In the present and next two
chapters, we shall indulge in a closer scrutiny and frank criticism of
Talmudic/Rabbinic hermeneutics. In this first part of our analysis of the
Thirteen Midot of R. Ishmael, we shall deal with Rules 1-7 and 12.

1. Exposition and

2. Inference of

3. Scope of Terms.

Exposition and Evaluation.

Traditional presentations of the principles and practise of Rabbinic
exegesis consist in listing the Thirteen Midot
of R. Ishmael (at least, though other techniques may be mentioned, in contrast
or additionally), describing roughly how they work, and illustrating them by
means of examples found in the Talmud or other authoritative literature.

Such an approach is inadequate, first of all, because the theoretical
definitions of the rules are usually too vague for practical utility, and for
purposes of clear distinction between similar rules. A simple test of
practicality and clarity would be the following: if well defined, the rules
should provide any intelligent person with a foolproof procedure, so that given
the same database as the Rabbis, he or she would obtain the same conclusions as
they did. The second important inadequacy in the traditional approach is the
near total absence of evaluation; there are no validation procedures, no
reductions to accepted standards of reasoning. There is no denying the genius of
R. Ishmael and others like him, in their ability to abstract rules of
intellectual behaviour from the observation of their own and their colleagues’
thought-processes in various situations. Nevertheless, as we shall see, their
failure to treat information systematically and their lack of logical tools,
yielded imperfect results.

We shall here propose some original ways to expose and evaluate Rabbinic
hermeneutics (mainly, the 13 Midot).
The most important step in our method is formalization;
this means, substituting variable-symbols (like ‘X’ and ‘Y’) for terms or theses
of propositions
Formalizing an argument, note, means: formalizing all explicit and tacit
premises and conclusions. The value of this measure is that it helps us to
clarify the situations concerned, the Rabbinical responses to them, and the
issues these raise. By this means, we move from a level akin to arithmetic, to
one more like algebra. When we deal in symbols, we reduce immensely the
possibility of warped judgement, due to personal attachment to some solution;
all problems can be treated objectively. It should be said that logical
formalization is not always the most appropriate tool at our disposal; in some
cases, epistemological and/or ontological analyses are more valuable.


We have two sets of data to thus formalize, or analyze in some manner:
(a) the theoretical pronouncements of Rabbis (defining or explaining the
rules, or guiding their utilization), and (b) the practical examples they give in support (illustrating or applying
their statements). This work allows us to compare, and if need be contrast,
Rabbinic theory and practise. As we shall see, they do not always match.


Another utility of formalization or similar processes, is the possibility
it gives us for comparing Rabbinic conclusions to the conclusions obtained by syllogism
or other such established logical techniques
. This is the ultimate goal of
our study, to determine without prejudice whether or to what extent Rabbinic
hermeneutics comply with deductive and inductive logic. As we shall see, they do
not always parallel the course taken or recommended by ordinary logic.

In anticipation of such divergences, it is important to study the
Rabbinic hermeneutic principles carefully, and distinguish between their natural
factors and their artificial factors.
The natural aspects are immediately credible to, and capable of formal
validation by, ordinary human logic, and thus belong to secular epistemology.
The artificial aspects, for which Rabbis claim traditional and ultimately Divine
sanction, are controversial and require very close examination, for purposes of
evaluation or at least explanation. Our task with regard to such additives is to
consider whether the rationales for them offered by the Rabbis are logical and
convincing, or whether these factors ought to be regarded as human inventions
and errors.

We shall in the rest of this chapter, and in the next, deal with the 13
rules of R. Ishmael under three large headings. “Inferences of
information” – including rules 1-3, and 12, i.e. qal
(a-fortiori argument), gezerah
(inference by analogy), heqesh,
meinyano, misofo (contextual
inferences), and binyan av (causal
inference). Then “scope of terms” – including rules 4-7, referred to
collectively as klalim uphratim
(genera and species). Finally, “harmonization” – including rules 8-11,
and 13, about which much will be said.

It should be clear that we have no intention, here, of masking any
difficulties, but propose to engage in a “warts and all” exposé. The
technicalities may be found hard-going by many people, but both secular and
religious scholars, who endure through the ordeal, will be richly rewarded. They
will find, not only an independent audit of Rabbinic hermeneutics, but a
methodological demonstration of universal value. By the latter remark, I mean
that the same method of exposition (by formalization) and evaluation (with
reference to formal logic) can be applied to other movements of thought in
Judaism, or outside it, in other religions or other domains (philosophy,
politics, or whatever).

Inference of Information.

We shall first consider the exegetic rules whose purpose is essentially to
infer new information from passages of Scripture, rather than to elucidate or
harmonize the text (the division is, admittedly, to some extent arbitrary).
Included here are both deductive and inductive processes, of varying degrees of
formality and certainty.

We have treated qal vachomer (R. Ishmael’s
Rule No. 1) in considerable detail
already, and need only here remind of certain details. This refers to a natural
thought-process, a-fortiori inference,
the most deductive form of Rabbinic argument. The Rabbis of the Talmud and those
which followed them, although they had an exceptionally well-developed
understanding of this form of argument, did not have a complete understanding of
it, such as one might expect in the event of Divine revelation. Their knowledge
of it was not formal; they did not clearly distinguish inductive and deductive
stages of reasoning; they misconstrued certain applications of the dayo
and they erroneously counted the number of a-fortiori examples in the Tanakh.

It ought to be remarked that R. Ishmael’s formulation, just ‘qal
‘, is very brief – at best a heading; he does not define the
processes involved. The distinction between miqal
and michomer leqal is not
given in the list of Thirteen Midot; I
do not know whether it is explicitly found in the Talmud or only in later
literature. To what extent were the Talmudic and post-Talmudic Rabbis aware of
the difference between positive and negative a-fortiori; did they ever note the
distinction between copulative and implicational forms of the argument, did they
use the secondary forms; at what point in history were the more complex Rabbinic
formulations that we find in contemporary literature developed: these are all
questions I ask myself, but have not researched the answer to. Historians of
logic have still much work to do.

With regard to the legitimacy of the use of a-fortiori argument. We
validated four (or eight) primary moods, namely copulatives, subjectal or
predicatal, positive or negative (and implicationals, antecedental or
consequental, positive or negative) and a number of derivative secondary moods.
Since the process has naturally valid moods, it follows that if
these moods are used properly, no formal objection to their use in contexts
not sanctioned by tradition is possible. Tradition can only restrict their use
with reference to the inductive preliminaries (as we discussed under the heading
of objections); but with reference to the purely deductive aspects, no Rabbinic
legislation is possible
It would be like trying to conveniently exempt oneself from the obligation of
honesty or consistency!

The same freedom of thought must be acknowledged for all other purely
deductive processes (or stages of processes), such as opposition, eduction,
categorical or conditional syllogism, production, apodosis, and so forth. Any
Rabbinic restrictions in such areas would be tantamount to an advocacy of
antinomy, and cannot be tolerated. Rabbinic interference, on the grounds of some
special Divine dispensation delivered at the Sinai revelation and transmitted by
oral tradition, can only conceivably be applied to inductive processes; that is,
with regard to situations which allow for more
than one
possible answers to a question, it is conceivable that there be a
Divine decree as to which answer to favour in some specified situation(s) or all
situations. However, we must keep in mind that the conceivability
of such powers does not constitute proof that they exist in fact; it only makes
logically possible a claim but does not justify it; and furthermore, that any
controversy surrounding such powers throw doubt on their legitimacy.

