1. Motives of the
Present Research.

2. Conclusions of our

Motives of the Present Research.

Logic: A Formal Analysis of Biblical, Talmudic and Rabbinic Logic

is not the work of a Talmudist, but that of a logician. The author, who made
significant contributions to various fields of (secular) logic in his previous
work, felt qualified in that capacity to analyze and assess, in novel ways, the
logical processes found in Judaism. A logician can claim to understand Talmudic
logic, without claiming more than minimal knowledge of the Talmud. A Talmudist
certainly has much greater knowledge of the Talmud’s content, and by virtue of
regular practise may well be a far superior practitioner of Talmudic logic. But
a logician has the advantages of theoretical knowledge and the habit of
apprehending the formal aspects of thought; he may not take into consideration
all the forms of reasoning used in the Talmud, but he can more deeply comprehend
those which he does encounter.

In an absolute, normative sense, the term “logic” must refer to
something universal. Logical mental processes are forms of thought which take us
closest to truth in a given context of raw data. The science of Logic is a
record of such forms combined with attempts to explain their distinctive
efficacy. The idea that there are “logics” particular to cultures is
not a denial of universality, not a claim that different peoples or periods are
subject to different epistemologies. A given culture may be defined and measured
by the sum total of its experiences and conceptual insights, as well as
imaginations and actions; and this collection of factors differs from culture to
culture. Logical practise and theory are aspects of culture, and are bound in
specific cultures to differ in scope and emphasis. The underlying human
apparatus of knowledge remains essentially the same, but it may develop in
various directions and to different degrees. Of course, judgements are feasible;
relativism is untenable. If different practises or views of logic are found not
to be in harmony, an evaluation is necessary: there must be some kind of
ignorance or error on one side or the other or both.

The present study was undertaken with three motives in mind:

To elicit from Talmudic logic any information of value to general logic.
Contrary to what might be thought, secular logicians have not exhausted their
field. The science of logic is an ongoing enterprise, which, in spite of the
great successes of Aristotle, Philo, Bacon, Mill, Russell and Lewis, still has
much to achieve. Its mandate is nothing less than a thorough observation and
evaluation of the forms of human thought (conscious or unconscious, commonplace
or rare), and their assimilation in an all-embracing epistemology. As it
happens, at least two forms of argument which were emphasized by R. Ishmael and
his colleagues, namely a-fortiori argument and reconciliation of conflicting
theses, have received little or no attention from Western logicians so far.

To provide Talmudists with more developed logical tools and techniques.
Although many teachers and students of the Talmud possess very impressive powers
of reasoning, they are apparently rarely aware of the abstract aspects of their
thinking processes and of the need to formally validate them. They are able to
formulate or follow enormously complex arguments, in their heads, orally,
without recourse even to pen and paper; but would be unable to capture and
explain the underlying patterns which ultimately justify the conclusions. Apart
from certain stock classifications, they remain suspended at the level of
content, untrained in formalization. Such a pragmatic approach can yield
valuable results, but a systematic approach is bound to be more efficient and is
more certain to avoid error.

To focus the debate between science and religion on epistemological
rather than ontological issues.
The integration of our secular knowledge and spiritual beliefs is a
fundamental need of the human mind and culture; the alternative of
compartmentalization involves a sort of mental or cultural forcing, and can only
be a temporary measure. Conflicts between experience and reason, on the one
hand, and faith, on the other, can best be diffused by a dispassionate
consideration of the underlying logical issues. Many disagreements can be
harmonized, by showing at the least that the sides are simply alternatives in a
disjunctive proposition, which though they may inductively be of varying
probability are deductively on equal footing, for all practical purposes a
matter of personal choice.

To what extent these goals have been fulfilled, readers will judge. In
addition to these theoretical purposes, the author had a personal motive, namely
the review of his own religious commitment. For this reason, and in order to
make clear to readers that the work has gone through a process of evolution, and
was not a pronouncement of preconceived dogmas, it was necessary to write the
book in such a way as to allow the various
archaeological layers of eventual thought to remain visible
, so far as
possible within the limits of consistency. During most of the writing period,
the book’s title was to include the word Reflections,
to signify return again and again to a topic, under the influence of new
discoveries or insights in other areas. Transparency makes the process as
important as the result. The result is, it is hoped, a lesson in independent
thought; meaning, not invention, but free research of the facts and
possibilities, commitment to reality and acceptance of eventual doubts.

