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A FORTIORI LOGIC

© Avi Sion, 2013 All rights reserved.

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A FORTIORI LOGIC

Appendix 1 – A fortiori discourse in the Jewish Bible

There are at least 46 instances of a fortiori discourse in the Tanakh (the Jewish Bible). Their dating is traditionally referred to the dates of the events in books concerned, viz. Genesis (Lamekh in ‘antediluvian’ times; Joseph’s brothers in patriarchal period); Exodus, Numbers, and Deuteronomy (Moses in the Sinai), 1 & 2 Samuel (Davidic kingdom), and so forth (subsequent history till the 1st Exile period)[1].

Of the 46 cases listed below, only 11 are given in the Midrashic work Genesis Rabbah; these are here marked as “Listed by GR.” In my Judaic Logic (1995), I listed another 24 cases[2] found through independent research, to which I later added 1 case in a footnote at the end of chapter 6 (which I found by chance in June 1998) and 1 case in Addendum 4 (which was suggested to me by a reader in 2001). However, I discovered while writing the present book that 13 of the additional cases listed in my book were in fact known to others (all apparently found by Wolf Einhorn in 1838, according to Louis Jacobs in 2005); these cases in common are here not marked at all. Still, the remaining 13 of the additional cases listed in my book seem to have been unknown to others; these are here marked as “New from AS.” To these must be added 1 more case, that I only recently discovered, namely Ezekiel 14:13-21. On the other hand, Louis Jacobs listed 8 cases (presumably found in Wolf Einhorn) that I had not previously found; these are here marked as “New from WE.”[3]

I have put the arguments in ‘if–then’ form, showing the minor premise and conclusion, but leaving the major premise tacit. If the subjects are different and the predicates are the same, the mood is subjectal. If the subjects are the same and the predicates different, the mood is predicatal. If there is ‘enough of’ the middle item, the mood is positive; if there is ‘not enough of’ the middle item, the mood is negative. I have formulated all the arguments in copulative form, even when an implicational form might have been closer to the original. If the mood is positive subjectal (marked +s), or negative predicatal (marked –p), the argument is from the minor term to the major term. If the mood is negative subjectal (marked –s), or positive predicatal (marked +p), the argument is from the major term to the minor term. Most arguments are purely a fortiori, but some are clearly intended as a crescendo (these are marked by a &). Note that some classifications here differ from those in my Judaic Logic; those here are more reliable[4].

The following table shows the number of instances of a fortiori argument in the Tanakh, classified by mood of copulative argument concerned. We see that the distribution is about even for the first three moods (14, 13, 15), while there are only 4 instances of the fourth (still, it is significant). It is interesting that 41% (19/46) of the arguments are predicatal, considering how little attention this form has received from most commentators. Only 13% (6/46) of the arguments are a crescendo, and yet many commentators have assumed this form to be the essence of a fortiori argument.

Mood

Instances

Of which &

Positive subjectal {+s}

14

3

Negative subjectal {–s}

13

3

Positive predicatal {+p}

15

0

Negative Predicatal {–p}

4

0

Table A1.1

Genesis 4:24. Lemekh ben Methushael: “If (ki): Cain shall be avenged sevenfold, then (ve): Lemekh [shall be avenged] seventy and seven-fold.” (Listed by GR.) {–s &} If an intentional killer is not abhorred enough to be punished immediately, then an unintentional killer will remain unpunished for a much longer time.

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?” (Listed by GR.) {+p} If the accused were honest enough to return found goods, then they must have been honest enough not to steal anything.

Exodus 6:12. Moses: “Behold (hen): the Children of Israel have not hearkened unto me; then (ve): how (ekh) shall Pharaoh hear me?” (Listed by GR.) {–s} If the Israelites, who have much faith, have not had enough of it to listen to Moses, then the chief of the Egyptians, who has far less faith (if any), will not have enough of it to do so.

