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JUDAIC LOGIC© Avi Sion, 1995. All rights reserved. Chapter
11.
THE THIRTEEN MIDOT (II).
In this second part of our analysis of the Thirteen Midot of R. Ishmael,
we shall deal with Rules 8-11 and 13.
Broadly put, the five remaining hermeneutic principles, which we shall
label 'harmonization rules', serve to resolve apparent redundancies,
discrepancies, doubts, tensions or inconsistencies between propositions. In some
cases, their results are identical with those of formal logic; in some cases,
they favour a course which is only a possibility among others according to
formal logic; and in some cases, they suggest a course which formal logic would
not have recommended. Note that these principles constitute units of
thought-process, which may be operative individually in simple situations, or
eventually successively in complex combinations.
Note that my formal analysis in this section is based on a possibly
limited sample, drawn from the derivative literature on the topic that I have
consulted. The few examples which are there presented as representative of the
Rabbinic tradition may not be fully representative of that tradition.
Furthermore, even if these examples are fully representative, it remains
possible, indeed likely, that direct and thorough empirical research into the
Talmud and other Rabbinic literature would reveal a much larger variety of forms
of thinking, legitimate or not, in actual use[1].
The observations of the Rabbis of the past 2,000 years interested in these
matters, and their conceptualizations and classifications of what they noticed,
need not be taken for granted. On the contrary, as we show here, their failure
to use formal methods make it very probable that they missed some of the
available data and misjudged the data they had. Much work can still be done, and
it is hoped that my initial efforts will be pursued further by others.
It should be noted that none of the harmonization rules here dealt with
are mentioned in the Soncino index[2].
So I have no inkling how often these rules are actually used in the Talmud.
Our interest here, note well, is not in the legal issues as such, but in
the logical structure of the exegesis. I have no Halakhic ax to grind; my
purpose is to institute a methodology for clarifying, classifying and evaluating Rabbinic
exegesis, with reference both to its theoretical and practical aspects (that is,
R. Ishmael's rules and their explanation by Rabbis, on the one hand, and
examples of their application in Talmud and other Rabbinic literature, on the
other hand). Our empirical data consists of traditional pronouncements and
actions, but our analytic approach to this data will be strictly objective and
scientific.
We shall now deal with the first three (actually, four) of the
hermeneutic principles which begin with the phrase kol davar shehayah bikhlal veyatsa... (Rules No. 8-10), which means literally 'anything which was in a
generality and came out...'[3].
Broadly put, in formal terms, these rules are concerned with the following
exegetic situation: Given: All S1 are P1
(major premise), and All S2 are P2
(minor premise), where All S2 are S1,
but not all S1 are S2, (subjectal
premise)[4], and P1 and P2 are in
some relation f{P1, P2}
(predicatal premise). What are resulting
relations: between S1 and P1,
and between S2 and P2, other than the above given; and between S1 and
P2, and between S2 and P1 (conclusions)?
This, then, concerns two subalternative subjects (S1 and S2, whose
genus-species relation is defined in what we shall call the 'subjectal
premise'), which are found in Scripture separately related to two distinct
predicates (P1 and P2, whose relation is defined in what we shall call the
'predicatal premise') [5].
The given relation of the genus (S1, the major subject) to its predicate (P1,
the major predicate) will be called the major premise; while that of the species
(S2, minor subject) to its respective predicate (P2, the minor predicate) will
be called the minor premise. The question asked is, what information can be
inferred concerning the various subjects and predicates (conclusions)? For
us, this question is two-fold: (a) what conclusions does Rabbinic
tradition propose, and (b) what conclusions does
pure logic propose; comparing these sets, we might find them to coincide or
intersect or entirely diverge.
The major and minor premises are given explicitly in Scripture
(presumably, though it is conceivable that they be only implicit, provided they
are derived from the text purely
deductively). The subjectal premise may be textually given (or, again, strictly
implied), or, as often happens, it may simply be obvious (natural knowledge);
likewise, for the predicatal premise. The form of the latter relation, f(P1,
P2), varies from rule to rule, and of course will affect the conclusions drawn.
One of P1 and P2 may be subordinate to the other, or they may imply each other
(being identical, or logically implicant); or P1 and P2 may be otherwise
compatible (subcontrary or unconnected), or they may be incompatible
(contradictory or contrary).
As for the 'conclusions' proposed, we shall see how they vary, and are
generated, as we proceed; note that they may be inductive, as well as deductive.
It should be remarked that in Rabbinic exegesis, one or more of the premises may
be altered in the course of the argument: an initially general proposition may
end up as contingent or as exclusive; such changes must be counted as
'conclusions' (or part of the overall 'conclusion'), too.
Needless to say, the Rabbis never
formulated their rules in such formal terms; I have expressed them in this
manner to clarify them and evaluate them with certainty. R. Ishmael's
definitions (roughly, but passably) specify the major, minor and subjectal
premises, as well as (though not always clearly) the putative 'conclusions', in
ordinary language. But they do not specify, or do not more than hint at, the
predicatal premises, which must be more or less guessed at, with reference to
traditional examples; our hypotheses in
this regard are confirmed by the symmetry and exhaustiveness of the combinations
they postulate. As for logical evaluation, R. Ishmael and his contemporaries
and successors do not make any effort at, or demonstrate any skill in, formal
analysis of the processes; we will endeavor to fill the gap.