Jewish tradition asserts that such intellectual explorations may be
spiritually dangerous. Going too deeply into questions is likely to increase
sources of doubt, and complicate spiritual life (with inner conflicts and lack
of social uniformity), if not cause sin and apostasy. To be sure, philosophers
have not historically been happy and well-adjusted people, or shining spiritual
examples. But one might also wonder how high a spiritual life based on imaginary
, though easier and less risky, more pleasant and impressive,
takes one. Knowledge and knowledge of one’s ignorance are tests. Like all other
tests, one may fail them – or pass them. It may be that failing them, one is
worse off than having not taken them; but passing them, one is better off than
having not taken them. In any case, to advocate that life be faced with open
eyes, is not to look for trouble. Life, for everyone, is rife with opportunities
for religious doubts; surely it is better to learn to take things of that sort
in stride, than to rigidly resist until one day perhaps some major experience or
insight shatters the whole defensive structure. A spiritual commitment out of
pure faith, transcending all empirical and rational forces, and of course
emotional forces, would seem more stable in the long run. And that presupposes a
certain intellectual openness and flexibility.

also Addendum 13


Conclusions of Our Study.

Now, we have already effectively listed, in the Abstract and table of Contents
at the beginning of this book, and we need not repeat them here, the various
topics covered by our inquiry. Our task, here, is to draw some sort of final

With regard to aspects of Judaic logic which can enrich Western logic, we have
extracted the following material:

historical interest

is evidence in the Torah (and Nakh), as well as in Talmud (and other Rabbinic
writings), of use and awareness of various complex forms of reasoning, in some
cases well before their assimilation by Western literature or philosophy.
Particularly noteworthy are the following:

There is clear
evidence in the Torah of knowledge of the two laws of adduction.
They are not merely used there, but
are expressed as principles (Deut.
13:2-4, 18:21-22); however, the principles are not formulated in purely formal
terms, as general logical methods, but in relation specifically to the
evaluation of prophecies and prophets. In any case, this antedates by centuries,
if not millennia, Western consciousness (though probably not, use) of adductive
procedures. Adduction is commonly practised, and ably so, in Talmud and other
Rabbinic writings, but (as far as this author knows) it does not receive
theoretical attention.

On the other
hand, we find in the Talmud another important inductive practise, with a
considerable measure of self-awareness (developed more fully in later Rabbinic
writings), namely, reconciliation of
conflicting theses
(kushya, terutz).
This process plays a major role in Talmudic discourse, and is counted as among
the 13 principles of hermeneutics. It is found used later in Christian (and
supposedly, in Moslem) debates of the Middle Ages, and acknowledged in Western
philosophy in the concept of dialectic (thesis, antithesis, synthesis), but has
otherwise not received due focus and formal treatment in Western logic. The
author of the present work has in his previous work, Future Logic, proposed a
thorough formal analysis.

argument is often, and properly, used in the Torah and Nakh (we have indicated
some 30 cases); however, though certain words recur in these contexts, the
terminology is not uniform or exclusive, and there is no evidence of
self-consciousness in this practise. In Talmud we find a very frequent resort to
a-fortiori, as well as a specialized
and the awareness of such argument as a distinct
. This practise continues in subsequent Rabbinic writings, which
furthermore develops a theoretical understanding of the argument, including distinction
between positive and negative moods
; however, though near-formal,
this understanding is not entirely formal, being expressed specially in terms of
the stringency or leniency of legal/ethical prescriptions, prohibitions and
indulgences. We have in this volume proposed a more formal analysis of the

There is
further evidence of logic in the Tanakh, in the sense that the characters within
the narrative make “if-then-” statements which suggest underlying
reasoning processes, but (so far as this author has noticed, apart from the
above mentioned) these processes are not very transparent, and so difficult to
identify precisely and classify. Furthermore, contrary to the claims of Jewish
tradition, there is no textual evidence that the hermeneutic principles were
known, or that Talmudic-style debate was engaged in, in Biblical days. Of
course, the Bible is not intended as a manual on logic and need not have
reported such matters. But the linguistic evidence in the case of a-fortiori,
the only identifiable process for which we have data, tends toward such
conclusion, especially when we compare later, Talmudic, terminology to the
Biblical, and consider the evidence of development from Mishnah to Gemara.