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.” (Listed by GR.) {+s} If someone causing paternal anger is culpable enough to deserve seven days isolation, then someone causing Divine anger is culpable enough to deserve seven days isolation.

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. ye will be rebellious]?” (Listed by GR.) {+s} If the people during Moses’ lifetime are unfaithful enough to rebel, then they after his death will be unfaithful enough to rebel.

Judges 14:16. Samson to his wife: “Behold (hine), I have not told it [the solution to my riddle to] my father nor my mother, and (ve) shall I tell [it to] thee?” (New from WE.) {–p} If Samson was not trusting enough to tell the secret to his parents, then he won’t be trusting enough to tell it to his wife.

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?” {+s &} If someone eating a little honey is energized enough to have his eyes brighten, then people eating lots of food are energized enough to do that and much more.

1 Samuel 17:37. David: “The Lord who saved me from the paw of the lion and the paw of the bear [= innocent animals], He will [surely] save me from the hand of the Philistine [= willful enemy].” (New from AS[5].) {+p} If David had spiritual credit enough to be saved from innocent creatures, then he has credit enough to be saved from evil ones.

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].” (New from AS.) {+p} If we were virtuous enough to practice abstinence on a common journey, then we are virtuous enough to do so on a special day like today.

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]?” (Listed by GR.) {+p} If we lack confidence enough that we feel fear while on our own territory, then we will lack confidence enough that we will feel fear when on enemy territory.

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?” (New from AS.) {+s} If someone who merely announced the death of Saul, David’s respected adversary, was judged wicked enough to deserve execution, then the people who actually killed a respectable man, Ish-bosheth the son of Saul, who did David no harm, must be judged wicked enough to deserve execution.

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?” {+s &} If David while his child still lived was sorrowful enough to be utterly distracted, then David now that the child has died will be sorrowful enough to cause himself some harm.

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.” {+p} If David was self-controlled enough to avoid reacting under attack from his own son, then David will be self-controlled enough to avoid reacting under attack from a more remote enemy.

1 Kings 8:27. 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]?” This is repeated in 2 Chronicles 6:18. {–s} If the heavens are not big enough to contain God, then an earthly house is not big enough to do so.

2 Kings 5:13. Naaman’s servants: “Granting (ki): had the prophet bid thee do some great thing, wouldst 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]” (New from AS.) {+s} If the prophet making some difficult request would have seemed powerful enough in your eyes to succeed in healing you, causing you to obey him, then his making an easy request suggests he may be more powerful than you expected and indeed powerful enough to heal you, and should cause you to obey him.

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]?” {–s} If the two kings were not strong enough to resist Jehu, then we are not strong enough to do so.

2 Kings 18:23-24. Rab-shakeh (emissary of the king of Assyria): “[Since] thou puttest thy trust on Egypt for chariots and for horsemen, I will give thee two thousand horses, if thou be able on thy part to set riders upon them. [But you are not able to do even that, and so cannot hope to defeat us.] How then (ve-ekh) canst thou [without gift of horses] turn away the face of one captain, even of the least of my masters servants?” (New from AS.) This is repeated in Isaiah 36:8-9. {–s &} If you had 2000 horses, you would not have enough power to defeat the Assyrian army, then without such a gift you do not have enough power to do so, not even to defeat a minor captain of it.

Isaiah 36:8-9. Rab-shakeh (emissary of the king of Assyria): “[Since] thou puttest thy trust on Egypt for chariots and for horsemen, I will give thee two thousand horses, if thou be able on thy part to set riders upon them. [But you are not able to do even that, and so cannot hope to defeat us.] How then (ve-ekh) canst thou [without gift of horses] turn away the face of one captain, even of the least of my masters servants?” (New from AS.) This is the same as 2 Kings 18:23-24. {–s &}

Isaiah 66:1. God: “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?” (New from WE.) This is comparable to 1 Kings 8:27 and 2 Chronicles 6:18. {–s} If the heavens are not big enough to contain God, then an earthly house is not big enough to do so.

