Appendix
4.

In this appendix, we review three currently popular texts on Judaic
logic. Our object here is not merely to summarize those texts, but to give the
reader an idea of the scope of traditional Talmud heuristics, and in passing
perhaps bring to light some topics of epistemological significance.

1. Feigenbaum’s Understanding
the Talmud.

2. Rabinowich’s Talmudic
Terminology.

3. The Ramchal’s Ways
of Reason.

1.
Feigenbaum’s Understanding the Talmud.

The student of Talmud
may know how a Talmudic discussion is generally running, but that is not enough.
He must also recognize and appreciate the role played by each line, how the
Gemara goes from premises to conclusion, who is talking to whom, whether a
statement is merely explaining or modifying previous statements, what question
it purports to answer, and so forth. Key phrases, which signal discursive
events, and logical structures, which shape the discussion, must be noticed and
correctly understood.

The student is advised to avoid pronouns; to know where a quote ends
(e.g. through signal words in the next
sentence) and what part of it is relevant; to know whether the person speaking
is a Tana or an Amora; to be aware at all stages of the issues at hand, what is
being said and why, what is sought and what for, etc.; to identify what means
are being used to deal with these issues: what kind of statements are involved
(as per classification sketched below), what each accomplishes, in relation to
which other(s), etc.; to chart the flow of discussions[1];
to understand in what way(s) the Gemara has affected the Mishnah – its
interpretation, its applications, its explanation (supposedly, in contrast to
the simple reading or pshat); and to
grasp the overall result (qualification, expansion, rejection, validation,
etc.).

A dispute occurs when two
authorities make conflicting statements about some issue. Conciliation is
eventually achieved through providing ‘proof’ one way of the other, which
may mean quoting an authoritative text or sharing a logical insight (svara). The interplay of authority of statements has to be carefully
considered: for instance, “a mishna, braita or posuk
(verse from the Torah) can only be taken as proof of a statement when the quote
cannot be explained in any other way“[2].
Various kinds of statements may be distinguished:

·
information
statements, which relate non-legal data with some function in the discussion;
including

explanatory statements,
which clarify something without however laying down or modifying or delimiting
the law; as well as

·
legal
statements, which as well as lay down the law describe the circumstances of
their applications (the ‘scenarios’ they concern); including

qualifying statements,
which define the limits of the law, by significantly qualifying the
circumstances or the cases where it is applicable.

To this we, with more of a logician’s eye than a Talmudist’s, might add assumptions,
temporarily taken up in the course of a discussion, which are subjected to tests
and finally adopted or rejected; This modal
element should not be ignored, as it makes manifest the inductive rather
than deductive course of the discussion.

Feigenbaum rightly stresses the dynamics of discovery. The student must
not rush to judgement but perceive and follow the intricacies of elimination of
theses, the multiple if-then statements and apodotic processes, which result in
a complex dialectic. In the Gemara, the course of argument is usually through
questions and answers. Different sequences of questions (Q) and answers (A),
shape varying ‘logical structures’, such as:

Q1 is posed,

A1 to Q1 is proposed,

Q2 to A1 is posed,

then A2 to Q1 (or to Q2) is proposed….

For this reason, it is important to know just what preceding statement(s)
each question relates to, and just what question each answer relates to. The
outcome is usually sorted out with reference to the wording of the last answer.
Questions may neutrally pursue information or signal fault-finding in a thesis
and in some cases ultimately the defense of some counter-thesis.

An information question (sheelah)
may seek the resolution of an independent legal issue, or the Torah or logical
source of a statement; or the authorship and location of a citation, or some
explanation; it does not in itself intend to put in doubt the authority or logic
of a previous statement. Whereas an ‘attack’ question (kushya),
seeks to show that (directly) some previous statement, or (indirectly) an
implication thereof, is false or needing qualification or superfluous, by means
of an authoritative quotation or logic; such questions may be quite long and
composed by many components, each of which plays a part in the whole attack. The
answers to questions may accordingly provide the requested information, or yield
to an attack, by limiting the statement under attack, or making it clearer
somehow, or parry or counter-attack, by weakening or discrediting the attack
question somehow.