We find in the
Talmud, and later Rabbinic discourse, highly developed deductive procedures in
the field of ethical logic: the
various kinds of ethical
statements, issues of awareness, motive, intention, attitude, transfers of
ethical modality from genus to species of action or vice-versa, are clearly
considered and understood by Talmudic participants and thereafter. To what
extent such factors were assimilated by the legislators of other nations in the
same period(s) of history has not been investigated by this author; but judging
from the comparatively deontic slant of Jewish culture (later transmitted into
the Christian and Moslem cultures), and from the fact that Western logic has
only recently began to study the formalities of ethical logic (under the name
practical or applied logic), one may assume that the Talmud was breaking new

Finally, the
Talmud is replete with other forms of reasoning, notably opposition, eduction,
categorical syllogism, apodosis, reductio
ad absurdum
, hypothetical syllogism, dilemmatic argument, argument by
analogy, generalization, particularization, and so forth. These are frequently
and skillfully used, and with a considerable degree of consciousness of their
workings, but one would hesitate to say that the participants had engaged in any
formal studies.

One may be surprised by the Rabbis’ ignorance of formal logic. One would
have supposed that the works of Aristotle would have found their way to Judea
soon after the conquests of Alexander the Great; or at the latest by Talmudic
times, considering the degree to which Hellenic culture (or, more precisely,
Hellenistic culture) had by then permeated the so-called civilized world.
Indeed, many Rabbis are reputed by the Talmud itself to have delved in Greek
knowledge; but while they may have absorbed some of its rationalism and
empiricism in a general way, they do not seem to have grasped its logical
formalism. Even later Rabbinic writings, such as Maimonides’, which are clearly
more systematic than the Talmud, seem devoid of any really formal approach to
methodology, despite the developments in logical science of the Scholastic
period, to which many Jews contributed, at least as translators of Greek works
from Arabic (often via Hebrew) to Latin. All this suggests the insulation of
Jewish culture from its surroundings, which was indeed willed by the Rabbis, and
it demonstrates in particular the relative independence of the developments in
Judaic logic.

scientific interest
to today’s logicians are, especially, two of the above
mentioned factors of Judaic logic, namely: dialectic
and a-fortiori logic. We
would suggest that these are, if not original and special (nothing in logic can
be truly unheard of, since it is ontologically an aspect of the world we live in
and epistemologically an innate capacity of the human mind), certainly sooner
and more fully used, developed and studied in Jewish culture than in any other.
More important still, is the fact that they have not till now been seriously
considered by modern logicians. The present author claims to be the first ever,
in 1989-90, to develop a formal theory of induction (factorization, factor
selection and formula revision), which elucidated the mechanics of
reconciliation of conflicting theses; and the first, in 1991-92, to deal with
a-fortiori argument in a thorough manner.

Yet dialectic is a fundamental
process of all-embracing epistemological significance, being the way the mind
responds to the continual contradictions of our world, from the ever-changing
impressions at the perceptual level, through concept modulation, to the repeated
adjustments of abstract scientific theories. As for a-fortiori, although a
comparatively specific part of man’s logical arsenal, it is still of
considerable epistemological importance, allowing us to maintain consistency in
the quantitative (degree) aspect of our concepts. In any case, logicians are
still bound to consider such processes, just as the mathematician is bound to
consider curved spaces or binomial equations.

the negative side of the ledger
, we may mention the following phenomena,
which are of interest to science and history only as examples of how very far
from logical thought people, individually and collectively, are sometimes able
to go

We may first
note that Talmudic and later Rabbis were
far from all-powerful or omniscient in
. This comment would be redundant, were it not for the mythical
dimensions they are given by Jewish lore to justify the finality and
immutability of Talmudic and subsequent decrees. These people did occasionally –
individually, if not always collectively
– make unconscious errors of logic (even if they were very often skilled
practitioners); and furthermore, their theoretical baggage in this field was
incomplete and faulty (though admittedly not negligible). In some cases, the
practical errors and theoretical gaps seem conscious; and we may suspect them to
have been made with a manipulative intent, to confuse people and thereby impose
predetermined legal outcomes on them.