Furthermore, I very much doubt that these hermeneutic procedures were
mechanically applied wherever their respective formal conditions were found;
rather, I suspect, they were treated as a set of tools, which could be used, or
ignored, as convenient, provided the Rabbis all approved. It is hard to imagine
how they could proceed otherwise, because as we shall see the conclusions they
draw are more often than not logically unnecessary (if not, in some contexts,
illogical); whence it follows that inconsistencies are bound to arise in some
cases, calling for a retreat from previous exegetic acts which caused the
trouble. But to prove this prediction, one would have to study the Talmud in
much more detail than I have done; ideally, one would need a well-ordered list
of all the cases where exegesis took place.
Now, by means of syllogism, we can without further ado make the following
inferences (side conclusions):
From the minor and subjectal premises, Some
S1 are P2 (mood
3/AAI).
From the major and subjectal premises, All
S2 are P1 (mood
1/AAA).
Yet other formal syllogisms may be possible, depending on the predicatal
premise involved; such eventual inferences will be pointed out as we proceed.
In some cases, these various deductive inferences lead to no antinomy and
are accepted by the Rabbis, though they may go beyond them and recommend some
inductive process (for instance, an a-contrario
reading or a generalization). In some cases, they lead to no antinomy, but are
refused by the Rabbis (for reasons we shall see), who inhibit them in some way
(for instance, by means of an anti-literal reading of the text or a
particularization). In some cases, deductive logic from the given data results
in a conflict, which must be resolved; and here again, the Rabbis may favour one
reconciliation over another.
We have above considered, and will continue to do so, only the copulative
forms of kol davar shehayah bikhlal;
that is, forms involving categorical
propositions. However, it should be clear that implicational forms of same are equally conceivable; that is, forms
involving conditional propositions.
Both types are used in Rabbinic examples, though perhaps the former more so than
the latter. As shown below, the overall format of implicationals is similar to
that of copulatives; all results are presumably the same, mutadis
mutandis. We need not, therefore, treat both types; nor will we do so, to
avoid repetitions. The significant difference between them is that, while
copulatives involve four terms,
implicationals involve four theses.
Instead of the subjects (S1, S2) and predicates (P1, P2), we are concerned with
antecedents (P1, P2 - not to confuse with the preceding symbols for Predicates;
here P stands for Proposition) and consequents (Q1, Q2), respectively. Thus, for
the record, we have, broadly put: Given:
If P1 then Q1 and If P2 then Q2
(major and minor premises), where P2 implies P1, but P1 does not imply P2
(antecedental premise), and
Q1 and Q2 are in some relation f{Q1,
Q2}
(consequental premise). What
are resulting relations: between
P1 and Q1, and between P2 and Q2, other than the above given; and
between P1 and Q2, and between P2 and Q1
(conclusions)?
The common phrase "kol davar
shehayah bikhlal veyatsa..." can now be interpreted more precisely.
"Kol davar" refers to the minor term (S2); "shehayah bi-,"
to the latter's subsumption under the major term (S1, through the subjectal
premise 'S2 is S1'); "-khlal,"
to the major premise (S1 is P1); and "veyatsa,"
to the minor premise (S2 is P2). Note that in all these rules, the underlying
subject is, normally, a person or persons (even if a beast, plant or mineral is
ever mentioned, the ultimate subject, to whom any law might be addressed, is
human). The effective predicate is clearly a law or set of laws, by which we
must in this context understand some prescription, prohibition, permission
and/or exemption. Let us now look at the hermeneutic principles concerned in
detail. Y
Rule No. 8 completes the said
common phrase with the words ...min haklal lelamed, lo lelamed
al atsmo yatsa, ela lelamed al haklal kulo yatsa. Translated literally,
the principle states: "anything which was in a generality and came out of
the generality, is to be taught: it is not to be taught 'about itself, it came
out'; but it is to be taught that 'about the whole generality, it came
out'".
We may suggest the following interpretation: "A subject (S2), by
virtue of its subsumption under another (S1), was included in a generality (All
S1 are P1); then it (S2) was treated distinctively (All S2 are P2). In such
case, the distinctive predicate (P2) is to be taught: do not just teach it (P2)
with reference to the singled-out species (S2), but also teach it (P2) with
reference to the whole genus (S1) [so
that All S1 are P2]".
Thus, "atsmo" refers to the
minor term (S2); "yatsa," to
the minor predicate (P2); and "haklal
kulo," to the major term (S1).
Although R. Ishmael's principle itself does not specify the following
point, judging by some examples given in the literature,
the rule of lelamed concerns cases
where
the minor predicate P2 is subordinate to the major predicate P1. Thus,
in this context, the predicatal premise undefined in our earlier general formula
is: All P2 are P1, but
not all P1 are P2
(predicatal premise), and the
main conclusion apparently suggested by R. Ishmael is:
All
S1 are P2 (main conclusion).
According to
deductive logic, the said predicatal premise does not provide us with any
additional inferences, other than the ones already obtained by other means (see
above). Therefore, R. Ishmael's suggested conclusion is at best inductive.
Deductive logic allows that a genus may have a generic predicate and a species
of that genus have a more specific predicate; it does not insist that the genus
follows suit and have the more specific predicate, too. R. Ishmael, on the other
hand, apparently considers that, with regard to the Torah, the minor premise, or
more precisely, the implication of the minor and subjectal premises,
'Some S1 are P2,' has to be generalized to 'All S1 are P2'.
The example, reported by Bergman, on which I based the above
formalization is: Exod. 22:18 sentences a sorceress to death (generality), while
Lev. 20:27 sentences a male or female medium or necromancers ("in whom is a
ghost [ov] or familiar spirit [yidoni]")
to death by stoning (particularity); whence, granting mediums and necromancers
to be included in the category of sorceresses (the textual basis for this
subsumption is not given, note; also, commentators include sorcerers, arguing
that the feminine is used only because most are women), it is inferred by such lelamed
exegesis that sorceresses (of all kinds) are to be stoned. I noticed that the
predicate change consists in adding a further precision (by stoning) to the
original predicate (death sentence); and assumed this to be a sine
qua non condition of application of this rule.