A rhetorical question, one with an ax to grind, of course may or may not
succeed in its intent to cause the rejection or adoption of a thesis: the
intellectual impact of the whole discussion
must be considered to evaluate the final level of credibility of each side. Note
well the common faculty of logical intelligence which must perforce be assumed
for all human beings, without which no rational consensus could ever be
attained.[3]

2.
Rabinowich’s Talmudic Terminology.

1.
Rabinowich’s work,
which is my favourite, begins by studying the
terminology of the Mishnah itself. We may characterize some of it as
analytical and some as synthetical. Analytical terms may indicate what is
included in or excluded from a proposition, to what or when it applies[4];
or compare and contrast items, for such purposes of classification; or order or
hierarchize the various items under consideration, on some basis or other; or
suggest implications[5].
Synthetical terms may give inductive evidence or counter-evidence, in support of
or in opposition to a proposition[6];
or give some deductive (or, at least, inductive) reason (taam)
for or against a proposition[7];
or define the sequence of development of concepts, as intellectual phenomena, or
eventually as ethical precepts (this is done through terms like lekhatechilah
(prima facie) and bedieved
(ex post facto), discussed elsewhere[8]);
or describe the parliamentary process through which the authorities debated and
eventually came to an agreement regarding some matter[9].

These broad categories are, be it said, applicable to Gemara as well as
to Mishnah; however, the specific terms used to fulfill each investigative task
differ considerably in the two texts. Moving on to a study of the Gemara’s
terminology, we find a richer field reflecting the increased complexity of its
overall tasks, due to the fact that it is essentially a commentary on the
Mishnah.

2.
The Gemara seeks first to clarify
the Mishnah through linguistic and logical analysis. Such investigations
proceed by means of queries[10]
which draw attention to an issue, following which a reply of some sort is
sought. The questions and answers have standardized wordings for each kind of
situation.

The analytic task of the Gemara
is to determine the subject-matter precisely. It may clarify the wording of a
Mishnah, its choice of words and sentence construction, progressively focusing
on different details. Or it may make explicit the cross-references within
sentences; or endeavour to understand the meaning of a term or proposition: what
kind of thing it is intended to refer to; or clarify the scope of applicability
of a term or proposition: what instances or subcategories of instances it is
supposed to include or exclude, specifying any qualifications, limitations,
unmentioned extensions, describing exceptions or different cases. Or it may
describe the case at hand, or its surrounding context or underlying conditions,
in more vivid detail.

The synthetic task is to
investigate the processes leading to or supporting the Mishnah statement(s) at
hand. Here, the Gemara labours to grasp the whys and wherefores of a statement,
what knowledge it adds, what goals motivated its formulation, and what evidence
or proof supports it, explicitly in the Scripture or indirectly by
interpretation; or to draw conclusions from given statements, by eduction,
deduction or inductive methods like generalization. Many of these concerns
include issues relating to inter-rabbinical debate, such as the distinction
between Babylonian and Palestinian opinions or between Babylonian schools,
differences in the opinions of individual Rabbis or in the ways they derive
their opinions, reasons for dissent, questions of authorship, all of which give
an opinion a larger context.

Having determined what the Mishnah is saying, the
Gemara then checks it for consistency and draws inferences from it. The
Gemara looks for hidden incoherences. A Mishnah term, phrase or sentence may
seem inappropriate or out of place in the context (causing the Gemara to
reinterpret the passage or add clauses). A Mishnah may use different words for
seemingly the same thing in the same passage or in different passages (in the
former case the Gemara regards them as equivalent, in the latter case as
incongruent). It may superfluously repeat something apparently already said or
state the obvious (in which event the Gemara may interpose some specific
difference or possible objection). A Mishnah’s wording of a law or provision may
appear overly vague or ‘incorrect’ to the Gemara (in which case the latter may
emend or even put in doubt the authenticity of the former).

