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SOME
PROBLEMS
IN THE RABBINIC
USE
OF THE QAL
VA-HOMER
ARGUMENT
A prominent form
of rabbinic reasoning is the qal va-homer, or a fortiori argument,
which in rabbinic hands reached a theoretical complexity and
exactness that it never achieved in Greek thought. Yet this
kind of reasoning too had a provisional, open-ended quality,
for which it has been hailed by Susan Handelman (though perhaps
not with complete justification) as a forerunner of the approach
of deconstruction.
The qal va-homer
is a reasoning appropriate to legal enquiry, rather than to
natural science, but this does not mean that it is unscientific.
It is a logic of analogy, not of classes or sets (the subject-matter
of Aristotelian logic). It controls the rabbinic basic legal
enquiry, which is to consider different human situations and
decide how alike or unlike they are, and thus how far legal
conclusions can be transferred from one situation to another.
The key phrase in qal va-homer arguments is usually 'all the
more so' , introducing a conclusion. If a conclusion is true
in a weak situation, it is true 'all the more so' in a strong
situation.
To give a simple
example: if a moderately good child deserves a sweet, what does
a very good child deserve? Someone might answer, 'Two sweets',
but this, in rabbinic thinking, would be wrong. The correct
answer is, 'All the more so, a very good child deserves one
sweet.' One must not go beyond the terms given in the premises,
or one would be landed in uncertainty. This is the principle
known as dayyo ('sufficient for it'), [in full, dayyo lav'o
min ha-din lihyot ke-nidon - note that here din means 'conclusion'
while nidon means premise; the transliteration, often found,
nadon is incorrect, as this is Biblical, not Mishnaic, Hebrew,
see Jastrow] and it is this that lifts the qal va-homer from
the status of rhetoric to that of science.(1)
The a fortiori argument is found in Greek rhetoric (e.g. Paul's
Epistles, where the argument is conducted in Greek rhetorical
style, without regard for the rule of dayyo)(2)
but was never isolated or identified as a fully valid mode of
argument in Greek theory of logic. It was Christian scholastics
who gave it its Latin name, but did not enunciate the principle
of dayyo.
A biblical source
was found both for the qal va-homer argument itself and for
the rule of dayyo . This was the incident of the punishment
of Miriam by leprosy, when God argues as follows: 'If her father
had but spat in her face, would she not be ashamed seven days?
Let her be shut out from the camp seven days, and after that
let her be received in again (Numbers 12:14)'. The argument
may be paraphrased as follows: if offending a father (a relatively
light thing) is punished with banishment for seven days, offending
God (a relatively heavy thing) should be punished all the more
so with banishment for seven days. The Torah here provides an
impeccable qal va-homer, studiously refraining from adding any
days to Miriam's punishment beyond the number yielded by the
rule of dayyo.
An example of qal
va-homer argument in rabbinic literature is the following (b.
Bava Metzia 95a). It is stated in Exodus 22:14 that a borrower
must pay the value of the borrowed article to the owner if it
is destroyed or (in the case of an animal) dies. But what if
the article or animal is stolen? Scripture does not tell us
explicitly, but a qal va-homer argument yields the answer, by
analogy with the case of a paid guardian:
1. A paid guardian
is free from payment if the article is destroyed, but is liable
if it is stolen (Exodus 22:10-12).
2. Therefore, all the more so, a borrower, who is liable if
the article is destroyed, should be liable if it is stolen.
The literal meaning
of qal va-homer is 'light and heavy'. The argument only works
if there are two terms, one of which is 'heavier' (i.e. stronger)
than the other. In this case, it is established that a borrower
is 'heavier' (has more responsibility) than a paid guardian.
This is proved from the Torah, but it also may be a matter of
common sense. If you do someone a favour by allowing him the
use of your property without payment, then you expect a higher
standard of obligation and of recompense, in case of a disaster,
than from someone who was not receiving a favour, but was merely
looking after the object as a job, without being allowed personal
use of the object. On the other hand, one might argue just the
opposite: a person who is being paid to look after an article
should be more vigilant than a person who is not being paid.
