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© Avi Sion
All rights reserved
Sundry notes and essays on Logic
© Avi Sion, 1995. All rights reserved.
Part II, Chapter 2: (Chapter 10 in 2008 reprint)
A Brief History and Evaluation
essay was first written in 1990, then completely revised in 1995.
All comparative and historical studies are likely to deepen and enrich
our understanding of logic in general. Reading the article on 'The History and
Kinds of Logic', in the New Encyclopaedia
one is struck by the total absence of any mention of Hebrew, Israelite,
Talmudic, Rabbinic, Judaic or Jewish contribution to logic before modern times,
except for a mention of 13th century logician Isaac Albalag. Since Jewish
(religious) literature, notably the Torah and subsequent books of the Bible, was
highly developed many centuries before the advent of Greek philosophical
literature, one may well wonder to what extent the former deserves to be ignored
by historians of logic.
Indeed, the said NEB article
itself admits that the Western view of the history of logic may be biased by
limited access to sources in other cultures. I quote:
Judging from the outline of the development of logic given so far, it
would appear that logic has been an exclusive product of Western culture. Some
historians of the subject, however, have found this view parochial and sought to
identify traces of logic in Indian and Chinese thought. But research in these
two fields is beset with tremendous difficulties: most of the texts remain
unpublished or untranslated; some of the monographs are unreliable; and scholars
well trained both in logic and philology are extremely rare. Thus, a fair
evaluation is, as yet, impossible.
The same difficulties and barriers beset historians, who wish to trace
logic history more globally, with regard to Judaic logic. The Talmud, in
particular, is a dense and complicated document, written in Hebrew and Aramaic,
not accessible to all comers.
To begin answering our question, we must first distinguish between the
art or actual practise of logic, and the science of or theorizing about logic.
This distinction applies equally well to individuals and whole cultures. So our
question is really two-fold: as of when is there evidence of logical thought in
Jewish culture, and when did Jews begin reflecting on their own thought
processes? Another, equally important, issue is: how extensive and how good were
their logic practise and theory?
It is clear that such questions could and should be asked in relation to
any culture, not just Jewish culture; but we will make this a case study of
sorts (as the topic happens to have aroused the author’s personal interest!).
Furthermore, we need to study the mutual influences, if any, between cultures:
who taught what aspects of logic to whom? In this regard, we may refer, on the
one hand, to obvious, manifest influences, one way or the other, and on the
other hand, to subterranean, assumable influences. The media often misplace
credit and attribute innovations to imitators. Here, a reflection is called for,
concerning the methodology appropriate to historical studies, which involve
We cannot, of course, in a brief essay, hope to solve all these problems.
It is interesting to start with an apperçu
of the claims made by Jewish traditionalists.
Talmudic and Rabbinic legal discussions are replete with complex
reasoning processes, which seem logical, at least at first sight. With regard to
historical record, these discussions began around the 2nd or 1st century BCE —
that is, when the Mishnah (the crux of the Talmud) was developed — stretching
to the 5th century CE. However, according to Talmudic and Midrashic literature
(the latter dates from about the same period), claiming oral tradition, Talmudic
debates were mere reflections and continuations of legal discussions dating from
Mosaic, and in some instances from Patriarchal and even Antediluvian, times.
Furthermore, Talmudic and Midrashic literature reports that Talmudic
legal decisions were based on a number of explicit interpretative, or hermeneutic,
principles, claimed to have been taught by G-d to Moses, and then faithfully
transmitted by word of mouth to Talmudic generations. These principles, or Midot,
were intended to facilitate and govern understanding of the written law given in
the Torah (the first Five Books of the Jewish Bible, revealed at Sinai some
3,300 years ago).
If these principles were rules of logic, and if they were indeed as
ancient as alleged, then the Jewish people had a functioning logic theory long
before the Greeks (whose known written work in the field started around the 4th
century BCE). This does not seem unreasonable, if we reflect that the Israelites
had a written language and developed literary culture several hundred years
before the Hellenes.
Now, this is the traditional thesis, very briefly put. Let us leave it at
that for now, and trace the history of Jewish logic in a bit more detail. (The
reader is referred to standard reference works for more ample details, such as
the Jewish Encyclopedia
and the Encyclopaedia Judaica.)