The Mishnah may seemingly redundantly mention analogous cases side by
side (this is presumed by the Gemara to be in anticipation of possible
objections due to minor differences in the cases, implying such differences to
be in fact incidental). The order of presentation of classes may be surprising,
in view of their habitual hierarchy. Or a listing of cases may be surprising, in
view of the a-fortiori inclusion of one in the other (in such event, the
intention is merely to emphasize the climax or anticlimax involved, the
hierarchy). The Gemara may consider a Mishnah list of the cases included in a
category as too limited; or notice that only some of a specified number of
subcategories are listed; or find the definition of a category too broad, due to
omission of relevant differentia, misleadingly suggesting more cases than
intended. Or again, a Mishnah may present a rule as ‘general’ which is not
really general according to the Gemara[11].

Various sorts of conflict may be spotted in a Mishnah by the Gemara: a
decision in a Mishnah may be contrary to already established principle; or two
parts of a Mishnah seem to have incompatible implications; or there may be
different decisions in two areas, which should have been the same; or a conflict
may be found between authoritative passages; or a case may be presented which is
contrary to the law preceding it. Such inconsistencies are reconciled by
assigning the conflicting passages different meanings or applications, or
different authors – which are constructed by the Gemara, backwards as-it-were,
from the case under review.

Acknowledged disputes in the
Mishnah are analyzed by the Gemara. The Gemara may elucidate the reason why a
Mishnah sage dissented, and the reply of his opponent(s) to his objection, or,
in the absence of an explicit reply, itself offer a reply. The Gemara may
contrast two or more seemingly identical legal opinions in the Mishnah, or point
out the different principles underlying conflicting opinions, possibly by
inferring divergent implications from them. Or it may indicate the areas of
agreement between conflicting opinions, and limit the differences between them
to specific issues; or clarify why a certain dispute in one case does not extend
over to another case. The Gemara may focus on the apparent inconsistency of a
Mishnah disputant, who seems to take different positions in two passages; it may
suggest that, in one of the passages, he is reporting another sage’s opinion
(rather than his own) or that another sage is (wrongly) attributing an opinion
to him. The same may occur for two disputants, in which event their opinions in
one of the passages may be regarded as having been accidentally interchanged.

3.
The Gemara uses special words to
quote from the various authoritative documents or oral sources. Thus, the
expressions matninan, tenan, among
others, will refer to Mishnaic sources; matnina,
tenu rabanan, tanya, etc. to Baraitot; and for instance tena, to Tosefta. A passage quoted is bound to be directly or
indirectly relevant to the presentation or discussion at hand, the purpose of
such quotation being, for instances, to illustrate or explain, support or
undermine, qualify or amplify. After quoting a passage a propos of some other topic, the Gemara may later return to it and
discuss it further for its own sake.

A memra
is a “reported teaching, opinion or decision of the Amoraim”, i.e. reported
by an Amora in the name of another Amora (that is, Gemara sage). The report may, according to the
expression used, concern a single, undisputed statement
(amar R. Ploni[12]),
or a single, contested statement, without its counter-thesis (R. Ploni amar),
or a controversy between two or more Amoraim (Itamar
R. x amar … R. y amar …). The
name of the reporter may be given, and it may be made clear whether the report
is direct (first-hand, oral transmission) or indirect (hearsay, via an
intermediary).

A single memra may be received
in the Gemara in a variety of ways. A memra may seem superfluous, because
already found explicitly in a Mishnah: but in such event, the memra
usually brings some additional new point. If the memra is only implicit
in a Mishnah, the ‘duplication’ is not an objection to the memra, since it
performs a useful function and is corroborated by the Mishnah. If a memra is
found to be corroborated by a Baraita, one need not wonder at its superfluity,
because
an Amora is expected to know every Mishnah, but not every Baraita. A
memra may seem to be in conflict with a Mishnah or Baraita, in which event the
former may be rejected, unless the said conflict is shown to be merely apparent.
A memra may be brought in to confirm another memra (e.g. a Babylonian supported
by a Palestinian). If two Amoraim report opposite memras regarding the same
topic, the original authors of the conflicting positions will be assumed
two/different persons. A memra’s authenticity may be put in doubt by some
other participant, on the basis that its alleged author expressed different
opinions elsewhere; since both the reporter and the objector are Amoraim, their
status is in principle equal, and some reconciliation must be sought (though in
some cases one side may win). A memra may at first be strongly objected to, then
finally admitted by the Gemara in rectified form to allow for the objections.