This is the kind of refuting argument that is often used in
the Talmud, which is by no means inclined to accept every proposed
qal va-homer argument. In the present case, the refuting argument
would not get very far, since the Torah itself clearly regards
the borrower as more liable than the paid guardian; but in many
cases, this is not so clear, so there is much room for discussion.
The qal va-homer reasoning is open-ended, in that it depends
on a distinction between 'light' and 'heavy' that is always
open to question. This aspect, however, does not invalidate
this type of reasoning, but differentiates it from the mathematical
or logical kind of reasoning, where intuition or grasp of human
values play no part. It is this undetermined character of the
qal va-homer argument that leads Susan Handelman to see it as
in accordance with deconstructionist thinking. However, she
lays no stress on the more formal and strict aspect embodied
in the rule of dayyo.(3) There
are also other kinds of doubt that may enter into a qal va-homer
reasoning. An interesting example is this disagreement between
Rabbi Tarfon and his fellow-rabbis, recorded in the Mishnah:
If an ox caused
damage by 'horn' in a public domain, its owner pays half-damages;
but if in a private domain, Rabbi Tarfon says, 'Full damages',
but the Sages say, 'Half damages'. Rabbi Tarfon said to them,
'In the case of 'foot' and 'tooth' there is leniency in the
public domain (no damages imposed) and stringency in the private
domain (full damages): therefore in the case of 'horn' where
there is stringency in the public domain (half-damages) [this
refers to the first two occasions of damage by `horn'; on
the the third occasion, the animal becomes `confirmed' as
aggressive , and its owner becomes liable to full damages,
since he should have taken more care over the animal; `foot'
and `tooth', however, are regarded as damage to be expected,
and therefore the owner of the animal is fully responsible,
except when the goods damaged have been carelessly left in
the public domain] , should not there be stringency (equal
to that of 'foot' and 'horn') in the private domain?' They
answered, 'It is enough if the inferred law is as strict as
the law from which it is inferred: if 'horn' pays half-damages
in the public domain, it should pay the same in the private
domain.'
He said to them, 'My inference is not from 'horn' to 'horn'
but from 'foot' to 'horn'. If in the public domain there is
leniency in the case of 'foot' and 'tooth' and stringency
with 'horn', then if there is stringency for 'foot' and 'tooth'
in the private domain, is it not logical that there should
be stringency in the private domain for 'horn'?'
They answered, 'It is enough if the inferred law is as strict
as the law from which it is inferred: if 'horn' pays half-damages
in the public domain, it should pay the same in the private
domain.'
It should be noted
that this argument is not about the validity of the principle
of dayyo in qal va-homer arguments, as some scholars have mistakenly
thought. Both Rabbi Tarfon and his opponents the Sages accept
not only the validity of qal va-homer, but also the validity
of its limiting principle of dayyo. Where they differ, in this
instance, is how to draw up the list of terms involved in the
reasoning. The Sages do not want to admit 'foot/tooth' as one
of the two terms in the reasoning (though they still lie in
the background as providing the basis for the light/heavy dichotomy);
instead they wish to confine the main steps of the reasoning
to 'horn'- the two terms involved are 'horn-in-the- public-domain'
and 'horn-in-the-private-domain'. Rabbi Tarfon, however, wishes
to extend the basic reasoning to 'foot/tooth' (they may be regarded
as one term here, since their law is identical in this context).
The two terms of his reasoning are thus 'horn' and 'foot/tooth',
and the distinction between public and private domain is applied
to both terms. Thus Rabbi Tarfon is not admitting that he is
making an unjustified leap from 'half-damages' to 'whole-damages'
in the case of 'horn'. He is moving from 'whole-damages-in-the-private-domain'
(in the case of 'foot/tooth) to 'whole-damages-in-the-private-domain'
(in the case of 'horn'). The Sages, however, see something illegitimate
about this move, since, in the process, 'horn' has been surreptitiously
promoted from 'half-damages' to 'whole-damages', which appears
to be a breach of the principle of dayyo. We see from this that
in a qal va-homer argument there may sometimes be an uncertainty
arising from the choice of appropriate terms. This choice of
terms may be a matter of intuition, rather than strict logic,
and thus one person's valid qal va-homer may be another's fallacy.