Most shocking
is the considerable number of fallacious
thought processes engaged in and defended by Talmudic and later Rabbis
. This
refers to the paralogisms involved in many Rabbinic hermeneutic principles and
practises, and also to the intimidation used to support them. The major cause of
such faulty thinking was the Rabbis’ ignorance of the formal
method of logical reflection (which they were apparently too proud to learn from
the Greeks). Consequently, processes which should have been recognized as
inductive or even unreasonable were ascribed deductive value. Lacking objective
and universally valid tools of evaluation
the Rabbis opted instead for disloyal methods: cutting corners; obscuring
uncertainties and antinomies by using overly tortuous and long-winded arguments,
without terminal organization
claiming Divine sanction for their arcane modes of thought; and parrying
criticism by means of irrelevant accusations and threats.

With regard to aspects of Western logic which can enrich Judaic logic, the
following may be said:

To begin with, it must be
understood that there is nothing foreign, i.e.
non-Jewish or anti-Jewish, in the science of logic
. It may have historically
been developed by non-Jews, with Aristotle, a Greek, discovering formalization
(that is, putting symbols in place of specific terms, in order to verify the
universality of a thought process, independently of its content) and the laws of
thought (identity, non-contradiction, exclusion of the middle), and studying the
categorical oppositions, eductions and syllogisms; and various other
individuals, some of them Christians or of other persuasions, following suit and
investigating the same in more detail or other forms of reasoning, such as
hypothetical and disjunctive argument, inductive logic, and so forth. But the
ethnic or religious identity of these people had no pertinence (any more than it
would in medicine or engineering).

The purpose of logic research is
not and was never to prove or disprove something about Gd or any religion. The
goal was and is, simply and innocently: to
understand and validate human cognition
, to know when one is right and when
one is wrong, to know what constitutes evidence and what may be inferred from
it, to avoid errors and to avoid being misled, to exercise intelligence and
defend oneself against foolishness.

Most Rabbis have had a phobia
towards “Philosophy”. But this is a straw man. Philosophy in its
purest sense, limited to epistemology and ontology (and excluding mere
metaphysical speculations, personal reflections on life, psychology, ethics,
politics, and all such relatively literary productions), is a neutral
investigation, whose results are unpredictable. Philosophy is not a
particular doctrine
, like Judaism – it is, at its best, an honest,
unprejudiced search for truth, or (if truth is not to be found) at least an
admission of ignorance. It is open to knowledge wherever it is to be found; and
those who think otherwise have not understood it. The science of Logic, in
particular, is a key discipline in this search for truth; neither quite
epistemology nor ontology, though a part of both, it stands at the interface
between them, as their motor and regulating mechanism, at once partly their
source and by feedback partly their outcome too.

To say that something is true, or untrue, and to keep piously insisting
on it, does not make it so; there has to be a convincing argument. Likewise, ad
praise or accusation, whether correct or incorrect, and hopes or
fears as to the moral or social consequences of information, have no ultimate
bearing on truth-value. Despite all efforts by the Rabbinic establishment to
interdict or ignore enlightened research and reflection, they have historically
not succeeded in preventing the statistically manifest diminution in belief and
observance among ordinary Jews
This conclusively proves the futility of intellectual arrogance and
dictatorship, and of an ostrich policy. There was a failure on the part of our
clerics to meet the challenge of rational and empirical truth head-on, and work
intelligently, and with respect for their opponents and their flock, on the
effective solution of real problems. We are all in the same boat; the problems
considered by secular logic, philosophy and science, are not goy
problems but human problems, for all
of us to take into consideration. They cannot be by-passed or waved-off, they
remain applicable to all human cognition, to all claims to knowledge. Left
without convincing validation, any claim to knowledge is effectively

Now, what we have tried to convey
in the present work, to students and teachers of Talmud and Jewish law willing
to think things through honestly and intelligently, is a
firm grounding in logic
. This means, first of all, a special way
of looking
at intellectual issues, which may be characterized as eidetic,
being an effort to consider above all the formal aspects of any argument, and
try to objectively clarify the processes involved in it by means of algorithms,
so as to determine its continuity or gaps, and be able to estimate its abstract
validity. Content is secondary, and may be affected by or affect the passions,
clouding judgement; what counts primarily is form. More important than piety is
the psychological attitude of openness and fair-mindedness, a willingness to
accept whatever reality has to offer; there has to also be a will to pursue
truth further and deeper, and not be satisfied with convenient superficialities
and complacent stereotypes, a willingness to repeatedly test and revise one’s
own current ideas.