Note well that, according to natural logic, R. Ishmael's suggested
conclusion is not impossible (no antinomy ensues from it); it is just a
non-sequitur (not formally inevitable). The minor premise's implication is lav
davqa, and may with equal possibility turn out to be general or contingent.
Also, no redundancy would be involved in a davqa
reading of 'Some S1 are P2,' contrary to R. Ishmael's generalization, i.e. such
that 'Some S1 are not P2'. The suggested course is therefore an artificial one,
recommended by a religious authority claiming Divine sanction. It is not
essentially an inference, but a proposal that the minor premise not
be read as exclusive.
Why the text did not simply say 'All S1 are P2' (instead of 'All S2 are
P2') in the first place, if that is what it intended, is not explained; perhaps
it would have been contextually inappropriate, suggesting false inferences from the
surrounding context. Also, why the proposed inference is made, rather
than reading the particularity as an exceptional provision, so that species
of S1 other than S2 are not P2, though
they are P1, is not explained. I would predict that the alternative reading of
the particular, as a contingent, sometimes does occur in Rabbinic practise; but
I have not searched for examples[6].
In any case, deductively, either outcome is formally acceptable; the proposed
mood can only therefore be considered as an inductive
preference, claimed as peculiar to Biblical exegesis. Y
Bergman informs us that above is one version of the rule of lelamed,
where the particular law teaches "about itself as well as the general
law". In another version, according to him, it teaches (not about itself
but) "only about the general law". From the example he gives, however,
I would strongly disagree with his rendering of the latter version, while quite
willing to grant that it exists in Rabbinic literature. But before discussing
our differences, let me present this additional version in formal terms.
Let us first look at Bergman's example. Lev. 22:3 sentences he who
approaches holy offerings while impure to the 'cut-off' (excision, karet)
penalty (generality); Lev. 7:20 sentences he who eats peace-offerings while
impure to the same penalty (particularity); peace-offerings are listed as among
other holy offerings in Lev. 7:37 (to be precise, this verse does not mention
the general category of holy offerings, but only lists various kinds of
offerings: burnt, meal, sin, guilt, consecration and peace). It is thence
inferred that the consumption (or approach?) of offerings of lesser holiness
than peace-offerings, such as those for Temple maintenance (Bergman does not
specify where in the text this distinction in degree of holiness is
established), are not subject to
cut-off. [7]
Although neither R. Ishmael nor his successors specify the following
point, judging by some examples given in the literature,
the variant rule of lelamed concerns
cases where
the major predicate P1 is subordinate or identical to the minor predicate P2.
Thus, in this context, the predicatal premise undefined in our earlier general
formula is: All P1 are P2
(predicatal
premise), and
the main conclusion apparently suggested by Rabbis is:
Some S1 are not
P2
(main conclusion).
Now, let us consider the syllogistic inferences we can make given this
predicatal premise; there is only one, shown below. Notice that the result below
is the same as the main conclusion of the original version of lelamed,
except that here it is obtained by deduction, without need of an inductive
extension.
From the major and predicatal premises, All
S1 are P2 (mood
1/AAA).
Note that 'All P1 are P2' does not tells us whether all P2 are P1 or not
all P2 are P1; either possibility is acceptable in the present variant,
presumably. In the case where P1 and P2 imply each other (i.e. are identical or
logically equivalent), nothing more can be deduced from the given premises.
There is a formal exception
to the application of the second variant of lelamed,
namely in situations where the rules of the klalim
uphratim type are applicable. For the compound propositions 'G and S are P'
and 'S and G are P', where S is subordinate to G, are each formally equivalent
to a conjunction of the two simple propositions 'G are P' and 'S are P'. And
according to R. Ishmael, the conclusions to be drawn in these situations are,
respectively, 'Only S are P' (davqa,
by rule No. 4) and 'All G are P' (general, by rule No. 5). It follows that, when
we come across subalternative subjects with the same predicate, we must first
decide which rule is applicable. According to Rashi (Shevuot, 7a), the klalim
uphratim rules would be used when the subalternative subjects are close to
each other in the text (in the same verse), while the said variant of lelamed
would come into play when the propositions are relatively far apart. The
conclusion obtained is different from that of lelamed
variant two, note well, in the case of 'SG are P'; but in any case, the process
as such is different even in the case of 'GS are P'. Similar comments apply to
other forms of klalim uphratim.
We thus see that, in this second variant of lelamed,
the 'conclusion' postulated by the Rabbis, 'Some S1 are not P2,' is precisely
the contradictory of the conclusion
required by deductive logic (taking the premises at their face-value)! I am
therefore very tempted to entirely reject this form of reasoning as antinomial.
In any case, I would bet that this procedure is not invariably followed in the
situation concerned, since it is very likely to lead to eventual
inconsistencies; but I have not sought for demonstrative examples. However, we
must try and understand what prompted the Rabbis to propose such twisted logic,
and how it can be formally expressed.
Apparently, what prompted the Rabbis to opt for such a convolution, is
the fact that the major predicate (P1) is less extended than the minor predicate
(P2), or of equal extension, whereas the major subject (S1) is more extended
than the minor subject (S2). Why would Scripture do so, rather than say 'All S1
are P2' in the first place, knowing that we could automatically draw such an
inference? Therefore, the Rabbis supposedly reasoned, Scripture does not want us
to draw such an inference.