There is certainly evidence of logic practise in the Torah and subsequent
Books of the Bible. A Midrashic work (Bereshith
Rabbah, 92:7) explicitly notes this, listing ten a-fortiori
arguments scattered in it (for example, Genesis, 44:8). In fact, as the present
author has shown elsewhere, there are many more a-fortiori in the Bible. Furthermore, as well as such deductive
practises, we find inductive practises (namely, adduction)
in it, which are even somewhat explicited (in Deut. 13:2-4 and 18:21-22).
However, apart from the just mentioned passages, there is no mention, use
or listing in the Bible of the hermeneutic principles which make their written
appearance in Talmudic times. The exception is a-fortiori
argument, which is used by
protagonists in the Biblical narrative (including G-d, Moses, patriarchs, kings
and prophets), though not explicited
or explicated in any way. Adduction,
though used and to some extent explicited (but not explicated) in the Bible, and
in fact widely used in the Talmud, is not counted by the Rabbis as a hermeneutic
As far as the written record shows, the hermeneutic principles used in
the Talmud and after were authored by sages of the time, notably Hillel
(to whom a list of 7 is attributed) and his rival Shammai
(both Tanaim, participants in the
Mishnah), R. Ishmael (to whom a list
of 13 is attributed, in Sifra, chapter
and his rival R. Akiba (both Amoraim,
participants in the Gemara). It may readily be admitted that, as is mentioned in
the Talmud itself, these men learned some of the interpretative rules they
taught from their own immediate teachers, or that they induced them by
observation of their own or their close colleagues' thought processes — but it
is hard to prove that these principles were already known in Biblical times and
were taught by Moses.
It is worth noting that, though the lists of hermeneutic principles
proposed by these various Rabbis have points of agreement, they also in some
instances exhibit significant differences. These methodological disagreements
predictably affected the reading of the Biblical text by the various Rabbis
concerned, and their respective schools, and caused divergences in their legal
opinions (ab-initio, though they were
eventually harmonized, by means like majority vote). If these various principles
had indeed, as claimed, a common, Mosaic origin, it is difficult to explain
convincingly why they were contradictory; if the contradictions were due to
erosions of memory, it is difficult to assign Mosaic authority to the
Furthermore, detailed analysis shows that the language in which the
hermeneutic principles was expressed went through a process of change and even
evolution. This is evident in the case of the one process which is found in the
Bible, and later in lists such as those of Hillel, R. Ishmael and the slightly
later R. Eliezer ben Yose ha-Gelili (whose list had 32 principles), namely a-fortiori
argument. In the Bible, the language used in such argument is colloquial and
unspecific; whereas in the Talmud and after it is much more technical, involving
specialized terminology (like the expression qal vachomer) not used in other contexts, which is clearly the
product of a theoretical reflection.
Additionally, if we compare the lists of R. Ishmael (who only mentions a-fortiori,
but does not describe or analyze it) and R. Eliezer (who distinguishes between
two variants of it, namely michomer leqal
and miqal lechomer, i.e. from major to
minor and from minor to major), we may well conclude that there were in fact
theoretical developments over time. We may similarly observe a development from
Hillel (1st century BCE) to R. Ishmael (2nd century CE) in other principles. For
instance, the klal uphrat, prat ukhlal
principle of Hillel is regarded by most authorities, traditional and secular, as
having been split up by R. Ishmael into several more specific rules (namely,
Nos. 4-7, and possibly 8-11).
We can thus say without fear of error that there was an evident
evolutionary trend, and reject the notion of a monolithic Rabbinic logic of
Sinaitic origin, unchanged by time. Such origin is only explicitly and
dogmatically claimed much later, anyway, having been apparently first proposed
by Saadia Gaon (d. 942 CE), and then echoed with more and more insistence
(because of the gradual perception of its capital importance in the
justification of Rabbinic law). The Mishnah of Pirke
which purports to name the trustees of the oral transmission of Jewish law from
Moses to its own day, does not specifically mention the hermeneutic principles.
Moreover, the evolutionary trend visibly continued in subsequent
centuries, with more and more refinements and restrictions proposed by
successive generations of Rabbis, as new queries and insights arose. The latter
always pretended to be mere vehicles of ancient traditions on the subject; but
there is no textual evidence to support such claims. We must rather see them as
'arguments by anachronism' — it was common practise in the Middle Ages (also
before, and since, in Judaism and elsewhere) to
try to justify a belief by attributing it to a past authority. This device
was buttressed by intimidation: accusations and threats which silenced potential
critics for centuries.