The technique of gezerah shavah (Rule
No. 2
) is also based on a natural thought-process, though a more intuitive
and trial-and-error one. It consists in inference
by analogy
. The expression means “distinctive sameness”, and
therefore refers to the fundamental epistemological processes of comparison
and contrast
, which are jointly the basic technique of all concept
formation. Applying them to textual analysis, we would quite naturally (i.e.
without need of special communication or dispensation of Divine origin) look for
homonyms and synonyms, to understand the language used and its conceptual
references. In all discourse, we may find labels used which are analogous
(similar in root, if not identical words), and apparently have similar or
various meaning(s) in different contexts; or we may find different labels used
in different contexts, with apparently the same meaning intended.

The scientific-minded approach to gezerah shavah would run somewhat as follows. The meaning of a
label, i.e. a word (every letter identical) or group of words (phrase), or
word-root (having certain common consonants, in the same sequence; though
possibly with some different vowels and consonants which indicate, on a wider
grammatical basis, varying inflexions) or group of word-roots, is suggested by
the various contexts in which it appears in the text(s) concerned, as well as in
other texts and current usage, and through comparative etymology.

Homonymy: If a,
b, c…
are all the occurrences of a label, and their assumed meanings
(based on the above suggested methods) coincide, and no other assumed meaning(s)
would be as coherent, then it may be assumed that the proposed single meaning is
the intended meaning. If in some isolated context(s) the meaning of a label is
uncertain, and it is coherent everywhere else, the same meaning can in all
probability be generalized to the uncertain instance(s). But if the label is ambiguous
elsewhere, there being one assumed sense in some contexts and some other
sense(s) in others, then if no clear differentiating conditions are apparent,
the sense most frequent elsewhere (if any) is the most probable, though some
doubt remains.

Synonymy: If A,
B, C…
are various labels and
their assumed meanings (based on the above suggested methods) are unambiguous,
and mutually identical or at least similar everywhere they occur, and not even
conditionally dissimilar anywhere, then these labels may be considered to be
equivocal and interchangeable; that is, they are different labels for the same
thing. If in some isolated context(s) the meaning of a label is uncertain, and
it is coherent everywhere else, the same meaning can in all probability be
generalized to the uncertain instance(s).

Once the general meaning of a label or the equivalence of various labels
is established, statements with the label(s) concerned may all be assumed to
refer to the same subject-matter. A detailed example of the kind of analysis and
synthesis here referred to may be found in the present volume, in our study of
a-fortiori in the Tanakh (ch. 5-6).

A traditional example of gezerah shavah is given by Enc.
(with reference to Pes. 66a).
The expression bemoado, meaning ‘in
its appointed time’, is used both in Num. 9:2, concerning the Pascal lamb, and
in Num. 28:2, concerning the daily offering (which includes the Sabbath); it is
thence inferred that the Pascal lamb may be offered on a Sabbath (coinciding
with Pessach), even though this entails activities forbidden on other Sabbaths.

It is obvious that such reasoning is highly intuitive and dependent on
one’s overall context of knowledge. It is built up from the perception of words
and the conception of their possible relations. The initial insights
into possible meanings derived from immediate and wider context are conceptual
acts dependent on the faculty of imagination; and subsequent ordering of the data, though a relatively mechanical process, is a
function of the amount of data available at the time and taken into
consideration. Such judgements can in no wise, therefore, be considered to have
deductive value, but are eminently inductive.

With regard to Biblical text, we have little material to refer to, other
than the document itself. This means that our conclusions are virtually
pre-determined, since the data available are finite, even if they constitute a
sufficiently large and varied sample of the Hebrew of the time concerned.
Actually, sometimes a word or phrase is only used once in the whole document,
and its meaning becomes a subject of conjecture; obviously the more often a
label appears in the text, the more certain its meaning. With regard to Hebrew
usage later in history, it is of course very significant
but it must be kept in mind that it has been and still is culturally influenced
by the interpretations suggested by the Rabbis, and therefore it cannot
necessarily be used to further justify those interpretations.

The natural interpretative process is adductive: an idea is floated, then
tested in every which way for consistency
It is, for this reason, susceptible to abuse. One may too easily stress
similarities and ignore significant differences; and thereby stretch the
application of an idea beyond its rightful borders. Or again, one may ignore
similarities and emphasize incidental differences, and thus artificially
restrict an idea. This is true of all argument by analogy; and repeated
consistency-checking in an ever wider context of information provides the
natural protection against error
, as in all induction.

Now, such a relaxed and patient attitude can hardly be practical in a
legal framework, where some decisive position may be required ‘right now’. On
the other hand, the necessity to decide does not logically imply an
impossibility to reverse the decision taken, later, in the context of new
knowledge or modified conditions. The Talmudic authorities had debated matters
and come to various conclusions which seemed wise to them. However,
post-Talmudic authorities, intent on preserving these very decisions, proposed
additional clauses to the hermeneutic principles which were to ensure they
always resulted in the same conclusions, no matter how the data-context changed.

Thus, in relation to gezerah shavah, they claimed that the Sages were occasionally
informed by tradition as to which topics were open to legal analogy, but left to
find the verbal analogy which would justify it; or again, that the Sages were in
some instances informed of words which could be used for such inference, but
allowed to find appropriate circumstances for their use; or again, that the
Sages were told in advance the number of valid gezerah
arguments there would be!
Now, I find all that hard to believe. Not only because it is very surprising
that such alleged ‘information’ is (apparently) not explicitly mentioned by the
protagonists themselves, but only makes its appearance in writing centuries
later; but because the transmission scenario itself is unreasonable.

Is it plausible that serious teachers would pass on vital legal
information to their students in the form of riddles? Why would they
engage in such games, and not get to the point, if they had the information? One
cannot imagine a functioning law system in which it is not the law and its
justifications which are transmitted from generation to generation, but
conundra. For then, one would have to consider that the laws in question (i.e.
those to be inferred by such means) had been inoperative until their formulation
in the Talmud. In which case, surely, the more basic thesis that the law has
gone on unaffected by time since Sinai – the very thesis these artifices were
designed to defend – would be put in doubt. It seems obvious, therefore, that
the above mentioned additional clauses are ex post facto constructs
based on no actual oral or written tradition.

The controversies surrounding yet other additional clauses to the gezerah
process, provide still more cause for suspicion that such additional
clauses are not Sinai traditions, but later constructs (in this case, Talmudic)

Thus, it is taught that the applicability of the gezerah
method depends on the ‘freedom’ of its middle term in one or both of
its manifestations. This refers to whether each manifestation of the middle term
involved, through which a legal factor is to be passed over from one issue to
another, has already been utilized to justify some other Halakhah. Such a
concern presupposes a principle that each
unit of information in the Torah can only serve for one inference
generic logic has no such restriction (a premise can be used in any number of
arguments), but let us grant it to be a tradition. On this basis, three
possibilities are considered: that the middle term is (a) ‘free on both sides’,
(b) ‘free on one side only’, whether the source side or the target side, or (c)
‘free on neither side’. Authorities say and agree among themselves that a gezerah shavah inference of type (a) is irrefutable. With regard to
type (b), some say it is always valid, while others regard it as conditionally
valid. With regard to type (c), some regard it as conditionally valid, while
others say it is always invalid.