With regard to logical means for such a position: granting the predicatal
premise, which distinguishes this midah
from the others and defines it, the only way we can prevent the conclusion 'All
S1 are P2' from being drawn, is to deny the major premise, 'All S1 are P1'. Note
well that if we do so and say:
Some, but
not all, S1 are P1
(particularization of major premise), then the
side conclusion that 'All S2 are P1' no longer follows, and the relation between
S2 and P1 remains problematic.
Objections which can be raised to this Rabbinical position are the
following. If the Rabbis are surprised in the present case that the text did not
immediately say 'All S1 are P2,' why were they not equally surprised in the
previous case that the text did not directly say it, if that was its intention?
Furthermore, in the case where P1 is subordinate to P2, there could be a contextual
reason for giving the major premise a more specific predicate, to avoid some
unwanted inference (such as a first variant lelamed
from another minor premise) which could otherwise be drawn from a generic
predicate. In the case where P1 and P2 are one and the same, the Rabbinical
surprise can only be due to the different extensions of the subjects, S1 and S2;
here again, a contextual explanation could be adduced: it is conceivable that
undesirable inferences might have been drawn from a misplaced generic subject or
specific subject.
Gd, the writer of the Torah, may have thought: 'I can allow Myself such
wording, since the Rabbis will recover My final intention eventually anyway, by
syllogism through the predicatal premise.' The mere facts that the text is
considered as written by a conscious Being and that syllogism is easy, does not
prove that Gd intended what the Rabbis say He intended. An alternative course is
sustainable, so their discomfort with the apparent redundancy was not justified.
So much for evaluation; let us go back to description.
In the new variant of lelamed,
the putative 'conclusion' denies the major premise. It is not a deduction (since
in deduction, a conclusion can never contradict a premise), nor a
particularization in reaction to textual inconsistency (since there was no
contradiction between the premises, no conflict calling for reconciliation).
Strictly-speaking, therefore, it cannot be called an inference, but at best a
reading motivated by a vague discomfort with the logistics of the text. The
Rabbis arbitrarily (without formal motive) reject literal reading of the major
premise, 'All S1 are P1,' and tell us that it is not davqa
general, but really contingent. Their alleged conclusion, that 'Some S1 are not
P2,' is the cause, rather than the effect, of such reading. The anti-literal
reading becomes necessary to prevent absurd consequences, only once the desired
'conclusion' has been artificially chosen; furthermore, that 'conclusion' does
not necessarily follow such reading, it is only made possible by it.
Thus, the second variant of lelamed
ends, rather than starts, with particularization of the major premise; no
process is involved in getting to its main conclusion. Note that, in this
context, the syllogistic inference from the original major premise (All S1 are
P1) and the supposed predicatal premise (All P1 are P2), namely 'All S1 are P2',
is Rabbinically interdicted.
It follows incidentally, from the main 'conclusion', as the Rabbis claim,
that 'there is at least one species of S1 unlike S2, call it S3, which is not
P2'; i.e. that the minor predicate is applicable only to the minor subject (and
eventually others like it); the trouble with this eduction, however, is that it
adds no concrete knowledge, since it cannot tell us in
what respect other species are 'like' or 'unlike' the given species[8].
In effect, then, though the minor premise as such (All S2 are P2) remains
unaffected, it becomes exclusive:
Only
S2 are P2 (additional
conclusion).
Note well that this exclusive proposition is not formally required as
such, but is approximately true granting some leeway for the subject to expand
somewhat (i.e. 'S2' here may include other species of S1 like S2, but in any
case excludes some species of S1 unlike S2). The syllogistic inference that
'Some S1 are P2', from the minor premise and the subjectal premise (All S2 are
S1), remains valid; and is of course to be conjoined to the Rabbis' conclusion
'Some S1 are not P2', to form a contingent proposition.
To repeat, the proposal of the Rabbis is logically untenable, unless we
doctor the premises in a convenient manner. To prevent
contradiction, the major premise 'All S1 are P1' has to be denied, i.e.
particularized to 'Some, but not all, S1 are P1'. However, this measure does not result in the desired main 'conclusion' being inferred
deductively; it remains a 'foregone conclusion' (a thesis without justification
in the premises, old or new). All that the adjustment of the major premise does,
is render the main 'conclusion' formally conceivable; its preference by the
Rabbis remains an inductive act. This
act would be acceptable to science, if put forward as a tentative hypothesis to
be tested by other data; however, pronounced as a fixed fiat, not open to
review, it becomes, from the scientific point of view, an arbitrary act.
The Rabbis, of course, claim Divine sanction for it; but we must point out that
such a claim is not verifiable by scientific means. We shall leave the matter at
that and move on.
We can now return to criticism of Bergman's formulation. The distinction
between the two variants of lelamed which he proposes is incorrect. In the first variant, we
could, indeed, say that the particular law teaches "about itself as well as
the general law," insofar as the minor predicate is Rabbinically applied to
the major subject. However, it cannot be said, in the second variant, that the
particular law teaches (not about itself but) "only about the general
law". The particular law is in fact unaffected by the process, and the
general law does not come to resemble it. The best we can say is that the
particular law is viewed by the Rabbis as an exception to the general law; it makes the latter cease to be
general. The minor predicate is reserved for the minor subject (and others
eventually 'like' it), and other members of the major subject ('unlike' the
minor subject) are deprived of the minor predicate.
Let us see, now, how we would have to interpret R. Ishmael's lelamed
formula, so that it covers the second variant. To adapt the sentence "kol
davar shehayah bikhlal veyatsa min haklal lelamed lo lelamed al atsmo yatsa ela
lelamed al haklal kulo yatsa", we must read into it something to the
effect that "A subject (S2), by virtue of its subsumption under another
(S1), was included in a generality (All S1 are P1); then it (S2) was treated
distinctively (All S2 are P2). In such case, the distinctive treatment (All S2
are P2) was intended to teach us something. It was not done just to teach us
something about itself (S2) that the species was differentiated (in All S2 are
P2), but also to teach us something [else]
about the whole genus (S1) from which it was differentiated [namely, that Not all
S1 are P2]".