The practical skills in hermeneutics did not change much; indeed, one may
well admit that the earlier masters in the art were superior to their later
disciples. (I do not mean to imply that later authorities, like Rashi or
Maimonides, were deficient in skills, but only that their forerunners were,
after all, their teachers). What evolved was theory; and it did so in two
directions. One good: improved definitions, clearer understanding of the
mechanics involved; one bad: a reduction of freedom of thought, an attempt to
control use of the processes, so as to prevent modifications in the law.
So much, here, for the history of Jewish logic in itself. Let us now
consider things in a broader historical context and with regard for the
objective value of processes.
To precisely determine the place of Judaic logic in world logic history,
we must evaluate it; that is, objectively assess it, determine how much of
it, if any, may be considered as really logic. In a broad manner of speaking,
any thought process is an act of 'logic'. What makes us, however, class it as
good logic, or logic in the sense of a scientific thought process, is our
ability to demonstrate its universal validity.
It is, without doubt, Aristotle
(a 4th century BCE Greek) who must be credited with the discovery of the
scientific method of validation of arguments. Prior to him, no one we know of
had come up with the idea; though his predecessors, Socrates and Plato, had
begun to become aware of the issue. The method of Aristotle was simple, though
brilliant. It was, firstly, formalization:
the substitution of symbols in place of specific terms, the consideration of
form irrespective of content. Secondly, the testing of processes (so denuded of
particular issues) with reference to the 'laws
of thought', namely identity (A is A), non-contradiction (A cannot be nonA)
and exclusion of the middle (either A or not A).
What is amazing, historically, is that Aristotle's method was never
grasped or adopted by the teachers and law-makers of Judaism, even though they
had had considerable contacts with the Greeks. Historian Chaim Raphael,
of Oxford University, describes their early relations as follows:
The Jews… had been aware of the Greeks as part of their world long
before the arrival of the Macedonians under Alexander the Great. Greek traders
had been familiar in the coastal towns of Palestine as early as the seventh
century BC. There were Greek mercenaries in the Egyptian and Babylonian armies,
including the army of Nebuchadnezzar. From the time of its greatness in the
fifth century BC, Greece had poured a profusion of explorers, adventurers and
scholars into the Near East, and the Jews had responded.
But I am not sure this is an entirely accurate picture. The fact is that
although Israel/Judea was conquered by Alexander, a direct pupil of Aristotle
and a man interested in cultural exchanges with the peoples he conquered; and
although he was, exceptionally, well-liked by Jewish traditionalists; and
although the Jews remained under Greek political dominion and/or cultural
influence for centuries thereafter (until the Roman takeover, and the Romans had
a Hellenistic culture, anyway) — Aristotle's conceptual breakthrough in logic
had apparently no direct effect on Judaism. However, perhaps we should not be so
surprised. After all, Alexander's empire stretched East all the way to India,
yet Indian philosophy seemingly never adopted formal methods of discourse,
Generally speaking, we may expect the interactions of peoples to involve
some give and take of information and methods. But we cannot predict, without
detailed study of the matter, precisely who influenced whom, and in what domain
and to what extent. It is as erroneous to presume that the politically dominant
party shall have the greatest influence, as to presume that the intellectually
or spiritually superior party shall have it. The historian must avoid pure
speculations, based on a very narrow context of data and driven by hidden
In the present case, we can on the basis of close study affirm the
regard to the Jewish Bible, a document which according to Jewish
tradition and most secular historians antedates Greek logical discoveries by
about 1,000 years (but, according to so-called Higher Critics, by only a couple
of hundred years):
There are evidently both deductive and inductive
reasoning processes in its stories and legal statements. Differences in this
respect between the various Books of the Jewish Bible do not seem significant
(i.e. are probably just happenstance), judging by linguistic and statistical
While use of categorical and hypothetical
syllogism may be found in the Torah and other Books (it would seem odd if it
were not, since thought by means of classes and theses is fundamental to human
thought), it is not there talked about in an abstract manner. That achievement
is undoubtedly Greek (Aristotle, Philo the Megarian, for examples).
