halo.

[8]          Addendum 4 of JL.

[9]          New York: Judaica Press, 1976.

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