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]?” (2 instances, listed by GR.) (Both –p) If you are not strong enough to cope with the easier challenges, then you are not strong enough to cope with the more difficult ones.

Jeremiah 25:29. God: “For, lo (hine), I begin to bring evil on the city whereupon My name is called, and (ve) should ye [who is less virtuous] be utterly unpunished?” (New from WE.) {–s} If those calling on my name are not absolved enough to escape my wrath, then you less virtuous folk are not absolved enough to escape my wrath.

Jeremiah 45:4-5. God: “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 [who is less valued] great things for thyself?” (New from WE.) {–s} If the things I worked for are valued by Me not enough to escape being undone, then the things you work for are valued by Me not enough to escape being undone.

Jeremiah 49:12. God: “Behold (hine), they to whom it pertained not to drink of the cup shall assuredly drink; and (ve) art thou [who is more guilty] he that shall altogether go unpunished?” (New from WE.) {+s} If people who are not reprehensible are implicated enough to be punished, then people who are reprehensible are implicated enough to be punished.

Ezekiel 14:13-21. God: “Son of man, when a land sinneth against Me by trespassing grievously, and I stretch out My hand upon it… and send famine upon it… [Or] if I cause evil beasts to pass through the land… Or if I bring a sword upon that land… Or if I send a pestilence into that land… though Noah, Daniel, and Job, were in it, as I live, saith the Lord God, they shall deliver neither son nor daughter; they shall but deliver their own souls by their righteousness… How much more (af ki) when I send My four sore judgments against Jerusalem, the sword, and the famine, and the evil beasts, and the pestilence, to cut off from it man and beast.” (New from AS.) {–p} If such holy men lack sufficient spiritual credit to prevent the execution of each of the four negative decrees separately, then they lack enough to stop all four of these decrees together.

Ezekiel 15:5. God: “Behold (hine): when (be) it [the vine-tree] 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?” (Listed by GR.) {–s} If when whole the vine-tree was not in good condition enough to be useful; then now when damaged it is not in good condition enough to be useful.

Ezekiel 33:24. God: “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.” (New from WE.) {+s} If one man is important enough to inherit the land, then many men are important enough to inherit the land. (Obviously, though God is reporting this argument, He is not its author. It is not very credible, and rightly rebutted in the verses 25 and 26: it is not numbers but moral worth that makes possible inheritance of the land.)

Jonah 4:10-11. God: “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?” {+s} If a mere gourd etc. can be appreciated enough to be cared for (as by Jonah), then a great city etc. can be appreciated enough to be cared for (by God).

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?” (New from AS.) This is the same as 1 Kings 8:27. {–s} If the heavens are not big enough to contain God, then an earthly house is not big enough to do so.

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 [presumed by the messengers as no different from other gods] not be able to deliver you out of my hand.” (New from AS.) {–s} If other national gods were not powerful enough to deliver their respective nations, then the God of Judah is not powerful enough to deliver his nation. (This of course wrongly equates God with non-gods, but it is how the Assyrian king thinks.)

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?” (New from AS.) {+p} If God is powerful enough to draw water from a rock[6], then He is powerful enough to feed His people with bread and meat.

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]?” (3 instances, New from AS.) (All 3 +p) If God is powerful enough to implant the ear and form the eye, then He is powerful enough to hear and see. If God is powerful enough to chastise nations, then He is powerful enough to reprove individuals.

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]?” {+p} If God is perspicacious enough to judge His servants/angels as untrustworthy and unwise, then He is perspicacious enough to judge mere human beings as untrustworthy and unwise.

Job 9:13-14. Job: “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?” (New from WE.) {–s} If Rahab’s helpers were not worthy enough to argue with God, then Job is not worthy enough to do so.

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]!” {+p} If God is demanding enough to judge His holy ones as untrustworthy and the heavens as unclean, then He is demanding enough to judge mere human beings as untrustworthy and unclean.