Similarly, there is a debate as to how much legal detail a gezerah
allows us to pass over from premise to conclusion. There is also a
debate as to whether once legal data has been transferred in one direction,
other data may be transferred in the opposite direction, so as to equalize both
sides, or whether the process is more restricted. It is irrelevant to us, here,
which opinions are correct in these various debates – what is significant is
simply the fact that there are at all disputes on matters so crucial.

Regarding the ‘freedom’ (mufneh) concept, an interesting remark may be added: it can be
viewed as an attempt, albeit a rather primitive one, to express the sort of syllogistic
reasoning which follows the drawing of analogies. The Rabbis ask: once a term A
is seen as analogous to a term B (gezerah
), can the laws applicable to A be applied to B and/or vice-versa?
Their answers by means of the ‘freedom’ concept may be understood as follows.

If both terms are ‘free’, it means that they were never before used in
syllogistic inferences, presumably because they are both sui
; consequently, the Rabbis assume them to be mutual implicants, and
allow syllogism hither and thither between them. If only one is ‘free’, the
Rabbis presume it to be a genus or species (I am not sure which) of the other,
and thus allow syllogistic inference of laws from the genus to the species,
though not vice-versa. If neither is ‘free’, it means that they have already led
separate logical lives, so the Rabbis presume that the terms are unconnected (or
at least that neither implies the other), and so avoid syllogistic inference.

This perspective explains the Rabbis’ concept, but does not fully justify
it. For the basis of their syllogistic reasoning is too imprecise; they do not
have a clear picture (even though this theory arose long after Aristotle) of the
conditions of syllogistic inference. Similarity between terms and the histories
of the use of such terms in inferences do not indubitably determine the
implicational relations between these terms. The Rabbis lacked a clear
understanding of opposition theory, as we shall see also in the section dealing
with harmonization.

We may, in my opinion, place under one heading, namely inference
from context
, the exegetic methods known as meinyano
and misofo (Rule
No. 12
) and those known as heqesh
and semukhim
(regarded as part of Rule No. 2). All
these take into account the textual closeness of an expression or sentence to
certain other(s), and on this basis assume that there exists a conceptual
relation between the passages under scrutiny, which makes possible an inference
of certain attributes from the context to the expression or sentence. There is,
we might remark, a small element of inference by analogy in such processes
though it might be characterized as extrinsic rather than intrinsic. The
differences between these four techniques are, however, less clear (to me, at

An example of contextual inference: the Rabbis inferred (by the rule meinyano)
that the commandment “thou shalt not steal” in the Decalogue (Exod.
20:13), refers to kidnapping, on the grounds that the two preceding
commandments, against murder and adultery, are both capital offenses, and
kidnapping is the only form of stealing subject to the same penalty (Enc. Jud., which refers to Mekh.,
, 8,5).


seems to loosely appeal to the surrounding subject-matter without precise
definition of its textual position relative to the passage at hand. Misofo
refers to a later clause or passage for the information it infers; though as
some commentators have pointed out, it could equally well refer to an earlier
segment of text. In these two cases, the conceptual common ground of source and
target text is to some extent evident. In the case of heqesh and semukhim,
however, the inference is based almost purely on textual contiguity, the
contiguous passages (within the same verse or in two adjacent verses,
respectively) having little evident conceptual relation

The natural justification of logistical inferences would be what we today
refer to as ‘association of ideas’. When two ideas are placed next to each other
in our thoughts, speeches or writings, it may be because of some logical
relation between them, or entirely by accident, or again because one contains
some incidental reminder of the other. This last possibility implies that in
some cases, even when purely logical considerations are lacking, an inference
might yet be drawn from the fact of proximity. However, the possibility of
chance conjunction still remains: topic X may be entirely spent and the
narrative moves on to topic Y, an entirely separate topic
This alternative possibility means that inference based solely on position is
tenuous. The Rabbis were apparently aware of this uncertainty, and would use
such processes only as a last resort, when the verse being interpreted involved
a doubt which they had no other way to resolve.

R. Ishmael did not mention the exegetic methods of heqesh
and semukhim, and attempts by later authorities to explain this silence
have a hollow ring. Thus, Bergman (with reference to the Sefer Hakerisus) says of R. Ishmael that “he regarded the hekesh
as the equivalent of an explicitly written teaching”. If R. Ishmael did not
even mention the subject, how can the later Rabbis know by tradition why he did not mention it. How can they have information on his
on an unspoken issue? The very notion is self-contradictory:
proving again that the authorities often confuse their personal assumption
concerning some matter with a ‘received tradition’ (refusing to admit that R.
Ishmael might not have known about these things, or that there might be no
tradition concerning them, and that such issues must be resolved adductively).

Again, R. Ishmael, apparently (and as the name given to the process
implies), did not regard or was not aware that misofo
inference was equally feasible in the opposite direction (‘mitechilato‘,
if we may say so), from an earlier to a later statement or clause. Later
commentators (Bergman refers to Middos
), who considered such reverse inference possible, explain R.
Ishmael’s silence by claiming, effectively, that in cases where the solution
precedes the problem, the inference is so obvious that listing it would have
been a redundancy. That is another anachronistic argument, whether we agree with
the validity of such inference in both directions or not. The commentators must
admit the possibility that R. Ishmael did not hold the same opinion, or more
likely still (since he himself does not mention it) that he just did not think
of the issue at all!

Inferences of the binyan
type (Rule No. 3) seem to
be a Rabbinical attempt at causal
– using the term ‘causal’ in its widest sense, including any mode
of causality; i.e. not only natural-mode causation, of motion or change, but
also extensional causality, of ‘static’ (i.e. class) differences, as well as
logical causality, or rational explanation
Causal inference has been much clarified in more recent times by John Stuart
who identified the ‘methods of agreement and difference’. It results from
observation of two kinds of events or things, such that the presence of one is
always accompanied by the presence of the other, and therefore that the absence
of the latter is always accompanied by the absence of the former. In such
circumstance, one may, from observation of the first event or thing, presume the
second even when it is not observable. This is an inductive process, involving
analogy and generalization. Symbolically, broadly-speaking, the essential
relation between a cause C and an effect E may be expressed by a hypothetical
proposition and its contraposite:

If C, then E (and if not E, then
not C).