This does not mean that this method of argument should be condemned
as subjective, but only that it belongs to the area of rationality
rather than strict logic. A method of reasoning can be enormously
useful even if it gives rise at times to irreconcilable disagreements.
The 'how much more so' is a relation of likeness which depends
on an if, not an is, and therefore conclusions are always relative
and are subject to further interpretation and application. There
are no categorical statements or proofs in a demonstration which
preclude further discussion. The if always remains apparent,
and subject to further revision and extension'.(4)
There is, after all, a way to reconcile such differences among
people who are not too dogmatically attached to their own opinions
- by majority vote. In this instance, the vote went against
Rabbi Tarfon, and he no doubt accepted the decision in practice,
though there was nothing to stop him from continuing to hold
his opinion in theory.
Thus rabbinic logical
theory anticipates modern scientific theory in some respects
(especially in the binyan 'av) but in other respects (especially
the qal va-homer) it enters a region of logic that transcends
the usual parameters of Western logic. The Amoraic discussion
of the mishnah (b. Bava Qamma, 25a) must be discounted, since
it shows no comprehension of the logical force of the dayyo
principle. Instead, it imagines that the rule is an arbitrary
fiat of the Torah, by which the conclusion of a qal va-homer
reasoning is cut in half (why by precisely a half is not explained).
Thus in the case of Miriam (the proof-text, Numbers 12:14),
it was really to be expected that God would banish her for 14
days (twice the number of days she would have expected from
an angry human father), but the Torah cut this expected number
by half. The Gemara then explains that Rabbi Tarfon, while acknowledging
the rule of dayyo, had a variant view of it which would excluded
the present case (he considered that a qal va-homer that, by
the application of dayyo, yields a result already derivable
from other sources is not subject to the rule of dayyo). This
implausible account ignores totally the plain reason which Rabbi
Tarfon himself gives in the Mishnah: that he was using different
terms as the basis for his reasoning from those used by the
Sages. It ignores also the fact that Rabbi Tarfon's expressions
in the Mishnah show that he is not arguing that this instance
is exempt from the rule of dayyo but, on the contrary, that
he is bringing it into the rule. It seems that in the Amoraic
period the rationale of the dayyo rule, perfectly understood
in earlier times, had been lost. In earlier times, too, the
derivation of the rule from Scripture (if made, which is doubtful)
was not intended to give it the status of an arbitrary fiat,
but to give authoritative approval to a deliverance of reason.
Unfortunately, medieval commentators on the Mishnah reproduce
the Amoraic discussion.(5)
Heinrich Guggenheimer ( pp. 181-85) gives a cogent account of
the dayyo rule in terms of pure logic, saying that, in virtue
of this rule, the qal va-homer argument is 'an admirable solution
(the only one known to me) of the problem of making an analogy
an exact reasoning'. Guggenheimer also gives a rendering of
the qal va-homer in the terminology of modern mathematical logic.
He does not mention, however, the Amoraic discussion which takes
the rule of dayyo out of the realm of logic, or the considerable
medieval discussion based on b. Bava Qamma 25a.
THE PARODIC QAL VA-HOMER
Perhaps because
of the flexible, open-ended nature of the qal va-homer argument,
we find in the rabbinic sources a rather surprising phenomenon
- instances of the argument which are not meant to be taken
seriously, and comprise a kind of parody of the argument. An
example is found in b. Sanh. 17a. Here it is said that one of
the qualifications of a member of the Sanhedrin was the ability
to prove that the body of a reptile (sheretz) was clean, i.e.
did not convey ritual impurity. This would seem an impossible
undertaking, since the Torah says explicitly that it is unclean.
