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JUDAIC LOGIC© Avi Sion, 1995. All rights reserved. Chapter
5.
REVISED LIST OF BIBLICAL A-FORTIORI.
This chapter should be of interest to Bible scholars and students, rather
than to secular logicians.
We stated earlier that, according to Genesis
Rabbah, there are ten cases of a-fortiori argument in the Bible: four of
them in the Books of Moses and the other six in various other locations. This
Midrashic work is traditionally said to have been compiled either by Rabbi Oshia
Rabba (a late Tana) or by Rabba bar Nachmani (a third generation Amora); in any
case, circa 3rd century CE[1].
We have already in earlier chapters analyzed in considerable detail the
four cases of a-fortiori spotted in the Chumash
by this Midrash, namely: Gen. 44:8, Exod. 6:12, Num. 12:14, and Deut. 31:27. The
other six cases mentioned by it are: 1-Sam. 23:3, Jer. 12:5 (2 cases), Ezek.
15:5, Prov. 11:31, and Esth. 9:12. Presumably, this is intended to be a full
enumeration; i.e. it is not just a list of ten cases among others, but an
exhaustive list.
At first, I took this authoritative tradition that there are just these
10 qal vachomer arguments in the Bible for granted. But I must admit
that over time, to my surprise (not to say, consternation, for I do not want to
excite the ire of my religion's orthodoxy), I have been forced to revise that
article of faith considerably. Closer scrutiny of the evidence makes indubitably
clear that there are more likely at least about 30 (thirty)
cases in the Bible, and furthermore that one of the cases listed by the
Midrash is open to doubt as a genuine case.
My first inkling that something was amiss was the quite fortuitous
discovery of an a-fortiori argument in Job 4:17-19, while leafing through
Maimonides' Guide[2]. I naturally assumed that the list given in the Encyclopaedia
Judaica[3], which was my initial source, was erroneous by
accident (this is not as far-fetched as it may sound: I once spotted a confusion
between 2nd and 3rd figure hypothetical syllogism in the 1967 Encyclopedia
of Philosophy[4]); and that the two cases counted under Jeremiah were
really one, while the said argument in Job was perhaps merely omitted by the
printers. I resolved to look into the original source, and confirm this
assumption (I of course did look into G.R.
eventually, but found the E.J. list
correct).
Meanwhile, having had my consciousness of the issue of logical arguments
in the Bible raised by my preceding research, I happened on a Shabbat, while
studying the "haftarah of the
week" (Tazriaa), to notice yet
another unmentioned case, namely 2-Kings 5:13. Again, my immediate reaction was
defensive, conservative; I did not want to belie the tradition. I had early on
in my formal researches looked with askance on the argument in Esther (we will
return to this detail further on); so I thought, well, if we ignore this
doubtful case, we still have a total of only ten a-fortiori arguments.
At about that time, as I described to people some of the difficulties I
was coming across in my Biblical research, someone mentioned that there may be a
case of qal vachomer in Daniel; but I
could not find it offhand (as we shall see, I did find a probable case
eventually).
Also, leafing through an ArtScrolls
commentary on Genesis, I noted to my relief their comment that 'some
editions' of the Midrash include Gen. 4:24 instead of Ezek. 15:5 in the list of
ten. The Rashi commentary on this alternative sample, I then found (see Soncino Chumash[5]), is clearly formulated as a qal vachomer. (Assumably, then, Rashi favoured the special editions
of the Midrash, since in his commentary to Gen. 44:8 he does not dispute the
claim that there are only ten qal vachomer
cases 'in the Torah' [in the larger sense of the term, meaning Tanakh] - this is
said in passing).
Thus, in fact, in practise, at least eleven sentences in the Bible are
recognized as a-fortiori by Rabbinical authorities taken collectively, and not
just ten (though some say these ten and some say those ten, and they all agree
on nine cases). How they reconcile this with the Midrash claim, which they
apparently all continue to uphold undaunted, is beyond me: a contradiction is a
contradiction. I do not know whether any among them have noted and acknowledged
yet other cases of a-fortiori in the Tanakh, and if so how they dealt with the
issues implied; but the issues are implied even with a joint list of just eleven
cases. The simplest solution, it seems to me, would be to regard the Midrash
claim as not intended as exhaustive; then there is no problem of doubting the
Midrash's infallibility.
I tell this story in detail to demonstrate my goodwill,
my reluctance to contradict authorities (but also my determination to find the
factual truth). By now, it had become obvious that the common tradition on this
topic was surely factually inaccurate, and that a systematic reevaluation was
called for. But, how, other than by rereading the whole Tanakh carefully with
this issue in mind? It was at this point that I had a very felicitous insight...
The a-fortiori arguments in the Tanakh are noticeably not
signaled by expressions like "kol sheken" or "qal vachomer"!
These expressions are utilized in Talmudic (Mishnah and Gemara) and
post-Talmudic (Rabbinic) arguments and exposés, but not so far as I know in the
Bible itself. If we actually look at the 10 cases mentioned by the (usual)
Midrash, we find exclusively the following language:
I saw almost at once that these various phraseologies might be viewed as
signals of an intention to formulate an a-fortiori argument. After a while, I
realized that these sentences have, indeed were bound to have, conditional form,
with an antecedent clause (a minor premise), signaled by an "if"
operator (one of the particles hen/hine,
ki, ve/u), and a consequent clause (a conclusion), signaled by a
"then" operator (one of the expressions ve
ekh, ve af ki, af ki, halo, and eventually meh).