However, the Rabbinical attempts at formulation of this natural principle
stressed more the side of ‘agreement’ than that of ‘difference’. R. Ishmael
refers to an inference ‘from one verse’ or ‘from two verses’. There were
subsequently disputes as to the meaning of these subdivisions (which disputes,
incidentally again tend to show the lack of a clear oral tradition). Some Rabbis
understood them, respectively, as follows: if two topics (X, Y) have a certain
feature (A) in common, then another feature (B) which the one (X) has may
be assumed to be had by the second (Y)
or, if three topics (X, Y, Z) have a certain feature (A) in common, then another
feature (B) which two of them (X, Y) have may be assumed to be had by the third
(Z). Other Rabbis claimed to understand R. Ishmael’s formula differently
They sought for a common feature
(A, say) of topics under comparison (X, Y) which would explain
their having in common some other property (B), in which case the reappearance
of that same feature (A) elsewhere (in Z) could be taken as a sign of the
same property (B) there (i.e. in Z). In fact, this formula is formally
identical to the second of the above mentioned
merely adding the (valuable) comment that A is to be considered as the cause of

The difficulty in these statements is their emphasis on the positive,
their attempt to generalize from a limited sample (X, or X and Y) without
readiness to conceive the possibility of deviation from the apparently set
pattern of conjunction (of A and B) in other cases, including, in particular,
the case at hand (Y, or Z, respectively)
Apparently sensing this weakness, the Rabbis tried to put a bit more emphasis on
the negative, by pointing out differences in features between the (two or three)
topics under scrutiny, thereby hoping to demonstrate other possible causes have
been considered and eliminated. Thus, they might say, in the two-verse form of binyan av: X has C and Y lacks C, so that Z having C does not prove
it has B; or again, X lacks D and Y has D, so that Z having D does not prove it
has B. However, it should be clear that such statements are irrelevant to the
main argument: they at best prove only that C or D do not cause B, but do not
prove that A does cause B

An example of binyan av, given
in Enc. Jud. (referring to B.M.
87b). The Rabbis attempt, with reference Deut. 23:25f., to determine whether a
hired farm hand may eat produce, while working in fields other than those with
vines or standing corn. To do so, they try to understand why the Torah allows
him to eat in vineyards and in cornfields. They argue: it cannot be in relation
to the obligation to leave gleanings for the poor (Lev. 19:10), since this
applies to vine but not corn; and it cannot be in relation to the obligation to
give the priest a portion of the dough (Num. 15:17-21), since this applies to
corn but not vine; ‘therefore,’ it must be simply due to their being both
plants, and the permission may be generalized to other produce.

It appears from such redundancies that the Rabbis confused somewhat the
trial and error mental process of looking
a cause (
and the formal conditions of the objective causal relationship
. Had they
known the latter clearly, they would rather have systematically first made sure
they had a complete enumeration of the appearances of features A and B in the
Torah, alone and/or separately, as well as their negations if any. Then, to make
possible the inference from A to B, in situations where A is mentioned in the
text but B is not mentioned, they would have to check, not only that A and B are
sometimes both affirmed together (at least once, but the more the better), but
also that A is never affirmed with an explicit denial
of B (that is the missing negative element). Furthermore, the probability-rating
of the inference would be proportional to the frequency of conjunction of A and
B, compared to that of A mentioned alone without mention of B
It is possible that in the cases where the Rabbis applied this principle, they
(who knew the Torah by heart) automatically performed these consistency tests
and probability judgements; but they did not always do so explicitly.

It must be stated that aetiology does not insist that the cause be one
event or thing, or that the effect be one event or thing; each of these (cause
or effect) may itself be two or more parallel things or events, provided the stated rules of induction
(agreement and difference) are adhered to for them all singly. Furthermore, if
the rules of induction are not invariably adhered to (whether by a single event
or thing or many of them), they might still be found to apply conditionally
or compositely: that is, provided we manage to identify and distinguish
the conditions under which our partial causes become complete causes or our
occasional effects become constant effects
Consequently, too, there may be circumstances in which one event or thing is the
cause of a certain effect and other circumstances in which another is so; or
again, a certain event or thing has some effect in one set of circumstances, and
another effect in another set.

These details of causal logic were apparently not entirely understood by
the Rabbis, judging from certain limiting suggestions they made. One such
Rabbinic limitation was that (with reference to the symbols introduced above)
if X and Y have in common yet another feature (E, say) which Z lacks, then Z
cannot be assumed to have B. I say,
viewing ‘A+E’ as a joint feature, this objection seems reasonable; but it still
remains possible that A causes B. Another Rabbinic limitation was the rejection
of the possibility that distinct features of X and Y, such as C and D (see
above), may independently cause B in their respective subjects, so that Z, which
has only the common feature A, but neither of the distinct features C, D, may
not have B. I say, it is conceivable
that the two compounds ‘A+C+nonD’ and ‘A+nonC+D’ might be parallel causes, while
the compound ‘A+nonC+nonD’ is not a cause: the issue depends on the negative
side, which they ignored in their initial definition
Such attempts at exception show, to repeat, that the Rabbis were not certain as
to the precise conditions of causality

There is a manifest failure of theoretical research in logic, independent
of any Torah related doctrines, by the Rabbinic authorities. Consequently, as
may be expected, there is a lot of controversy between them on methodological
issues (which, of course, ultimately affect the law); and worse still, sometimes
the controversy revolves around a totally artificial issue (which naturally
enough emerges from some general belief to which the disputants are all
attached). What amazes me is that the existence of such controversies does not
cause any of the people involved to frankly question the ‘orthodox’ doctrine
that the hermeneutic principles, in their entirety, are Sinaitic revelations.

A case in point is the discussion concerning the ‘two verses coming as
one’ principle, according to which if a law L is stated in relation to two
subjects, S1 and S2, and logically L(S1) implies L(S2), and/or vice-versa, so
that one of the statements is redundant, then L may only
be applied to the two situations specified. This principle has no natural basis,
as far as I can see; i.e. it does not formally follow that L(S1) and/or L(S2) cannot logically imply some other, unstated application, say L(S3).
If such implication does logically occur, it cannot be inhibited by Divine or
Rabbinical fiat (Gd does not contradict His own natural laws, nor allow them to
be by-passed by humans)
for this reason, the restriction must be classed as artificial. Analytically, it
seems to be merely an outcome of R. Akiba’s claim that there is no superfluous
statement in the Torah; which idea is itself controversial, since R. Ishmael
(theoretically) rejects it, claiming that the Torah speaks in the language of
men. Whatever its source, there is controversy concerning the precise
formulation of the proposed principle, from Mishnah onward. Some authorities
(among them Tosafot) claim that at least two redundancies are required for such
restriction. Some (among them Rashi) say that the restriction is in any case not
general to all inference, but limited to attempts to extend the law concerned by
means of binyan av inference. But I
see no formal basis for these subjacent disputes, either.

The deep intellectual cause of such deviations from natural logic is, in
my opinion, initially a naive non-formalism,
gradually developing into a systematic anti-formalism
(which is also naive, in other respects). The historical cause is an
unfortunate, at first emotional and later ideological, antipathy to what they
called ‘Greek knowledge’, which blocked any attempt to learn from the
discoveries of others. For these people, logic
has to adapt to the requirements of pre-conceived contents (the Halakhah),
rather than all contents yielding to the dictates of an objective, formal logic.
This Rabbinic claim of total control is evident, for instance, in Bergman’s
statement in this context: “The rules regarding Scriptural texts… reveal
a law only in relation to the place they are applied and not elsewhere”.