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]?” {+p} If God is perfectionist enough to judge the moon as obscure and the stars as impure, then He is perfectionist enough to judge mere human beings as obscure and impure.

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].” (Listed by GR.) {+s} If the just man is imperfect enough to be recompensed on earth, then the wicked and sinner are imperfect enough to be recompensed on earth.

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]?” {+p} If God is powerful enough to look into hell and destruction, then He is powerful enough to look into people’s hearts.

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?” {+p} If the poor man is disliked enough that his brothers avoid him, then he is disliked enough that his friends avoid him.

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].” {+s} If for a fool to have luxury is inappropriate enough to be unseemly, then for a servant to have rule over princes is inappropriate enough to be unseemly.

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]?” {+s} If the sacrifice of the wicked brought with a ‘sincere’ intent is abominable enough to be rejected, then the sacrifice of the wicked brought with a wicked intent is abominable enough to be rejected.

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? [i.e. surely many more!]” (Listed by GR.) {+s &} If the Jews in Shushan have found and destroyed as many as 500 anti-Semites, then the Jews in provinces have found and destroyed many more than 500 of their enemies. (Not sure of a fortiori intent, in my view; but kept because traditional.)

Daniel 2:9. Nebuchadnezzar: “Thus (lahen): tell me the dream, and (ve): I shall know that you can declare its interpretation to me [since it is more difficult to tell it than to interpret it].” (New from AS.) {+p} If Daniel is powerful enough to tell the dream, then he is powerful enough to interpret it.

Nehemiah 13:26-27. Nehemiah: “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?” (New from WE.) {+s} If king Solomon, who was not very weak, was weak enough to be brought to sin by foreign women, then we, who are much weaker, are weak enough to be brought to sin by foreign women.

Postscript: To my surprise, in the fall of 2014, I stumbled upon two more instances of a fortiori discourse (both -p) in the Jewish Bible, raising the total to 48.

One is in Proverbs 17:7. “Overbearing speech becometh not a churl; much less (af ki) do lying lips [become] a prince.” (New from AS.) {-p} If boastful speech is not becoming enough to be indulged in by a person of lowly character, such speech is not becoming enough to be indulged in by someone of noble character.

The other is in Proverbs 30:2-3. The speaker is Agur bin Yakeh: “Since (ki) I am brutish in comparison to other men, and lack understanding of men, and have not attained wisdom, how then (ve) would I have knowledge of things holy?” (New from AS.) {-p} If I am not knowledgeable enough in mundane matters, then I am not knowledgeable enough in holy matters.

(Actually, though I label these two instances as “New from AS,” I spotted them thanks to the translation and commentary by Rabbi A. Cohen in the Soncino ed. of Proverbs.)



[1] I do not here give traditional chronology, based on Seder Olam calculations, because modern secular historians do not advocate quite the same dates. The present work is obviously not the place here to debate this hot issue.

[2] Although in chapter 6 of my Judaic Logic, I rejected three of the instances here counted as genuine a fortiori, I now see more clearly how they can be so construed. See 2 Kings 18:23-24 and its repetition in Isaiah 36:8-9, and 2 Chronicles 32:15.

[3] The transliteration of Heb. words in “(italics)” are sometimes given here because they were helpful indices in the research process. The remarks in square brackets “[xxx]” are my own interpolations to facilitate the proposed a fortiori reading where necessary. I also on occasion reorder the clauses involved to accord with the perceived sequence of reasoning or show up the utility of an operator.

[4] I there (in chapter 5.4) had Dt. 31:27 as +p (here it is +s), 1 Sam. 23:3 as +a (here it is +p), Jer. 12:5 as +a (here they are –p).

[5] But actually found by Mark Leroux.

[6] The subject of “he struck a rock” could be Moses, but the cause of the water gushing from it must be God. Likewise, it is God that provides bread and meat. This is obvious from the Torah account (Ex. 17:6, 16:12).

2016-08-05T04:49:06+00:00