A multiple memra, reporting
conflicting opinions, may be variously dealt with in the Gemara. The source of
the conflict may be that a Mishnah expression was interpreted in different ways
or that the reason for a ruling was understood in different ways. Or the dispute
may reflect a doubt regarding the final decision in a case; or about some legal
principle not clearly stated, or concerning some subsidiary case not considered
by the Mishnah. The Gemara will look for and consider the different practical
consequences of each position, identifying points of agreement and eliminating
them from the discussion. The Gemara may then arbitrate (supporting one side,
rejecting the other) with reference to a Mishnah or Baraita, or find therein
support for both (or neither?), or subject the arguments pro and con to
evaluation by common-sense, or find reason to admit both sides (no deep dispute
being apparent, only a different case or circumstance of application), or even
remain undecided. Sometimes, the wording of the memra leaves unclear which of
the conflicting Amoraim held which of the two opinions: in such situations, and
other doubtful situations, the Gemara may look at previous pronouncements of the
Amoraim in question, to determine their previous lines of thought. Sometimes,
the divergence between Amoraim may be rooted in a similar divergence between
Tanaim.

4.
Questions are often rhetorical,
serving to put forward a foregone conclusion: an intent to affirm (X is) may be
cast in the form of a negative question (isn’t X?); an intent to deny (X is
not) as a positive question (is X?). However, interrogations are usually
way-stations in the Gemara’s inquiries. Four kinds are distinguished. (a)
Questions expressing astonishment at some unexpected
statement or inquiry contrary to what is obvious; such questions may serve as
sufficient answer or may result in a more developed reply. (b) Questions asking
for the meaning, reason, sources or
purpose of some statement or part thereof. (c) Questions which raise an objection,
pointing to a difficulty or conflict…

A retort to an
objection is termed peruka (to redeem,
rescue). A difficulty is termed kushya,
and its resolution, terutz; the latter
may be a single thesis, or multiple theses (two or more alternatives of equal
force given), or a thesis offered then contested. A difficulty may, however,
remain without resolution. There are various kinds of disagreement, incongruity
or contradiction. Contrasts between statements of equal authority, such as two
Scriptural passages or two Mishnah and/or Baraita passages, are termed rumia (to cast in opposition). Conflicts of statement by an Amora
with the higher authority of a Tana are termed tiuvta (Aram.; Heb. equiv. teshuvah).
A distinction made, with reference to the cases or circumstances concerned,
between statements seemingly in conflict, to show their compatibility, is termed
shinuia.

An objection may be countered by revealing a dilemma (ma nafshekha, what is
your wish) – such that one way or the other a similar objection (or defense) may
be raised. Lo tsrikha signifies the
possibility of a further alternative, such as a middle ground, which dissolves
the dilemma; leolam (still,
nevertheless) signifies the maintenance of one of the alternatives, though
possibly with small modifications[13].
An objection may, after attempted replies, be reinforced by a
“rejoinder”, which serves to invalidate proposed replies, showing them
somewhat weakly argued, or not sufficiently wide-ranging in their
considerations, or merely relative to opinions not universally held.

(d) A question may be used to point out
a problem (baayah) – that is, any sort
of doubt with regard to the interpretation of wording of a Mishnah, or the legal
decision in a case (of practical significance, yet not provided for in the
Mishnah), or the source or reason for a law. The solution, if any, is a Baraita
or an Amoraic statement, and may be indicated by the verb pashat.
If no solution is found, they say teku
(let it stand). Sometimes, problems within the possible solutions to a problem
are anticipated, to intensify the initial problem. Sometimes the issues raised
are simply ignored, being too petty or theoretical (unlikely to arise in
practise).