The doctrine of the Sinaitic origin of Rabbinic hermeneutics is not
primary, but a derivative of the doctrine of the Sinaitic origin of Rabbinic
law. The Rabbis thought they could manipulate logic however they saw fit, so
long as they arrived at the required legal results. Controversies occurred only
in relation to the necessity or efficacy of this or that manipulation, but not
in relation to the underlying epistemological assumption.

These reflections need not be taken radically. Our concern, here, is with
Judaic logic as such, not with Jewish law. If we throw doubt on the former, it
does not necessarily follow that all, or any, of the latter is wrong; for, as
logic teaches, denial of the antecedent (in this case, some aspects of Rabbinic
hermeneutics), does not imply denial of the consequent (in this case, Rabbinic
law) – unless their relationship happens to be exclusive. A law may be
correct (i.e. truly Divinely-willed), but improperly derived from the text (i.e.
from the wrong place or in the wrong manner). A law may, of course,
alternatively, be incorrect, as well as improperly derived. These are not
matters which can be dealt with in general ways; but each case must be reviewed
carefully, after which the consistency of the whole must also be verified. In
any case, logic cannot itself be made an issue of faith, something optional.

A statistical note. I have not so far found out just how many times each
form of exegesis described here is actually used in the Talmud and other
Rabbinic literature. For the moment, here is some information gleaned from the
Index Volume of the Soncino edition (1952) of the Babylonian Talmud. As we saw
in an earlier chapter, this index contains some 137 references to qal
argument (under various headings). With regard to various forms of
argument by analogy, there are some 161 references (analogy, deduction by, 58;
comparisons, for purpose of deriving laws, 1; gezerah
, 81; hekkesh, 17; semukin,
1; texts, proximity of, 2; textual reading, 1). Whether this index is complete,
and whether each reference concerns a distinct sample or there are repetitions,
and whether some references relate merely to theoretical discussions, I cannot
venture to say

Note also that we must distinguish between use of an argument: (i) within
the Bible itself (e.g. we know of four or five cases of qal vachomer in the Torah, and two dozen more in the rest of the
Bible); (ii) by the Rabbis, especially
those of the Talmud, in their efforts of exegesis from
the Bible, as a document, of Halakhic or Hagadic material; and (iii) by
the Rabbis, especially post-Talmudic ones, in relation to the non-exegetic
pronouncements of other Rabbis.
Clearly, the statistical question constitutes a large and difficult research
project in itself.

also Addenda 6 and 7.

Scope of Terms.

Obviously, in the reading of any text, understanding the terms used is of
the essence. This has two aspects: a qualitative
aspect, which by its very nature presupposes knowledge of the language involved,
and a quantitative aspect, which
relates to determinations of scope. Rabbinic tradition has, of course, had much
to say about both these aspects. The first aspect, elucidation of the
denotations and connotations of terms, is in part dealt with within the
hermeneutic principles, by way of inferences by analogy and context; and in
part, it depends on cultural and religious tradition and the insights of
commentators. The second aspect, concerning subsumptive issues, is covered by a
set of hermeneutic principles which we shall now consider.

The methods of exegesis known as collectively klalim
are efforts to interpret the effective subsumption of logically overlapping
terms found in the Torah (and thence applicability of the proposition(s)
involving those terms). Miklal
(Rule No. 4) is the
interpretation of a genus + species combination, in that sequence, as having a
limiting effect, signifying ‘only the species mentioned’ (the species is
mentioned for purposes of excluding others of the same genus); whereas miprat
(Rule No. 5) is the
interpretation of a species + genus combination, in that sequence, as having an
enlarging effect, signifying ‘the species mentioned and others like it’ (the
species is mentioned as a sample of those in the genus). An easy way to remember
these two rules is to say that the result is equal to the second of the two
given terms. Other such rules, as we shall see, have an overall limiting result.
(See Diagram 2.)

To put us into the picture let us note that, in everyday discourse, we
would (depending on the precise wording) understand the conjugate scope of
logically overlapping terms as follows, granting that G is an overclass and S1,
S2… one or more of its subclasses, and that G and G’ are two classes which
partly intersect without either subsuming all of the other’s instances and S,
say, is the entire subclass referring to the G’ part of G. A statement whose
subject is “GS” or “SG” would be interpreted minimally as
concerning the species “S”
though in some cases the genus “G” might be appropriate. “G such
S1, S2…” might be read as “S1, S2…” (if ‘such as’ is
taken to mean ‘similar to’) or as “G” (if ‘such as’ is taken to mean
‘for examples’). A listing of the form “S1, S2… indeed
G” would likely be intended as “G”, though without a qualifier
like ‘indeed’, a doubt might subsist. Lastly, “GG'” or “G’G”
is usually intended as “G and G'” (i.e. “S”, their common
ground), though occasionally might mean “G or G'” (including both
their grounds, as well as “S” or even possibly to the exclusion of

There is evidently much vagueness in ordinary language, which logical
science can easily overcome by instituting conventions. This field of inquiry is
not class logic proper, but a linguistic preliminary to it. Note that a mental
act of ‘reconciliation of conflicts’ is involved, insofar as the terms dealt
with are in some tension, according as we understand reference to a genus as
concerning the whole of it (davqa) or most or an unspecified portion of it (lav
), and reference to a species as concerning it at least (lav
) or it exclusively (davqa).
When the terms are mentioned together as subjects of propositions, there is
therefore doubt as to whether the result is a generality, a contingency or an
indefinite particularity. The logical rule, in case of doubt, is to acknowledge,
by dilemmatic argument, the indefinite particularity (at least some) as true; deductively, we remain open-minded as to
whether the generality (all) or contingency (some, but not all) is true;
inductively, we opt for the generality, because it introduces no new polarity,
unless or until conflicting evidence is found.

For the Rabbis, in the klal uphrat
case, the genus is mentioned as a first approximation of the meaning intended,
and the species is added to more precisely pin-point that meaning. For instance,
in Lev. 1:2, “of the livestock (behemah),
of the herd and of the flock,” the general term is one of variable
connotation (it could be taken to include other types of animal, such as asses
perhaps) and is clarified by means of the mentioned species. To explain why the
species were not simply mentioned alone, without the genus, we are told that extensions
unintended by the writer might then have been proposed, or alternatively that
certain details suggested by the genus might have been missed; opinions differ
among the authorities on this point. We could accept an amalgam of both as
reasonable: the genus is there, effectively, to say “but do not include
with these species, other dissimilar
species of the same genus”.

In the prat ukhlal case, some species are first listed to indicate the kind
of thing intended, and the genus is added in conclusion to indicate “and
other things of the same kind” to be also intended. For example, in Exod.
22:9, “an ass or an ox or a sheep, or any beast (behemah),”
the species exemplify the things intended and the genus serves to extend the
application of the law concerned to other similar things, implying the initial
list not to be exhaustive. To explain why the genus was not simply mentioned
alone, without the species, we are told that exceptions
unintended by the writer might then have been proposed, or alternatively that
certain details suggested by the species might have been missed; opinions differ
among the authorities on this point. We could again accept an amalgam of both as
reasonable: the species are there, effectively, to say “and be sure not to
exclude from this genus, other similar
species of the same genus”.