Secondly, there is a need to
learn the specifics of existing theoretical logic, and why not when necessary
try to make further developments in the field, so as to be prepared and have the
technical means for the job at hand. Logic theory and practise are to concepts
in general, what algebra and arithmetic, respectively, are to numerical
concepts. In the domain of religion, as in any other, one cannot expect, without
adequate training, to avoid the pitfalls and limits of ordinary thinking; one
must adopt a more conscious and advanced methodology. Furthermore, the pursuit
of coherence and profundity calls for periodic bouts of systematization; the
various elements of our apparent knowledge must be ordered, and their
interrelationships clarified and judiciously checked. Dubious forms of reasoning
must be dispassionately identified as such, and ultimately rejected if they
cannot be improved upon, without yielding to intimidation. These are obvious
instructions, but always worth reminding.

Lastly, we may address a message
to Talmudists, exegetes, and Jewish lawmakers. The spiritual yearnings of human
beings will surely never cease, but they may well be dulled by the arrested
development of religion. Torah scholars, rather than trying to inhibit secular
education, ought to rather encourage all knowledge and respond creatively to the
virtue of enlightenment and hunger for more knowledge that it generates. It is
evident that the thinkers who produced the Talmud greatly enjoyed themselves;
they were, in their time, at the cutting edge of intellectual development. Men
like the Rif, the Rambam, particularly through his Mishneh Torah, or Joseph Caro, through his Shulchan Arukh, further enriched and perpetuated Judaism, because
they had the courage to rethink the Talmud, summarizing and ordering its
results, using methods which in their respective epochs were more ‘modern’. If
the approaches used in Judaism in the past are not again updated – today,
tomorrow – then the enterprise is at a dead end.

Life is movement, life is participation. Spiritual guides cannot just
re-enact the intellectual adventures of their predecessors, they must rekindle
the flame and produce light visible to their contemporaries. The Jewish market
is not buying, simply because the goods offered are rather dusty and shabby. The
impasse Judaism finds itself in today is due in large measure to an intellectual
bankruptcy, a tendency to aloofness and sclerosis. Mimicry of the style and
ideas of past achievers is not enough, there has to be a contribution relevant
to present levels of education. Many would-be defenders of the Faith seem merely
to be trying partake in the glory of famous persons (very “humbly”, of
course) and project an image of piety (for the social dividends). But most
people are not fooled by posturing; they demand more challenging and inspiring
products, which they do not have to pretend interest for, in a sort of
“Emperor’s New Clothes” frame of mind. Not all present production
falls into such weary categories; the innovative work of R. Adin Steinsaltz, for
instance, does not.

The task now, we here suggest, is
to systematize, not the content
of the Talmud and subsequent Jewish law, but their reasoning processes
It is not a matter of organizing and ordering the conclusions of past
legislators, nor even of identifying in an abstract manner the categories and
principles of Judaic hermeneutics and heuristics; but to stringently clarify and
evaluate, step by step, like in a computer program, every
argument put forward by these legislators, for each step indicating the kind of process involved

major finding of the present work is the extent to which Talmudic/Rabbinic logic
is inductive, rather than deductive.
This means that conclusions drawn by
the legislators are much more dependent on knowledge-context and technical skill
than traditionally assumed, and therefore more subject to review and likely to
need revision
On the deductive side, in any case, a great many of the arguments are enthymemes
(they are abridged, excluding “obvious” factors); wherever there are
discontinuities, a clear distinction must be made between given premises or
conclusions and propositions assumed to fill the gaps. Wherever, eventually,
mistakes or weaknesses are spotted, they must be freely admitted without regard
for the prestige of the source, without presuming against all evidence that some
unknown data or insight motivated the problematic statement, and undaunted by
covert or overt threats, by clerics, of Divine retribution (confident that Gd approves
of truthfulness).

major finding of this study is the extent to which Talmudic/Rabbinic logic is
We may no longer, today, tolerate fuzzy logic, with regard to
the foundations of religion’s methodology or with regard to its routine
arguments. These issues must be considered with an impartial and steady eye.