However, in response to the assertion, Rav offered to prove
this impossible proposition by means of a qal va-homer argument.
It ran as follows: the dead body of a snake does not convey
impurity. Yet a snake is the means of spreading impurity, for
it causes many deaths. How much more so should a reptile (which
is harmless) be regarded as not causing impurity! This same
argument is attributed to Ravina in b. Eruvin 13b . The Gemara
immediately refutes this argument by denying the 'heaviness'
of the heavy term. Being a cause of impurity indirectly by causing
death has nothing to do with causing impurity by direct contact.
Otherwise, we would have to regard a thorn as a cause of impurity
by contact, since it may cause death to someone who becomes
impaled on it. Clearly, this qal va-homer argument was meant
simply as an exercise, perhaps even an exercise in how to refute
a faulty qal va-homer.
Sometimes, however,
constructing a faulty qal va-homer deliberately was regarded
with distinct disfavour, not merely as an interesting exercise.
It is recorded that a certain rabbi (Rabbi Jose ben Taddai of
Tiberias) was actually excommunicated for presenting a frivolous
qal va-homer argument, since this was held to bring rabbinic
methods of argument into disrepute (Derekh Eretz Rabba, 1).
The condemned argument was as follows: I am forbidden to marry
my daughter; yet her mother is permitted to me. All the more
so, I should be forbidden to marry the daughter of someone who
is forbidden to me. My neighbour's wife is forbidden to me;
therefore I should be forbidden to marry her daughter. Therefore
all marriages should be forbidden except to the daughters of
unmarried mothers, widows or divorced women. No formal refutation
of this argument was offered: the response was to kick its perpetrator
out of the academy!
Of course, it is
possible to produce parodies even of syllogistic arguments -
many such were produced in the Middle Ages. Perhaps we should
attribute such parodies merely to high spirits, not to any flaw
in the type of argument itself. But such arguments do point
to features of the argument which require care when the argument
is used seriously. There is, however, a certain acknowledgment
of the vulnerability of the qal va-homer in general in the dictum
that it should never be used to impose an extra penalty not
explicitly mentioned in the Torah (`ein `oneshin min ha-din,
b. Sanh. 54a and frequently). The qal va-homer is acknowledged
to be a purely human reasoning, and as such to be always open
to criticism and to have limited authority.
QAL VA-HOMER IN
AGGADAH
An apparently glaring
infringement of the rule of dayyo is in Mishnah Makkot, 3:15:
Moreover R. Hananiah
ben Gamaliel said: If he that commits one transgression thereby
forfeits his life, how much more, if he performs one religious
duty, shall his life be given to him!(6)
This is a very feeble
argument, and it also seems inconsequential, since it does not
show any connection with R. Hananiah's immediately preceding
remark that those who are condemned to 'cutting off' (karet)
can escape this punishment by undergoing flogging (malqut).
Rashi therefore feels constrained to provide an elaborate explanation,
based on the notion that reward for good deeds is much greater
(at least 2000 times greater, he argues on the basis of a proof-text)
than punishment for transgression. Rashi thus seems to imply
that the usual rule for a qal va-homer can be ignored, since
there is such a gap between the two terms 'transgression' and
'performance'. This, however, might possibly be granted if the
conclusion echoed the premise, but it does not. The premise
speaks of forfeiting life, and the conclusion speaks of gaining
life. No amount of weighting can turn a negative premise into
a positive conclusion. If another method of argument were used
(instead of the qal va-homer) some semblance of consecutive
reasoning can be achieved, e.g. If a man who commits a transgression
forfeits his life, it seems reasonable that the opposite behaviour,
the fulfilment of a commandment, will produce opposite results,
namely the gaining of life, especially if we know that reward
is always far greater than punishment. But this reasoning by
opposites is not a qal va-homer, and Rabbi Hananiah makes it
crystal clear (by his use of 'how much more') that he is attempting
a qal va-homer.