In this modified version, we read the implicit word "else,"
meaning "other than the distinctive treatment," into
the formula, so that the 'conclusion' be different for the genus than it was the
species. Here, "yatsa"
refers to the whole minor premise, rather than to the minor predicate, note.
Thus, we might distinguish the two variants of lelamed,
by labeling the first "lelamed oto hadavar leshar haklal" (teach the same
thing, P2, with regard to rest of the genus, S1), and the second "lelamed
hefekh hadavar leshar haklal" (teach the opposite
thing, notP2, with regard to the rest of the genus, S1). Compare this to
Bergman's differentiation, "as well as the general" and "only the
general," and you can see that he was inaccurate.
Let us now review the technical similarities and differences between
these two versions of lelamed, other than their common grounds with the other rules of the
type kol davar shehayah bikhlal veyatsa.
(a) In both, the predicatal premise, which serves as the distinctive condition
to application of the rule, asserts implication between the predicates; however,
in the first version, which we have called lelamed
oto hadavar, the minor predicate is subordinate to the major
predicate; whereas in the second version, called lelamed hefekh hadavar,
the major predicate implies the minor predicate. (b) The main conclusion of the
first is general positive (All S1 are P2), while that of the second is
particular negative (Some S1 are not P2); they agree, however, that Some S1 are
P2.
Finally, (c) they involve distinct thought-processes: lelamed
oto hadavar proceeds by inductive
generalization of a particular implication of the minor premise (viz. Some S1
are P2), whereas lelamed hefekh hadavar
proceeds by arbitrarily postulating a conclusion contradictory to an implication
of the major premise (viz. All S1 are P2) and consequent reconciliatory
particularization of the major premise itself. Neither process is called-for or
necessary according to natural logic, neither constitutes deduction from the
predicatal premise which prompts it; but the artifice involved in the former is
relatively straightforward, while that involved in the latter is more twisted.
In view of the similar predicatal premises, the traditional
classification of lelamed hefekh hadavar
with lelamed oto hadavar seems sound.
But at the same time, in view of the radical differences in process and
conclusion, we may well doubt that the second variant was intended in the
original definition of R. Ishmael. I suspect its formulation was a later
development, even if it was used unconsciously earlier. It could equally well
have been instituted as a distinct rule of the kol
davar shehayah bikhlal veyatsa type. It resembles the rule of the liton
toan acher, shelo kheinyano type (see below) in that it involves a
particularization of the major premise, though for quite different reasons.
The next two rules (Nos. 9 and 10) continue the common phrase kol
davar shehayah bikhlal veyatsa... with the words ...liton toan acher. We
shall now analyze these. Y
Let us first deal with Rule No. 10,
which is easier. It completes the preceding clauses with the phrase ...shelo kheinyano, yatsa lehaqel
ulehachamir, and may be translated literally as "anything which was
in a generality and came out to posit another thesis, which is incompatible,
came out to lighten and to harden". The expression 'shelo
kheinyano' tells us that the major and minor predicates are, by their very
nature (or by virtue of some other part of the text, perhaps), incapable of
conjunction in one and the same subject. They are not merely different, but
mutually exclusive; there is a radical cleavage between them.
Thus, although neither R. Ishmael nor his successors specify the
following point, judging by some examples given in the literature, the
rule liton toan acher, shelo kheinyano
concerns cases where the major predicate P1 and
the minor predicate P2 are contrary or contradictory. Thus, in this
context, the predicatal premise undefined in our earlier general formula is,
minimally: No P1 is P2
(and No P2 is P1)
(predicatal premise).
Note that this gives a minimal definition of the incompatibility between
P1 and P2 referred to. The bracketed clause is redundant, being implied anyway.
In the case of contradictories, we must additionally say: No
nonP1 is nonP2 (which implies No nonP2 is nonP1). While in the case of
contraries, we must add: Some nonP1 are
nonP2 (which implies Some nonP2 are nonP1).
A comment should be made here regarding compound
predicates. If one predicate X consists of two concepts a + b, while the
other predicate Y consists of only one of these concepts (say, a), without
mentioning the other (b), then three readings are possible[9]. (i)
X = 'a + b' and Y = 'a + b' or
'a + notb'. Here, knowing that either event may actually occur; the result is
that X is included in Y, or in other words, Y is a genus
of X (as well as of some other species, Z = a + notb). Therefore, we would apply
the rule lelamed; opting for the
variant hefekh hadavar if P1=X and
P2=Y, or the variant oto hadavar if
P1=Y and P2=X. (ii)
X = 'a + b' and Y = 'a + b'. Here, we have generalized factor 'b' from
the 'a' in the case of X, to 'a' in all cases, including that of Y; the result
is that X and Y are identical.
Therefore, whether P1=X and P2=Y, or P1=Y and P2=X, we would apply the rule lelamed hefekh hadavar. (iii)
X = 'a + b' and Y = 'a + notb'.
Here, we have generalized from the non-mention
of 'b' with regard to Y, to the actual
absence of 'b' in Y; the result is that X and Y are incompatible[10].
Therefore, whether P1=X and P2=Y, or P1=Y and P2=X, we would apply the rule shelo
kheinyano.
Often, as Bergman acknowledges, Scripture displays a discrepancy, not by
commission (assigning incompatible predicates to subalternative subjects),
but by omission (as just described).
As the above analysis shows, in the latter case, before we can apply one of the
hermeneutic rules, a decision process must be followed[11].