These methods, and other variations (mentioned below), are R. Ishmael’s;
R. Akiba proposed others in the same contexts: he determined the scope of
statements with reference to the principles of ribui
and miut uribui (amplification and limitation, and vice-versa). The
technical difference between these approaches is essentially one of emphasis.
Whereas in klal uphrat, the mention of
species serves to more precisely define the initial genus; in ribui
, the explicit mention of species stresses the exclusion of certain
dissimilar things, not explicitly mentioned, belonging to the initial genus. And
whereas in prat ukhlal, the final genus serves to more broadly define the full
extent of the list of species, adding to those explicitly mentioned more species
not explicitly mentioned, while also incidentally somewhat limiting, as all
definitions do, excessive extrapolations; in miut uribui, the mention
of the genus stresses the limits of extrapolation more, excluding certain
unmentioned species of it too extremely dissimilar to the mentioned species,
while also incidentally suggesting certain unmentioned species to be included

These forms of interpretation seem to me natural enough in themselves. In
many cases, the wording is clear and no discussion is possible, anyway. However,
in some cases, the results do not seem formally inevitable: one might sometimes
view genus+species as signifying ‘genus, of
a sample species is…’
and species+genus as signifying ‘species, of
the relevant genus is…’
in such cases, note, the term mentioned in second place is effectively in
brackets, suggesting a proposition which communicates, in passing, some
incidental information (not necessarily of immediate legal relevance).
Consequently, if we take the rules as ex
pronouncements, and attempt to always tailor our interpretations to
fit their given formats, we are not unlikely to be occasionally misled. Clearly,
behind such regulations is the rigid mode of thought which denies stylistic
license to a document of Divine origin


With regard to the other combinations and permutations of these
inferences of scope (classed as Rule No. 6), notably klal
uphrat ukhlal
and (apparently a later addition
prat ukhlal uphrat, we need only add the following comments. These
involve successive operation of the preceding two principles, with the klal
stages having a broadening effect, and the prat
stages a narrowing effect, the overall result being relatively narrow
There is a proportionately greater opportunity to force the text into
preconceived formats, rather than interpreting it naturally. It seems to me that
we should always try to grasp the simple reading (pshat),
and avoid deviation from it without overwhelming justification.

An example: Num. 6:3-4 forbids the Nazirite from drinking wine or strong
drink or their vinegars or liquor of grapes, or eating fresh or dried grapes or
anything made from the grapevine, from the kernels (chartsanim)
to the husks (zag)
According to Bergman, Nazir 34b reads
this passage as prat ukhlal uphrat,
but this seems to me unjustifiable, if ‘strong drink’ (shekhar,
which can make one drunk) refers to alcoholic beverages other than wine and
such. For in that case, ‘wine and strong drink’ cannot be wholly regarded as a prat
in relation to ‘products of the vine’, which is a klal
at best only in relation to wine and other grape-based drinks, fresh or
dried grapes, and kernels and husks. The way all these items are listed is
natural enough, in three classes grouping together alcoholic drinks (not all
grape-based), normally eaten forms of grape, and parts normally wasted by the
consumer, respectively, and additionally mentioning a wider class which most (but
not all
) of the items fall under. To insist on fitting them into the format prat
ukhlal uphrat
is artificial and inaccurate.

We should also mention here the principles miklal hatsarikh liphrat and miprat hatsarikh likhlal
(general term requiring a particular
and particular term requiring a general
which R. Ishmael’s list groups together as one (Rule
No. 7
We may classify these, as Bergman does (presumably following previous
authorities), with the klalim uphratim. The distinction between them is, he suggests,
effectively: whereas klal uphrat and prat
and their ilk concern the collective effect of separately clear
terms, the hatsarikh rules relate to vague terms whose precise meaning is only
clarified by their mutual impact on each other. This distinction is very fine
indeed, and rather forced judging by the examples given in the literature

I would say, rather, that a case could be made for distinguishing between
functionally independent terms (broadly speaking, classes of entities, which may
however have a hierarchical relation; e.g., ‘animals’ and ‘bulls’) and dependent
terms (more precisely, a relatively independent term, like ‘bulls’, and its
complementary clauses; e.g. ‘the horns of
or ‘the goring of people by‘). The
relation between independents is at best simply subsumptive (bulls are animals),
whereas the relation between dependents is a more complex one, like possession
or action (bulls have horns and bulls gore people)
The former supplement each other, the
latter complement each other. I do not
mean to say that the Rabbis did classify their inferences under this or that
heading on the basis of the distinction I am proposing (though perhaps they were
trying to), but rather that if they insisted on making some kind of subdivision
of the phenomena at hand, they might relatively usefully have selected it
instead of the above mentioned
I say ‘insisted’, because my distinction too is not radical enough to justify
the formulation of additional hermeneutic rules. For one can usually (and much
formal logic is based on this operation), perform what is known to logicians as
a ‘permutation’
and change the complementary term into an independent one (bulls are
‘horn-having things’ and bulls are ‘goring things’).

A note on statistics. The Soncino general index has 77 references to the
topic of klalim uphratim (supposedly, but I did not check). These come under
various headings: amplification, 5; amplification and limitation, 15;
amplification following amplification, 2; extension in exegesis, 5; general
principles and exceptions, 1; general rulings, 2; generalisation, 2;
generalisation and specification, 28; limitation in exegesis, 6; rule, general
and particular, 1; rule, extension and limitation, 1; ribbui, 1; ribbui umiut,
1; specification, 1; specification as exegetical rule, 2; specification and
generalisation, 4. As before remarked (in the discussion of Talmudic
a-fortiori), to what extent such a list is exhaustive and non-repetitive, is
hard to say without further investigation. In any case, it does not tell us
precisely how many times each rule is actually used.


The present analyses were made possible thanks mainly to Bergman’s
detailed presentation of the 13 Midot.
Though I dislike that author’s pompous tone and unquestioning fanaticism,
and disagree with many of his specific positions, he is to be commended for
his unusual efforts to clarify the hermeneutic principles. All too often,
authors are simply content with listing examples with a minimum of
reflection; he at least tries (if not always successfully) to sort out
logical relations explicitly.

The formalization of relations
is not technically valuable (apart from saving space), and tends to alienate
and confuse readers; for these more abstract features of propositions, we
shall stick to ordinary language.

We may regard the Rabbinic principle ain
mikra yotse miyedei pheshuto
(quoted by Enc.
, p. 371, with reference to Shab.
63a and Yev. 24a, and there
translated as “a Scriptural verse never loses its plain meaning”,
with the added comment “i.e., regardless of any additional
interpretation”), as an implicit recognition that interpretations using
the hermeneutic principles were not always natural. It may be asked how they
managed to mentally accept conflicts between a midah-generated
reading and a simple reading (pshat),
given such a principle!

I am referring here to the Rabbinical subdivision of the dayo principle discussed earlier, in ch. 4, footnote 10.