These key words or phrases were limited in number, some half a dozen, and so
could with relative ease be used in a search for other cases, if any, in a
Concordance of the Bible (which is effectively a word index). Of course,
there might be other significant expressions, besides those, but I left the
question open; at least, this was a starting-point.
The following stage was painstaking research: each reference to a keyword
in the Concordance was looked up in the Bible, to see whether or not it signaled
an a-fortiori argument. In truth, I did not research all the keywords: I looked
up all occurrences of ekh,
ve-ekh, af, af-ki, ve-af, ve-af-ki, hen, ve-hen, halo, va-halo;
but I did not have the patience to also research the words hine,
ki. It was quickly evident that not all occurrences of the keywords
signaled a qal vachomer (only about 6 percent did so); on the other hand, I
found by this method many new cases of the argument, i.e. cases not mentioned in
the Midrash (about twenty). In all, I looked up some 500 references in the
Bible; by that time my point was proven, since I had about three times the
number of a-fortiori arguments I started with, and it did not seem important to
pursue the matter further and attempt to be exhaustive.
As already said, I was not immediately conscious of the logical role
played by the key words/phrases. At first, my approach was pragmatically
philological; but once I grasped that what I had to look for were if/then
operators, it became obvious that a more detailed linguistic analysis was called
for: this laborious research is presented in the next chapter. In this context,
I gradually understood the following (which ex
post facto perhaps seems obvious, but was not immediately evident). Whereas
in modern Hebrew, im/az are the
closest and most commonly used equivalents of if/then, in Biblical Hebrew the
language is more varied:
a.
There are various alternative expressions for "if", such as hen/hine,
reu, ki, ve/u, im, be; all these announce an antecedent: behold, see, if,
when, because, in, etc. The prefix vav
(and) fulfills this function, like the other words, by presenting a context, in
which certain later mentioned events occur.
b.
There are various alternative expressions for "then", such as af,
ve, ki, im; all these announce a consequent: all the more/less, therefore,
then, so, etc. The word af, often
translated as 'all the more/less' (its distinctively a-fortiori reading), more
broadly means 'also, similarly'. The word ki,
which in modern Hebrew usually has the limited meaning of 'because', has
evidently in Biblical Hebrew a broader range of meaning, including even 'then'.
The use of vav (and) in the sense of
'then' is also found in English (e.g. "Press the button and the motor
starts"), and therefore needs no explanation.
c.
Antecedents and consequents need not in Biblical Hebrew, anymore than in
the modern idiom or in English or French, be signaled by any "if" or
"then" operators; they may be tacitly understood by the context, or be
left out to avoid repetitions. (Nowadays, we often use a comma to signal a tacit
"then" in written texts.) Grammatically, logical operators are merely
'conjunctions', they serve to bring sentences together in various ways.
d.
Although initially expressions like hen,
af-ki, ve-af-ki, ve-ekh, halo made it possible for me to discover a-fortiori
arguments, I eventually realized that they were not or not-wholly in fact
logically essential factors in these arguments. Ekh (how) and halo (is it
not that) are never then-operator of arguments, but always an integral part of
the consequent/conclusion in which they appear, serving as rhetorical devices:
how will you do this? meaning, you cannot do it; is it not that so and
so? meaning, it is so and so. As for af-ki,
ve-af-ki, although the af particle
serves as then-operator of arguments, the ve and ki may have a role
either as if-operator of the argument, or as if or then operator of its premise
and/or conclusion.
In this context, I would like to refer the reader to Esra Shereshevsky's
very interesting analysis of Rashi's interpretative techniques, where some of
the fine nuances in the meaning of words like ve
and ki are discussed[6].
Apart from that, please note that my use of the operators if/then
is here very loose, generic (and not exclusively logical); I do not here push
the analysis on down to deeper levels, to distinguish between the different
modal types of conditioning: the logical (if),
the natural/temporal (when, at such times
as), and the extensional (in such
instances as). The if/then operators of any logical argument are of course
of logical modality, but the conditional premises and conclusions (if any) they
enclose may be of other modal types. 3. The
Data and their Analysis.
The table below lists the results of these researches,
my own proposed list of Biblical a-fortiori arguments. I repeat, it is not
necessarily exhaustive; and it should be added, some of the arguments are
strong, unassailable, some are comparatively weak, open to rebuttal, but I think
they are all reasonably clear samples of the form. Opposite each Biblical
reference I indicate the apparent if/then logical operators (if any), and
parenthetically any of the typical a-fortiori expressions hen, hine, lahen, af-ki, ve-af-ki, ve-ekh, halo, which helped me
personally find the case in addition to the operators themselves. Table 5.1
Proposed list of Biblical
A-Fortiori.
We see that there are at least 31 cases of a-fortiori in the Tanakh, 5 of
them in four books of the Torah proper, and 26 more in eleven other books
(counting Samuel and Kings as two each). Some of these arguments are repetitive,
and perhaps should not be counted as distinct. For instance, 1-Kings 8:27 and
2-Chron. 6:18 are definitely one and the same argument, reported in two
different books. The three arguments in Job might be counted as one and the same
thought, in spite of small verbal variations; and similarly the two in Jeremiah.
The two arguments in Ps. 94:9 have the same major premise, and might be viewed
as a compound. On the other hand, Ps. 78:20 might be viewed as two arguments
with the same premises but separate conclusions, instead of a single argument
with a compound conclusion. Thus, the total number may be as small as 26, or as
large as 32, depending on how we count. In any event, the above table may be
summarized as follows: Table 5.2
Frequencies of A-Fortiori
Operators.
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