Thereafter, if the compounds involved are found incompatible, we apply shelo kheinyano; otherwise, one of the variants of lelamed.
It is noteworthy that the rule shehu
kheinyano, as defined further on, never comes into play in this context![12]
Now, let us consider the syllogistic inferences we can make given the
said predicatal premise, 'No P1 is P2':
From the minor and predicatal premises, No
S2 is P1 (mood
2/EAE),
From the major and predicatal premises, No
S1 is P2 (mood
1/EAE).
No additional inference is possible with the additional clause (No nonP1
is nonP2) of contradictory predicates, nor with that (Some nonP1 are nonP2) of
contrary predicates, note. Now, comparing these new results to the implications
of the major and minor premises in conjunction with the subjectal premise,
namely 'All S2 are P1' and 'Some S1 are P2', we see that they are respectively
contrary and contradictory propositions. Thus, if, in the text, we come across
subjects in a genus-species relation which have incompatible predicates, we are
facing a situation of formal inconsistency.
This is not an antinomy due to a Rabbinic interpretation, but one inherent in
the text, note well. A formal resolution of the conflict is absolutely required.
It is a principle of inductive logic that harmonization is to be sought
by effecting the minimum retreat from generalities, necessary to restore consistency;
this is the most likely outcome[13].
If it can be shown that the subjects are not subalternative and/or that the
predicates are not incompatible, we are of course no longer in the same
situation and some other process may be appropriate. But, granting that the
subjectal and predicatal premises are correct, the only
way to achieve the required result is to particularize
the major premise. With regard to the minor premise, if it is particularized
alone, a conflict remains; it may of course also be particularized, but that
does not affect the result. That is, logic indisputably demands that:
Some, but
not all, S1 are P1 (resolution
of conflict, leading conclusion). The
proof of what we have just said will now be presented: ·
If we particularize only the minor premise, so that 'Some, but not all,
S2 are P2', and we keep the major premise, then the following sorites remains
possible: 'All S2 are S1' (subjectal) and 'All S1 are P1' (major) and 'No P1 is
P2' (predicatal), therefore 'No S2 is P2'; but the latter conclusion disagrees
with 'Some S2 are P2' (from minor); therefore, we still have an inconsistency. ·
On the other hand, if we particularize only the major premise, so that
'Some, but not all, S1 are P1', and we keep the minor premise, then the
following sorites remains possible: 'Some S1 are S2' (converse of subjectal) and
'All S2 are P2' (minor) and 'No P2 is P1' (converse of predicatal), therefore
'Some S1 are not P1'; and the latter conclusion agrees with 'Some, but not all,
S1 are P1' (altered major); therefore, this measure resolves our contradiction. ·
If we particularize both premises, no such sorites can be constructed.
The results are equally acceptable; but this measure involves a more radical
reaction than necessary, it goes beyond logical necessity. Thus, the minor
premise might or might not be denied; what counts is denial of the major
premise. The difference in behavior is due to the minor term being narrower than
the major term.
That is, we must say that the text, which at first sight led us to
believe 'All S1 are P1', was not intended to be taken literally, but only to
suggest that 'a great many, perhaps most, but not all' of S1 are P1. The
syllogistic consequences of this new result on the relations between S1 and P2
and between S2 and P1 are as follows.
From the minor and subjectal premises, Some
S1 are P2 (3/IAI).
From the major and predicatal premises, Some
S1 are not P2 (1/EIO).
From the major and subjectal premises, no
conclusion
(1/IA?).
From the minor and predicatal premises, Some
S2 are not P1 (2/EIO).
The latter consequence is true whether the minor premise is
particularized or not. If the minor premise is
not particularized, we can moreover
infer 'No S2 is P1'; if, however, it is
particularized (for independent reasons, for we have here no reason to do so),
then whether 'No S2 is P1' or 'Some S2 are P1' remains an open question,
formally. These consequences, together with the altered major premise (Only some
S1 are P1), constitute our conclusions, according to formal logic. Now, let us
turn to the Rabbis, and see what they say.
An example of liton toan acher
shelo kheinyano given by Scherman: Exod. 21:2-6 presents a set of laws
relating to the release of a Hebrew slave (eved ivri, this is taken to refer to a thief sold by the courts to
repay his theft, as per Exod. 22:2; for the self-sold poor, see Lev. 25:39-43);
then Exod. 21:7-11 presents a very different set of laws for the release of a
daughter sold as maid-servant (amah);
conclusion, the initial set was for male Hebrew slaves only, and the laws of
each group cannot be applied to the other group.[14]
Thus far, the formal conclusions apparently suggested by R. Ishmael are identical
to those of natural logic, in the present rule. However, the above example
suggests that the Rabbis take a more definite position and additionally
conclude:
No S2 is P1
(additional conclusion).