Another line of
exegesis (see Bertinoro on the Mishnah) tries to provide some
continuity between Rabbi Hananiah's first and second sayings,
such continuity being demanded by the conjunction ve linking
the two sayings [in the Gemara Mishnah; the conjunction may
have been omitted in editions of the Mishnah under the influence
of exegetes, also quoted by Bertinoro, who denied any continuity
between the two sayings of R. Hananiah]. This interpretation
sees the one 'who fulfils the commandment' as none other than
the one who transgressed a karet law, but later repented and
accepted flogging as his punishment, thereby escaping the heavier
punishment of death by the hand of God. Rabbi Hananiah's second
saying thus becomes: If one who transgresses forfeits his life,
how much more so shall one who accepts punishment (thereby performing
a commandment) escape with his life. Here there is certainly
some continuity, but the faultiness in the qal va-homer argument
has not been remedied. The negative in the premise has turned
into a positive in the conclusion, and the argument, if valid,
is an argument by opposites not by qal va-homer.
I suggest a very
simple solution to all these problems. The expression notel
nafsho has been wrongly translated by all commentators as 'forfeits
his life', but is much better translated as 'receives his life'.
The verb natal can mean either 'to remove' or 'to receive'.(7)
If the meaning here is 'remove', then the expression should
be notelin nafsho, 'they remove (or `one removes') his life',
for the singular verb notel would signify that he takes or removes
his own life, and noone is suggesting that we are concerned
here with suicide. I am suggesting, in other words, that the
expression notel nafsho means the exact opposite of what commentators
have thought it to mean. With this correction, the difficulties
of continuity and logic disappear. The translation of R. Hanania's
second saying now becomes: 'If he that commits one transgression
(i.e. the transgressor of a karet law) receives his life (i.e.
has his sentence commuted from death by the hand of God to flogging),
how much more so will one who performs a commandment be given
his life!' This is a perfectly valid qal va-homer argument,
since no term in the conclusion fails to appear in the premise.
Also, the continuity is also excellent, since R. Hanania's second
observation is indeed a reflection based on his first. The unconvincing
idea (quoted by Bertinoro), aimed at continuity, that it is
the transgressor who is the performer of a commandment is eliminated.
The transgressor is indeed a transgressor, yet he preserves
his life; how much more so should someone who is not a transgressor
but a performer of a commandment preserve his life!
It may be objected
that if the two expressions notel nafsho and yinaten lo nafsho
have identical import, why is the expression varied in this
way? The reason may be merely stylistic. The person who, against
the odds, having been condemned to death, is reprieved, snatches
at this unexpected relief and is made the subject of an active
verb of receiving. The person who has deserved reward waits
for his due without desperation and is content to have it bestowed
on him. This variation in expression does not affect the logic
of the argument.
On the other hand,
it may be objected that the rules of the qal va-homer, and especially
the rule of dayyo (that the conclusion must not contain any
term not contained in the premise) is not so strictly applied
in aggadic as opposed to halakhic reasonings, and that therefore
R. Hananiah's argument should not be subjected to such severe
criticism. There is truth in this, and an example of what appears
somewhat loose aggadic qal va-homer reasoning is to be found,
as it happens, in this very same mishnah. R. Shimon ben Rabbi
reasons: abstaining from blood, which causes revulsion, brings
reward; all the more, abstaining from robbery and incest, which
the soul longs for, should bring reward for all generations
to come up to the end of the world. The last part of this reasoning
constitutes a breach of dayyo, for nothing was said in the premise
about all generations to come. Yet in this reasoning, faulty
as it is by halakhic standards, the actual terms are not changed
from premise to conclusion. There is only an intensification
of the conclusion, in an enthusiastic, homiletic style. Even
in aggadic reasonings, the rules are never so flagrantly breached
as in R. Hananiah's saying, in its usual interpretation. It
is therefore justifiable to look for another interpretation.
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