Notwithstanding, the Sages were, in my view, very wise to reject
corporeal punishment for breach of prohibitions discovered through qal
argument, or for breach of Torah prohibitions whose penalties
were inferred through qal vachomer
argument. In practise, we can rarely if ever be 100% sure of having freed
our deductions of all possible material uncertainties; and therefore some
injustice might be caused. What is true of qal
, the most deductive of Talmudic arguments, should be all the
more true of the other hermeneutic principles. (According to Enc. Jud. pp. 371-2, this canon concerning inferred prohibitions or
penalties, is R. Ishmael’s: ain
oneshim min hadin
; R. Akiba disagreed. We are referred to J.T. Yev. 11:1, 11d.)

We are not here dealing with a dead language, so the job is less

e.g. does ‘take’ (qach) always
signify acquisition by monetary payment, or must other meanings of the term
be supposed, and if so how are they to be distinguished? It is not enough
that an analogy is applied in one instance (without problems ensuing from
that one application); it has to be tested in all other cases where the term
appears, throughout the text at hand.

The references given by Bergman for these three provisions are all
post-Talmudic: Halichos Olam for
the first two, and Rabbeinu Tam and Tosafot for the third.

Or, to be more explicit: pretensions, lies – made in support of a
certain ideology, that of unchanging oral law. Note well the basis of my
accusation: precisely in the attempt to buttress their concept of the
fullness and continuity of tradition, these people are forced to acknowledge
the occurrence, in the case under consideration, of incomplete transmission
of information, and thus imply a loss of data in the interim and the
unreliability of the transfer. The proposed formulae are therefore
inconsistent with their own motive, and therefore must be inventions.

Enc. Jud. , p. 368, refers
us to Shab. 64a and J.T. Yoma 8:3, 45a. Enc. Jud.
explains the development of the idea of “free” (mufneh)
terms, as a way to prevent abuses of gezerah
in the schools; it adds that this is a R. Ishmael requirement,
which R. Akiba apparently disagreed with.

Not to be confused with the principle of R. Akiba that in the Torah
no word is superfluous and no word-placement is accidental.

Note, however, that in some cases, traditionally classed as heqesh
(see Abitbol, pp. 100-104), Scripture itself explicitly establishes the
parity between the two areas of law. For instance, Deut. 22:26, which
compares rape and murder, saying “for as when… even so…” (ki kaasher… ken hadavar hazeh.). In such cases, an inference is
much more certain, though it may well have some limits, because it is
analogical rather than contextual.

Heqesh and semukhim are classified by commentators with gezerah shavah; but I am not sure why (except for analogies given
explicitly in the text) – they are not really subcategories of it, being
based on neither homonymy nor synonymy, but on textual proximity. Perhaps it
is because they often involve elements of gezerah
, that they were rather grouped with it. Also note, the
distinction between them is ambiguous: in text originally devoid of
punctuation, like the Torah, how to tell the difference between the two
parts of the same verse or two touching verses? It only becomes meaningful
once the subdivisions of the text are established.

Looking further into the issue, I found
some interesting remarks in J.E.
Apparently, gezerah shavah
initially referred to “analogies in either word or fact”, but
eventually was restricted to verbal analogies (homonymies), while heqesh became used for factual analogies (synonymies). If that is
true, my presentation of these terms, based rather on Bergman’s account, is
inaccurate (terminologically, though not in essence). With regard to semukhim,
it is attributed by J.E. to R.
Akiba, quoting him as saying “every passage which stands close to
another must be explained and interpreted with reference to its
neighbor” (with reference to Sifre
Num. 131); it adds that ‘according to Ishmael, on the contrary, nothing may
be inferred from the position of the individual sections’. In view of this, semukhim
cannot strictly-speaking be counted as implicitly included in the 13 Midot
of R. Ishmael.

A case in point seems to be the above given example (Exod. 20:13):
supposedly the next two commandments (against bearing false witness and
coveting) are not subject to death penalty; in that case, why should
stealing (or kidnapping) be a capital offense? Of course, if a proposition
is surrounded on both sides by a
certain subject-matter, it becomes more likely that the common
subject-matter of the two adjacent propositions somehow concerns the
boxed-in proposition. Nevertheless, the possibility of accidens
remains; there may well be significant underlying differences, which can be
pointed to. An example is Exod. 21:15-17, where a law concerning kidnapping
is found between two laws concerning striking and cursing parents,
respectively. (Note that, as an acquaintance of mine, Dr. M. Izbicki, has
pointed out, the laws on striking of parents and kidnapping both concern
violent acts. Also, see Cohen, p. 474; the law assigns a penalty of
strangulation for these two, but stoning for cursing parents).

Regarding heqesh and semukhim, Bergman adds additional details, which we will not comment
on, here, to avoid repetitions. I want only to point out that the semukhim
inference he gives as an example at the end of the section is very odd: from
(Deut. 22:11) the proximity of the prohibition
of ‘shatnez’ and the prescription of ‘tzitzit’, the conclusion is drawn that
shatnez is allowed in the case of
the tallit! This is far from normal inference, since the conclusion is an
to one of the premises, although there was no inconsistency
between the premises. Formally, the argument runs as follows: ‘You mustn’t
do X. You must do Y. Therefore, when you do Y, you may do X’. Since the
conclusion formally implies ‘you may do X’ it is contradictory to the major
premise; such argument thus depends on an anti-literal particularization of
the major premise.

Our identification of binyan av
with causal arguments may be too narrow; some examples in the literature
seem like mere extrapolations with nary an underlying cause and effect
thought-process (though we might construct one, ex post facto). An example
given by Scherman illustrates this: Just as one may neither marry one’s
sister from the same two parents, nor one’s father’s full sister; then,
since one may not marry one’s sister from the same mother but different
father, ‘it follows that’ one may not marry one’s father’s maternal
half-sister (ref. to Yevamos, 54b). Scherman says binyan
is also known as mah matsinu?
(“what have we found?”), though Bergman informs us that these two
were counted separately in Hillel’s list. I suspect the Rabbis at first
engaged in generalizations with little reflection, and then gradually found
it necessary to clarify conditions.

English logician (1806-1873), author of A
System of Logic
(1847). Mill’s formulation of these methods is more
complicated than the one proposed here: ‘agreement’ is observed constant
conjunction of two phenomena, ‘difference’ is the constant conjunction of
their negations; thus, the formal relationship is mutual, i.e. the same in
both directions: this is the strongest form of causality, in which the cause
is not only sufficient for the effect, but necessary or a sine
qua non
for it. Note that, in all such definitions (as Mill was aware),
cause and effect are difficult to distinguish: to do so, we must look at
their temporal or conceptual sequence. Note also that Mill suggested other
important methods, namely ‘residues’ (elimination of alternatives) and
‘concomitant variations’ (see Appendix 1, section 3).

This approach is known as Chada
(Aram., ‘one from one’). If the one-verse variant is so called,
then the two-verse variant may presumably be called ‘one from two’ (but I do
not know what it was actually called).

According to Bergman, this second school claimed the one-from-one
inferences obvious and not needing to be included in the 13 Midot.
How they viewed the ‘one from two’ formula, he does not say.

Heb. tsad hashaveh.

Added proof of which is the lack of distinction, in the ‘common
feature’ approach, between one-verse and two-verse inference in accordance
with R. Ishmael’s formula. That is, if in this approach ‘one-verse’ means
‘one from two’, then what might ‘two-verses’ mean?