First, with regard to the grounding
of Talmudic/Rabbinic method. It is
reasonable that whatever methods of interpretation are ultimately adopted to
elicit ordinary laws from the Torah, if those methods are themselves claimed to
be based on Torah text, the reading of them therein must be literal and obvious
to everyone. That is, while
non-methodological laws can conceivably be “derived” from the
proof-text in weird and wonderful ways, methodological
cannot (without circularity) be similarly justified, but must
be clearly explicit in the text
, if not obvious by natural means
. This
important logical precondition applies, to start with, to the reading of
‘constitutional’ laws, like the law giving legislative authority to the judges,
the law of majority ruling, the law about neither expanding nor diminishing the
law, and so forth. With regard to the hermeneutic principles, other than
a-fortiori and adduction (which are both natural, as well as Biblical), there is
no evidence for them in the written Torah. The claim that they are part of the
oral Torah is not an argument: that there is an oral tradition seems
sociologically likely and is hinted at in the text; but whether such a tradition
originally contained these specific, or any, hermeneutic principles is
impossible to establish.

Second, with regard to
Talmudic/Rabbinic rhetoric. (a) When the illogic of certain forms of thought used
traditionally is demonstrated, we are told that the hermeneutic principles are
not really a logic, but a Divinely decreed way to decode the Torah. On the other
hand, if we look at actual Talmudic/Rabbinic discourse, it is clearly designed
to appear as a process of rational argument yielding a convincing result. They
cannot have it both ways. (b) The illogic of traditional argument is masked in
various ways. Terms and doctrines are loosely defined, and used in incompatible
ways in different contexts as convenient
(i.e. not by virtue of formally demonstrable distinctions)
Corners are cut, ostensibly for the sake of brevity, but actually to get away
with fake reasoning. Arguments are long-winded, with many side-digressions, with
the effective premises and the conclusion kept as far apart as possible, so that
the lack of connection or even contradiction between them is well hidden. There
is no honest effort at transparency. (c) When one has Reason and Truth on one’s
side, there is no felt need to ‘get heavy’ and use intimidation. Yet religious
authorities freely accuse people who say or do scientific things of being apikorsim
and threaten them with loss of heaven for raising doubts concerning religion.
One might suspect that such accusers are unsure of their own arguments, since
they resort to such techniques.

There has to be a continual and
sincere effort on our part to review and maintain both internal
, with Judaic texts themselves (with the data properly
hierarchized), and external
, with secular knowledge (again, taking into account the latter’s
degrees of probability). Logic is
something universal, which cannot be
ignored or overridden.
If there is an inconsistency in knowledge, at any
level and between any two parts thereof, it must be taken seriously and resolved
if possible, without prejudice one way or the other. Any revision called on by
strict logic, in a given context, must be accepted. This is to guarantee truth;
something is true, not merely because it is said to be, but by virtue of the
quantity and quality of effort undertaken in honestly establishing it as such.
Where an act of faith is required, so well and good; but it must be recognized
as such, and not falsely claimed to be an act of empirical or rational

Judaism can only gain, in scope
and strength, from such a programme, both in general credibility and in specific
content. For such thorough analysis would very probably bring to light problems,
the attempts at solution of which would generate new and important insights, and
might even make possible considerable revisions of the law by the established
authorities themselves
The work required can only be carried out by highly-educated and superior
intellects, people expert equally in Talmud and Rabbinic law, logic and
philosophy, and the special sciences. These would be the true Rambams and Joseph
Caros of the day, those who would ultimately inspire the Jewish people anew.