As already stated, there is a distinctive
deductive process in several of the Jewish Books, namely a-fortiori argument; again, this is repeatedly used, but never
talked about. This form of argument may have been used by the Greeks (it remains
to be shown), but they never noticed it or elucidated it theoretically (as far
as we know). The fulfillment, to a large extent, of these tasks may safely be
attributed to the Rabbis of the Talmudic period and after. A-fortiori
arguments do occur in the Christian Bible (notably, in Paul), but their abstract
discussion in Western philosophy appears much later, in the Middle Ages.
As already stated, too, we find in the Book of
Deuteronomy a nearly formal expression of the two laws of adduction, concerning
the confirmation or elimination of hypotheses. These laws are there stated in
relation to the empirical testing of prophecies and prophets; but, nevertheless,
they are so clearly formulated that they may be viewed as a universal lesson in
inductive cognition. Furthermore, since these statements concern evaluation of
what religion conceives as the highest level of consciousness (namely,
prophecy), they are perforce applicable to lesser levels. Western formulation of
the two laws of adduction is a much later phenomenon, in the era of Francis
Bacon and Isaac Newton.
Other kinds of reasoning, deductive and
inductive, are doubtless manifest in the Jewish Bible, though in much less
differentiated form. If arguments appear, they are enthymemic rather than full;
and they are used, but not discussed as such.
regard to the Talmud (whose legal debates began to all evidence a couple
of centuries after the Greek conquest of the Holy Land) and after:
We find there much more complicated reasoning
processes (inductive and deductive) and much more developed linguistic tools
used, as well as considerable theoretical reflection on many of these practises.
Rabbinical thought processes included, not only arguments by analogy and causal
inferences, but also (though less consciously) opposition, eduction, syllogism,
production, dilemma, generalization and particularization, adduction and many
more forms. However, contrary to orthodox claims, the Talmudic and later Rabbis
were not infallible and all-knowing; they (individually and collectively)
made practical and theoretical mistakes.
On the positive side, we may mention especially
two processes, which were more developed in Rabbinic logic than elsewhere,
namely a-fortiori argument and reconciliation
of conflicting theses. With regard to these (the first and thirteenth Midot of R. Ishmael), there is no doubt that the Rabbis were in
advance of their time for centuries, both in the quantity of their practise and
in the quality of their theoretical awareness. However, though these processes
are demonstrably valid, it does not follow that their use by Rabbis was
invariably faultless, nor that their understanding of them was complete.
It must be stressed that Aristotelean logic did not take into account degrees
of possession of qualities (as does a-fortiori
argument), nor the 'balancing of opposites'
aspect of logic (as does harmonization of conflicting theses). The species of a
genus might have a hierarchical relation to it, but this was not brought out in
the syllogism (which merely confirmed the common ground between the terms); and
when two arguments arrived at opposite conclusions, there was no conscious
attempt to reconcile them (the reasoning process stopped or became unconscious
as of the discovery of conflict, with the thought that 'one thesis or the other
or both must be wrong'). Greeks evidently functioned in a more 'either-or' (or
'all or nothing') mode than the Jews, who rather sought to find the nuances
between predicates and the commonalties of disparate views. In Rabbinical
debates, this attitude served to maintain the credibility and authority of all
On the negative side, Rabbinic thinking included
many wholly or partly questionable if not demonstrably invalid forms. 'Logic'
was to the Rabbis very often merely a way to buttress predetermined
'conclusions', rather than a means to discover unknown facts. This is evident in
many of the interpretative techniques they adopted. There were always, in those,
an appearance of verity; but closer analysis shows them to have been fallacious.
fallacy consisted in drawing a possible
conclusion and declaring it necessary; that is, an inductive alternative was attributed the status of a deductive
certainty. Another sleight of hand consisted in starting with a general premise and (even though it not give rise to a
conflict) particularising it along the way, so as to obtain a conclusion
contradictory to what it would otherwise have been. The arguments passed,
being often too intricate for non-logicians to sort-out. 
Thus, though their approach was not always
lacking in objectivity, it was essentially unscientific. Their ultimate
arguments, stated or tacit, were that they had Divine sanction and traditional
continuity, and that whoever disagreed with them was merely expressing rebellion
against the powers that be and deserved punishment accordingly. Because the
Rabbis did not have a concept of impartial validation of thought processes by
formal means, they could not see how they might possibly err.