Various terms and phrases are used
to introduce an argument, i.e. the reason (taam)
used to prove or disprove any matter.
The argument may start with premise(s) or with a conclusion. ‘Direct’
arguments show the truth of something; ‘indirect’ show the falsehood of the
contradictory (a sort of reductio ad
absurdum). The following classification of arguments is proposed. (a)
Argument from authority, called proof or evidence (rayah), are the overriding basis of Jewish law; this may comprise a
Torah, Mishnah, or Baraita text or an Amora’s teaching or a “Sinai
tradition” or an “established principle”[14].
(b) Argument from common sense (svara)[15].
(c) Argument from careful analysis of construction and implication of law (diuqa),
including inferences from positive to negative or vice-versa, based on davqa reading of law. (d) Argument by analogy (heqesh or dumia[16]),
the similarity of two cases being used to extend a decision made in one case to
apply to the other case as well. (e) Argument a-fortiori
(qal vachomer), by means of which a law’s applicability is extended
from one case, where circumstances are less favorable, to another, where they
are more favorable; in Hagadah passages the expression used is al
achat kamah vekamah.[17]

Refutation means showing a
proposition false: by disproving it (tiuvta,
to reply), or overthrowing the arguments supporting it, i.e. rebuttal (pirka,
to break in pieces, dechiah, to push
over)[18].
Disproof may be direct, showing a
conflict between the statement in question and a Mishnah or Baraita, or
indirect, showing that if the statement were accepted then a certain Mishnah or
Baraita would have been expressed differently or would be unexplained. Rebuttal
depends for its method on the type of argument attacked. If the argument is by
authority, it is shown to be based on misunderstanding of the passage it refers
to; or it is shown that the passage refers to other cases than those under
consideration; or it is shown that the passage referred to is not
authoritative, being an individual opinion not accepted by all. If the argument
is by common-sense, it is shown that its approach is logically faulty or another
approach is shown better (adaraba…,
on the contrary…); sometimes, note, the objection raised is mild/polite, not
strong/decided, it is merely pointing out a certain possibility
which could invalidate an argument, showing that alternative approaches are
available, without implying these to be superior or exclusive or established. If
the argument is by construction or implication, it is shown too arbitrary, since
the same construction or implication applied elsewhere (to another clause of the
same passage) could lead to contradictions (between the conclusions drawn from
the two clauses); such rejections are often found in Talmud[19].
If the argument is by analogy, the resemblance between the cases equated is
shown superficial, significant differences between them having been overlooked.
If argument is indirect, it is shown that a similar objection as was raised by
the argument can be raised against the
argument itself or its conclusion. Many arguments are rebutted by showing that
their implications are excessive in some way, leading to inadmissible
side-conclusions in addition to the conclusions aimed at.

Besides minor discussions, consisting of punctual questions and answers,
objections and rejoinders, etc., there are more elaborate debates (pilpul[20])
in the Gemara, usually concerning the interpretation or applications of a law or
the development of a new general principle. These debates were between equal
members of an academy or a teacher and his prominent disciples. Only the names
of important participants are mentioned in the text, the rest remaining
anonymous. The list of pilpul debaters is on the whole rather limited; for the
rest, their discussions are more restricted in scope.

3.
The Ramchal’s Ways of Reason.

The two books above are
modern, though quite traditional presentations of Talmud heuristics. It is worth
our while to look also into a rather older work, The Ways of Reason (in Hebrew,
Derech Tevunot) by R. Moshe Chaim Luzatto, also known by the acronym RaMChaL[21].
What distinguishes this work (in my view) is that it purports to be at once an
aid to Talmud study and a discourse on logic – a logic resembling, and no doubt
influenced by, Western logic of Greek origin.

The Ramchal was born in Italy early in the 18th century, later emigrating
to the Netherlands[22],
and in his brief life-span of four decades, he wrote several books on various
subjects (ethics, theodicy, Qabalah), which have deservedly become classics and
are still widely read in Jewish religious circles today. His work is
distinguished by its clarity of exposition, and the ability to organize and
order traditional ideas. The Ways of
Reason is an intelligent, readable work, on the whole; but exceptionally for
the Ramchal, I am sorry to say, it has many serious flaws – perhaps he wrote it
in a rush[23].