Whether the Rabbis invariably go that far, or only occasionally, I cannot
say without a full list of examples; but offhand, it seems pretty typical. This
conclusion can be due to either of two policies. Either the Rabbis consider that
the minor premise ought to be kept general, i.e. as 'All S2 are P2'; in which
case, the said additional conclusion follows from the minor and predicatal
premises deductively. Or the Rabbis consider that the minor premise ought to be
particularized; in which case, their arrival at the additional conclusion is due
to a generalization from the implication 'Some S2 are not P1' of the minor and
predicatal premises. The first alternative is preferable to formal logic, in
that no unnecessary doctoring of given data is involved. The second alternative,
if used by the Rabbis, would constitute an inductive act (regarding which we can
reiterate the remarks previously made in similar circumstances; namely, that
such an act is arbitrary, if presented as a fixed rule; though scientifically
acceptable, if presented as a tentative hypothesis). Y
Rule No. 9 completes the
common phrase kol davar shehayah bikhlal
veyatsa... with the words ...liton toan acher, shehu
kheinyano, yatsa lehaqel velo lehachamir, and may be translated
literally as "anything which was in a generality and came out to posit
another thesis, which is compatible, came out to lighten and not to
harden". The expression 'shehu
kheinyano' is at first unclear; but we can arrive at its intended meaning by
a process of elimination. 'Shelo kheinyano'
(see rule No. 10, above) clearly refers to an incompatible predicate; so, 'shehu
kheinyano' must refer to some kind of compatible predicate; however, it
cannot refer to a minor predicate which subalternates or mutually implies or is
subalternated by the major predicate, as such relations have already been
treated under the headings of lelamed;
therefore, 'shehu kheinyano' must
specifically refer to a subcontrary or an unconnected predicate. That is, here,
though the two predicates are by their natures different, in the sense of
distinguishable, they are not mutually exclusive, but conjoinable.
Traditionalists may not agree with this definition of shehu
kheinyano. They might distinguish it from shelo
kheinyano, by saying that both concern somewhat divergent predicates, the
former's are 'of similar subject-matter', while the latter 'of different
subject-matter', or something to that effect. But such a distinction is of
little practical value, because it is difficult to determine by its means what
is "different, but not very" and what is "very different";
the distinction in practise becomes pure guesswork, or (they might say) a matter
of 'oral tradition'.
Though I try my best, I see no way to enshrine such a distinction in
formal terms. It cannot, for instance, be ascribed to the issue of compound
predicates (see above). A genetic explanation may be the relation between two
degrees of a concept X, say X1 and X2, and an incompatible of it, say Y
(implying nonX): we could say that the the greater X (X2) is further than the
lesser X (X1) to nonX (considered as X=0); but both X1 and X2 remain in conflict
with Y. The notion of "less" or "more" incompatible is,
strictly speaking, a mixed bag. For formal logic, all incompatibilities are
equivalent, without degrees; things either cannot
coexist, or they can coexist (under
certain conditions).
The examples which commentators usually give for the two processes are
clearly identical from a formal point of view: substitute symbols for the terms,
and you will see that the predicates are formally incompatible in both sets of
examples. It follows that there is no way to justify different procedures for
the two situations. Furthermore, if both rules of
liton toan acher indeed referred to incompatible predicates, then R.
Ishmael's hermeneutics would be short of a comment on compatibles (in the sense,
unconnecteds or subcontraries).
Thus, although neither R. Ishmael nor his successors specify the
following point, we can say that the rule liton
toan acher, shehu kheinyano concerns cases where the major predicate P1 and the minor predicate P2 are unconnected
or subcontrary. This hypothesis is based on the said process of
elimination, and hopefully will eventually be confirmed by some examples
given in the literature. In this context, then, the predicatal premise
undefined in our earlier general formula is, minimally: Some P1 are P2 and
some P1 are not P2, and
Note that this gives a minimal definition of the sort of compatibility
between P1 and P2 referred to. The clause 'Some P1 are P2' serves to eliminate
incompatibilities, which are dealt with under the heading of shelo
kheinyano; the bracketed clause 'Some P2 are P1' is implicit in it, and so
could be left out. The clauses 'Some P1 are not P2' and 'Some P2 are not P1'
serve to eliminate implicational relationships, which are dealt with under the
heading of lelamed. In the case of
subcontraries, the clause 'All nonP1 are
P2' (which implies 'All nonP2 are P1') would have to be added; in that case,
the clauses 'Some P1 are not P2' and 'Some P2 are not P1', being both implied by
the larger clause, could be left out. In the case of unconnecteds, the clause 'Some
nonP1 are not P2' (which implies 'Some nonP2 are not P1') would be added,
instead.
Now, let us consider the syllogistic inferences we can make given the
said (compound) predicatal premise. In conjunction with the major premise, all
we can formally infer is that Some P2 are
not S1 (mood 2/OAO). However,
this information tells us nothing of the relation of S1 to P2 (in that order),
other than what we already know from the minor and subjectal premises, viz. that
Some S1 are P2 (which is indefinite, note). Similarly, we can infer, from the
predicatal and minor premises, that Some
P1 are not S2; but this information tells us nothing of the relation of S2
to P1 (in that order).
[15]
Before we can present and evaluate, by formal means, the conclusion(s)
proposed by the Rabbis in such case, we have to find a statement or example
which somewhat clarifies the matter, as we did in other cases. The problem,
here, is that the statements and examples I have so far come across concerning
the present rule are ambivalent[16].
So we have to proceed in a different manner, and look for an example which, had
the Rabbis been more aware of the formal issues involved, they might well have
classified under this heading. This proposed approach is admittedly highly
hypothetical. For the present research project is not essentially prescriptive,
but descriptive; its purpose is primarily, not to tell the Rabbis how they should interpret texts, but to discover how they do
interpret texts. We wish to evaluate their
methods, not invent methods for them. A value-judgement is ultimately intended,
but only after we have something of theirs to evaluate.
Nevertheless, remember, we arrived at our hypothesis concerning the form
of shehu kheinyano, not out of the
blue, but by a gradual discovery of the forms of the other subdivisions of kol
davar shehayah bikhlal veyatsa. Our hypothesis was therefore grounded in
Rabbinic practise to that extent, being the only leftover form available. It is,
of course, conceivable that R. Ishmael and his successors never had to deal with
the situation of compatible (but not subalternative or implicant) predicates in
practise, and therefore had no need to develop a hermeneutic response and
corresponding rule. This empirical issue is hard for me, personally, to resolve
at this time, since I do not have a full inventory of the instances of Rabbinic
exegesis at hand. However, I have found a couple of examples in the literature,
in which the predicates are objectively
in the required relation, even though they are classified differently by
tradition (see Appendix 6).