As already remarked, it is very surprising that
the formal method and specific discoveries of Aristotle were not understood or
adopted by the Rabbis; nevertheless, that is historical fact and the main
explanation for their practical and theoretical problems. In early centuries,
this avoidance of the scientific method was perhaps naive, a side-effect of
Jewish rejection of the mores and morals of non-Jews; in later centuries, it
became dogmatic, an intractable ideological position.
I think the existence of such distinctive currents in Judaic logic, for
good or bad, proves the point, that it has been an independent and distinct
enterprise. R. Shmuel Saffrai, of Hebrew University in Jerusalem, author of the Encyclopaedia Judaica article 'Hermeneutics', reaches a similar
It is debatable whether (as suggested by the 12th century Karaite author
Judah Hadassi) any Greek influence can be detected, though terminologically some
of the rules have Greek parallels.
Much later, of course, mutual influences between Jews and non-Jews
developed considerably. Christian (and Moslem) scholars in the Middle Ages and
after were influenced by Rabbinic methodology, whether through study of written
texts or in oral disputations.
And Jewish scholars, like Maimonides,
did eventually study Aristotelean logic.
Some Jewish commentators attempted to justify this new openness by interpreting
(quite logically!) 'the commandment to maintain correct scales, weights and
measures (Deut. 25:13-15) as referring to the rules of logic', in addition to
its literal sense.
The role played by Jewish translators in logic history should also be mentioned;
they helped to revive interest in Aristotelean logic, bridging the contemporary
Moslem and Christian cultures.
Nevertheless, to repeat, Greek formalism never found its way into
Judaism. Logical skills can, indeed, as Jewish tradition claims, be adequately
taught and passed on by way of examples,
which may moreover be classified under rough descriptive/prescriptive
principles. This continues to occur in Jewish circles, and therefore can be
assumed to have occurred in the past; furthermore, it occurs in non-Jewish
circles. The communication of any knowledge content always involves passing on a
'way of thinking'; this is sometimes more effective than teaching logic by
explicit principles. Nevertheless, non-formal methods are deficient, in that
they do not permit a proper evaluation of the material transmitted; only the use
of variable-symbols makes certainty possible.
The New Encyclopaedia Britannica: Macropaedia, 1989 ed.
is well established on the basis of archeological evidence, the Greek
alphabet was a relatively late offshoot (c.
6th century BCE) of the Phoenician, which was almost identical to the
Hebrew. The alphabet from which the Phoenician and Hebrew evolved is
estimated as dating from the 17th century BCE.
York: Funk and Wagnalls, 1968.
To 'adduce' information, means to put forward data which continues to
buttress some hypothesis, or (in the negative case) henceforth eliminates it
Bulka, Reuven P. As
A Tree By The Waters. Jerusalem:
Feldheim, 1980. (pp. 19ff.)
The Road from Babylon: The Story of Sephardi and Oriental Jews.
London: Weidenfeld and Nicolson, 1985. (p. 31.)
individual's error is collective if uncorrected by the peer group.
here merely highlight two examples. See
especially the analyses in chapter 10-12 of my work Judaic
Similar disputations are reported by the Talmud to have occurred in
Greek and Roman times.
Maimonides (Spain, Morocco and Egypt, 1135-1204) was very impressed
by Aristotle's presentation of logic and at the age of sixteen wrote a book
on logic in Arabic, the Makalah fi Sana'at al Mantik. (See Enc. Jud., 11:459-460.) His later and better-known Guide
for the Perplexed, which defines many logical and philosophical terms,
was highly influential on Christian (and Moslem) thinkers, including Thomas
Aquinas and Leibniz, as well as on Jewish thinkers like Spinoza. (See
Heschel, Abraham Joshua. Maimonides: A
Trans. Joachim Neugroschel. New
York: Farrar, Straus, Giroux, 1982. p.
209.) More important, without such logical studies, it is doubtful whether
Maimonides would have become the powerful systematizer of Jewish law he
became, notably with his Mishne Torah,
influencing all subsequent treatment of the subject.
In some cases indirect influence seems evident, though direct study
is doubtful. This is I suspect true of R. Moshe Haim Luzatto, known as the
Ramchal (18th cent.), in his Derech
Tevunot (The Ways of Reason. Trans.
D. Sackton and Ch. Tscholkowski. Jerusalem:
Heschel, p. 168.
Raphael, p. 102; and Enc. Jud.
Written in Geneva, 1995, to correct an article called
Jewish Logic written in 1990 and published in World
of Chabad of Vancouver, B.C.