Logicians refer to the underlying logical fallacy as post
hoc ergo propter hoc
(i.e. ‘after this, therefore because of this’).

Unless, of course, it is already proven that A, C, D are the only
alternative possible causes of B; so that the inference consists in
elimination of two out of three possibilities. But that is not everywhere
the case.

The logical naivety of such argument should be obvious. Say a boss
calls three of his employees to his office (intending, say, to congratulate
the first for his new-born son, give a raise to the second, and fire the
third). No one knows the boss’s reasons, but the third employee tries to
guess why he has been invited, by looking for a ‘common factor’ in the two
others. He says: “it cannot have to do with hair colour for the first
is blond and the second is a brunette; it cannot have to do with honesty,
because the first is dishonest and the second is honest; it must therefore
have to do with nose shape, because both, and indeed I too, have the same
nose shape.” His whole argument is utterly fallacious and beside the

For it always remains conceivable that non-mention
of B in certain passages signifies negation
of B, even though there are no known cases of presence of A with absence
of B, which fact inductively allows us (indeed, obligates us) to generalize
and say that A implies B.

Conditional/partial causes, considered together with their conditions
or allied parts (i.e. collectively), constitute unconditional/complete
causes. Occasional effects, in loosely defined surrounding circumstances,
become constant effects, when the significant circumstances are more
precisely pin-pointed. All such variations on the theme of causality are
obvious to anyone who has studied hypothetical logic, considering multiples
and compounds of antecedents and consequents, and nesting; it is no great
secret (at least nowadays).

Where X, Y, Z have in common A, and X, Y have in common B; and they
would conclude that Z has B, also.

It does not surprise me, therefore, that, according to Bergman, ‘the Gemara
does occasionally raise such a refutation’. He adds that ‘the commentators
(to Kesubos 32a) have formulated principles to explain these
exceptions’; I have not seen these principles, but we must keep in mind that
they are ex post facto rationalizations, since natural logic allows
alternative causes.

Another issue they raise is whether the exceptions have to be
‘significant’ or not – claiming that refutation of a ‘one from one’ binyan av requires a legal exception (‘stringency or leniency’),
whereas against a ‘one from two’ binyan
any exception (legal or non-legal) will do. I can only say that such
a distinction is not made by natural logic.

I refer here, of course, to deductive logic; if the ‘implication’ is
merely inductive, i.e. not necessary
but only recommended as probable,
it might conceivably be preempted with reference to wider considerations.

See also, possibly, the items: exegetical principles, 2 references;
rules by which law is expounded, 2; texts, exposition of, 3; texts,
implication of, 1.

This phrase is wrongly translated by Bergman as “generalizations
and specifications”; we would prefer “generalities and
particularities” or “genera and species”. Strictly speaking,
the term generalization, in English, refers to a mental process moving from
a particular statement to a general one, and specification refers to a
movement from a vague statement to a more precise one. Here, however, the
issue is finding out how wide or narrow was the intent of the writer of the

Note, however, that in English an adjective usually precedes a noun,
while in Hebrew if follows it.

A way to explain the mention of the overclass is to regard it as
intended to allude to its
instances or subclasses not included in (or alluded to by) the mentioned
subclass; which are to be the subject of an unstated proposition of opposite
polarity, which makes the stated particular a contingent.

Albeit the theoretical formal convergence between these approaches,
they in practise often led to divergent material conclusions (with R.
Akiba’s often ending up as Halakhah). I would need more specific knowledge
of the Talmudic debates concerned to be able to explain why. But, assuming I
have correctly understood the formalities and basing myself on the few cases
I have studied, I would say that such differences simply go to show the
amount of subjectivity involved in the ‘inferences’, in practise.

e.g. ‘logical arguments,
syllogism, adductions, are means to knowledge’ does not restrict the genus
to the listed species. One might construct a sentence in this way, if one
thought some auditors unable to grasp the generic subject’s name without
apposition of some more familiar species names.

e.g. ‘Aristotle’s syllogism, a deductive argument, yields categorical
conclusions’ does not intend the genus as a whole but only the species. The
genus, here, serves only to place the specific subject in a larger context.

It is interesting to note that the rationalistic philosophy, trying
to explain every word and word placement in a certain preconceived manner,
which is assigned to R. Akiba, is here, and in other instances, really at
the basis of R. Ishmael’s inferences, as well as R. Akiba’s.

It is noteworthy that R. Ishmael mentioned only the first of these as
one of his rules, ignoring the second and also klal-klal-prat
and prat-prat-klal. My explanation
of such repeated gaps in R. Ishmael’s list is simple: as often in the early
stages of an investigation, thinkers do not initially work out an exhaustive
analysis of the topic concerned with reference to symmetries,
but rather concentrate on cases which happen to arise before them in the
context of their less abstract concerns. It is only later that they, or
their successors, look into other possible combinations and permutations
suggested by reshuffling the terms at hand. R. Ishmael did not get around to
that systematizing stage; his successors did. (All well and good; what is
annoying is their attempts to justify their results by imputing them
anachronistically to him.)

A technical distinction suggested by the Rabbis between the two
stated principles is that, quoting Bergman, the first “dictates that
every item which bears even one similarity to the specification is
included,” whereas in the second “the item to be included must
resemble the specification in at least two aspects.” He adds: “How
significant the resemblance had to be was left for the Sages to determine.
Occasionally, they considered several aspects as one.” Here again, I
must say, I see no natural basis for these added details.

These words are variously understood by the Rabbis.

Another kind of example is Num. 18:16, which according to Bergman is
interpreted in Shevuot 4b as klal ukhlal uphrat. Here, the forcing consists in reading a subject,
predicate and qualification of predicate as classes (broad, broader and
narrower), ignoring entirely their relative positions (logical roles) in the

Why he should do so, when he separated klal
and prat ukhlal, is a
mystery to me; or alternatively, why were not the latter two and their
multiples grouped together, similarly? I would suggest, here again, a
failure to stand back from accumulated knowledge and re-order and
systematize the results obtained.

For instance, the example from Lev. 1:2 given earlier would,
according to Bergman’s definitions, constitute a klal
hatsarikh liphrat
rather than a klal
, as well as I can tell. Note, however, that Bergman hints that
‘there are many varying opinions’ concerning the definition of hatsarikh processes; so we might reserve judgement.

This distinction is reminiscent of that which logicians make, between
categorematic and syncategorematic terms, though not exactly identical. Note that,
unlike independent terms, dependent terms are not conjoined by a mere ‘and’,
but by more intricate relations like ‘of’, ‘by’, ‘for’, ‘through’.

A Torah example might be Num 18:16: “according to your
valuation, five silver shekels” (mentioned in an earlier note), where
‘five silver shekels’ makes no sense by itself, apart from the concept of
‘valuation’ (in this case, for redemption purposes).

It should be noted, however, that certain terms, which are
colloquially put in a similar format (notably, ‘capabilities of’ and
‘metamorphosis of’) cannot be freely permuted without causing eventual
contradictions. But such issues cannot be addressed in so narrow a context;
they are fields of logic in themselves.