Objectively, these examples should be classed as shehu
kheinyano; but traditionally, one of them is classed as shelo
kheinyano (rule No. 9, above), and the other as lidon badavar hechadash (rule No. 11, below; but note, regarding the
latter example, that it may also be classed as shelo kheinyano, according to how the major premise is read). Thus,
the conclusions they yield vary in form. But we cannot, in any case, presume to
predict, on the basis of such reclassifications, what the formal conclusions
preferred by the Rabbis might be for shehu
kheinyano situations; for if they had been aware of the compatibility of the
predicates in the suggested examples, they may have proposed other conclusions
than those they proposed while unaware. To know for sure, we need an example
which is both objectively shehu kheinyano
and regarded as such by tradition, which to date I have not found.
The issue must therefore be left open, pending the gathering of more
data. That is not a big problem, because, whatever the response of the Rabbis
happens to be, we have by now made clear the method by which such response is to
be treated: it is to be formalized (substituting symbols for content) and
compared to the results syllogistic logic.
We shall now venture some remarks regarding the final clauses of R.
Ishmael's liton toan acher rules,
concerning leniencies and severities.
Rule No. 9, shehu kheinyano, ends with
the phrase ...yatsa lehaqel velo
lehachamir (meaning: was singled out to alleviate and not to
aggravate); and rule No. 10, shelo
kheinyano, ends with the phrase ...yatsa
lehaqel ulehachamir (meaning: was singled out to alleviate and to
aggravate). Traditionally, these phrases are taken to characterize the result of
exegesis, by comparing the general and particular law.
Examples. (a) 'Alleviation and not aggravation': Scripture prescribes the
death sentence for killing someone, except in a case of manslaughter, for which
the sentence is exile instead of death; thus, for manslaughter, the sentence is
lighter and not heavier. (b) 'Alleviation and aggravation': Scripture prescribes
payment of a ransom for his life to the master of an ox which kills someone,
except in a case where the victim is a slave; in the latter case, the ox's
master pays the slave's master a fixed sum (30 silver shekels), whatever the
market value of the slave; since the market value of the slave may be more or
less than the fixed sum, the latter sentence involves both leniency and
severity.[17]
These characterizations have no formal moment, according to our analysis.
We cannot predict, on formal grounds,
how the general and particular laws, so-called, will compare with respect to
leniency or severity. It is clear that such characterizations are essentially ex
post facto summaries based on material
data[18].
If it so happens that wherever shehu
kheinyano or shelo kheinyano exegesis has been used, the results are found to
have this or that character, the summaries are true; otherwise, not. It is
conceivable that Scripture and Rabbinic exegesis happen to conform to those
patterns, but there is no logical necessity that they do. For as far as logic is
concerned, anything goes in this respect. This means that the phrases in
question do not play a role in getting us to the conclusions; they are
technically useless in determining the Halakhah.
With regard to the material issue, I have no direct interest. But it is
worth pointing out that R. Ishmael's said clauses do not seem to be based on complete
enumeration, as they ought to be, but on generalization from a few instances. This is suggested by Bergman's
comment concerning shehu kheinyano that
"(Although the formulation of this rule states 'to be more lenient rather
than more severe,' the converse also holds true.) If the item is specified for
purposes of stringency, it is not given the leniencies of the general law."
It is also evident, in several Rabbinic examples, that the characterizations are
often forced, in an effort to fit R. Ishmael's statements. Clearly, R. Ishmael
based these phrases on overly hasty generalization, from observation of a
limited sample of cases. Therefore, they are not only formally unjustifiable,
but empirically inaccurate. Consequently, R. Ishmael's formulations are overly
restrictive, in practise.
Nevertheless, let us look further and see whether we can anyway draw some
useful information from R. Ishmael's last clauses, of a formal or methodological
sort.
A possible formal interpretation is the following.
If we consider the overall outcome of shelo
kheinyano exegesis, what essentially happens is that the major and minor
premises are respectively narrowed down and made exclusive, so that the major
and minor subjects end up with separate
predicates. We could say, loosely speaking, that this result 'both alleviates
and aggravates', in that, whatever they are, the leniencies and stringencies of
the major premise are not applied to the minor term and the leniencies and
stringencies of the minor premise are not applied to the major term. Thus, the
final clause of R. Ishmael captures the 'spirit' of this rule, though not its
'letter'.
If, now, we turn to the shehu kheinyano rule, and R. Ishmael's final clause 'alleviates but
does not aggravate', and we assume that, here too, he was referring to the
'spirit', rather than the 'letter', of this type of exegesis, we might suppose
that the conclusions he would recommend, in situations where subalternative
subjects have compatible predicates, are such that the minor premise ends up
'lighter' than the major premise. A relatively formal interpretation of this
(with reference to a number of predicates), would be that the minor subject ends
up with only its own predicate exclusive of the other predicate, while the major
subject exclusive of the minor subject ends up with both predicates[19].
I offer this remark very speculatively, without even looking for
examples; I very much doubt that that was R. Ishmael's formal intention. Note
that, in any case, some residue from the original text must remain: at least
some S1 have to be P1 and at least some S2 have to be P2[20].
Our best bet is a methodological
interpretation, which goes as follows. This explanation refers to advice broader
in scope than the concerns of deductive or formal-inductive logic. With reference to shelo kheinyano, we could impute R. Ishmael as saying that, since the major premise has been proven, by ensuing inconsistencies, not to be universal, we must henceforth proceed very carefully and, unless or until o |