The Ramchal seems to be to some extent acquainted with Aristotelean
thought, but not as fully as one might expect from a reading of the latter’s
works. Most important, the Ramchal seems totally unaware
of the formal-symbolic method of logical analysis which Aristotle
inaugurated; his approach is to describe features and processes in general
terms, and appose examples from the Talmud. Consequently, his logic is a mere
sketch, at best an outline, of the subject, apparently without awareness of some
deeper issues in it (like, validation), and without an acquaintance with the
technical tools which had been developed by that time (like, squares of
opposition); also, he does not systematize, nor make exhaustive analyses. On the
other hand, his range is somewhat wider than that of logicians up to his time,
evidently because of his Talmudic background.

In his listings of logical tools and processes, the Ramchal tends to mix
apples and oranges. All propositions are put on the same level; they are not
classified with reference to their structural differences, nor are their
structural relationships brought out. Thus, for instance, we find (in ch. 3) an
inventory which lumps together actual categoricals (“simples”,
according to the translators), modal categoricals (“qualifieds”),
exclusives, exceptives, ethical conditionals (“conditionals”),
hypotheticals, propositions with two or more subjects or predicates in
conjunction or disjunction (“compounds”), and others still. There is
no analysis of the features of these propositions, no groupings are attempted,
no explanations given.

The doctrine of oppositions and eductions of the Ramchal (in ch. 4) is
complicated by his attempt to compare propositions with different terms.
Obviously, his frame of reference is Talmudic debates; there, propositions with
different subjects and/or different predicates are dynamically interrelated; the
Ramchal seeks to address these practical issues immediately. But in Aristotelean
logic, such issues cannot be dealt with directly; it is only at a later stage,
through the theory of the syllogism, that they can be formally resolved[24].

It is interesting that (in ch. 5) the Ramchal adopts the Talmudic, rather
than the Aristotelean, interpretation of particular propositions (i.e. as
definite, rather than indefinite). That is, “some X are Y” excludes
“all X are Y” and includes “some X are not Y”. He does not,
however, so far as I recall, make a distinction between deductive and inductive
contexts, nor realize that the said relations are sometimes in the last analysis
overturned. With regard to syllogistic argument, I find no fault in what he
says, except that he does not say much (see ch. 7). There is no discussion of
the figures of the syllogism, or of its various moods, nor of the processes of
validation – yet these matters are the most impressive achievements of
Aristotelean logic.

This is what is missing throughout the Ramchal’s treatise: formalization,
systematization and exhaustiveness. Did he not know all about the syllogism?
Perhaps he never read about it, but merely learnt a little on the subject by
word of mouth or absorbed it osmotically from the surrounding culture of his
time.

The Ramchal additionally mentions some other forms of mediate inference,
including apodosis (hypothetical or disjunctive “syllogism”). He
mentions argument by analogy: X1 is like X2, in that they are both Y, and X2 is
Z, whence X1 is Z, pointing out that such arguments can be rebutted. As well, he
mentions a-fortiori argument, in the
form: X1 is greater than X2, and X2 is Y, therefore X1 is Y; we may notice,
however (see chapter 3 of the present volume), that the middle term which
explains and justifies the process, being the
respect in which X1 and X2 are compared, is lacking, and also that he is not
apparently aware of the formal varieties of the argument (but the form of his
argument is correct, as a positive subjectal).[25]

For the Ramchal, logic is something we grasp intuitively (ch. 1). He
distinguishes literal truth from the allusive, the figurative, the hyperbolic
(ch. 6). He is sensitive to the dynamics of reasoning (ch. 8, 9). He is aware of
many of the categories which our conceptual faculties tend to refer to (ch. 10,
11).

If the purpose of Ways of Reason
is to give Jewish students of the Talmud a raised awareness of the underlying
logical issues, then I would say that it is valuable. It is not a copy-cat
compilation, but a thinking man’s reflections on the subject. If however those
who read it think that they are getting a proper concept of what the body of
knowledge called the science of Logic has to offer (or even, had to offer, in
the Ramchal’s time), I would say they are misled[26].
There is more to the subject than Ways of
Reason lets on. The book is interesting, but not necessarily the best
primer. Its chief advantage is the kind of examples it gives; but there are
better organized and thorough teaching tools today. Students can always find
appropriate examples for themselves, in the way of an exercise.

Back to
Chapter 9