With regard,
finally, to our third stated goal, that of promoting more harmony between
secular science and philosophy, on the one hand, and religious texts and
beliefs, on the other, little more need be added to the above. The general
methodological guidelines, for both sides, are obvious enough. There is need for
openness and realism, humility and courage; looking impartially at the different
sides of an issue; attention to nuances and alternatives, and avoidance of
over-simplification; not drawing more conclusions than logically legitimate from
the data available; insistence on evidence and cogency, and consideration of
logical possibilities and probabilities; testing and re-testing all ideas –
etc., etc., etc. These are primarily attitudinal
prerequisites of valid knowledge, reflecting a certain readiness and effort of
the will, as well as a wisdom regarding the powers and limitations of the human
cognitive apparatus. Such attitudes, while not directly impinging on results,
make any results obtained more credible.

On the religious side, we have before us, firstly, the
, a text we believe, out of pure faith and respect for our forefathers,
to have been Divinely revealed. This text is often ambiguous and often
equivocal. A distinction must therefore at the outset be made between its
strictly literal meaning, to the extent that such is clearly discernible, and
all interpretations read into the text over time, by people, however
authoritative, whether in response to noticeable vagueness or incogency, or
motivated by unrelated beliefs or agendas. With regard to the relative
credibility of exegetes, there is a need to realize that the concept of
authority itself is not unassailable: taken as absolute, it involves
circularities in argument; status can only healthily be attributed by virtue of
and to the extent that, and maintained so long as, the doctrines of an advocate
are credible – the status is an
effect, and cannot be viewed as a cause, of doctrinal credibility. The possible
interruptions, and subtractions and additions, of an oral tradition must be
taken into account, when considering its end-results; critical review based on
solid information and tightly reasoned argument need not imply total rejection:
unrelated matters remain in force.

oral tradition
is claimed by its defenders to be perfect; where it seems
imperfect, a failure of vision or knowledge is imputed to the beholder, and
eventually a moral accusation and social ostracism. But a-priori
definition of the content of “orthodoxy”, as against
“heterodoxy”, implies a prejudice without appeal: it cuts short all
possible reflection and can only win the allegiance of people unconcerned with
objective standards of truth. An independent thinker would suggest that, even
granting the founding document (the Torah) to be of Divine origin, albeit the
difficulties it presents, the exegesis of that document remains liable to human
error and therefore subject to review. Errors of fact and errors of logic have
to be expunged, as in any area of human knowledge: men made them and men can
unmake them.

Furthermore, not only are
traditional statements relating to nature or history open to review, but legal
statements would seem to be also, insofar as they are based on material
assumptions and reasoning processes which may later be found wanting (i.e.
contrary to empirical findings or inconsistent). So long as they can withstand
scrutiny, so well and good; but once definite error is found, they can no longer
sincerely be upheld. Errors made in explicit statements about nature are easiest
to admit, though the more extremist authorities even today would be reluctant to
go even that far. Maimonides, who as well as a great legal expert was a true
philosopher, expressed himself clearly in this matter:

not expect that everything which (our sages) have mentioned regarding astronomy
should agree with the actual facts; for the theoretical sciences were deficient
in those days, and they did not speak of them on the basis of a tradition
received from the prophets, but rather because they were scientists by the
standards of their times, or because they had heard about these matters from
such scientists.

But, though assumptions
concerning nature or history do not always affect legal dispositions, they often
do. It would seem justified, in such cases, to demand review of the legal
conclusions, if the non-legal premises prove wrong. However, strictly speaking,
it would be a non-sequitur, since as logic teaches refutation of a premise does
not necessarily imply rejection of its conclusion. Unless
– and that proviso would seem to apply in enough cases – the conclusion could
not have conceivably been based on an alternative, acceptable, premise; that is,
unless the conclusion was manifestly exclusively
implied by the original premise (so that denial of the premise implies denial of
the conclusion).

Examples of such errors are common enough in the Talmud. The following
are obvious samples, which would not seem radically threatening:

“The time from one molad
(new moon) to the next is halakhah
l’Mosheh mi-Sinai
– ‘law revealed to Moses on Sinai’ – and is given as 29
days, 12 hours, 44 minutes, and 3-1/3 seconds. Those who understand the elements
of astronomy know that the time interval between one occlusion and the next
varies by as much as 13 minutes, owing to the varying speed of the sun and the
moon along their elliptical paths. To find the accurate average by observation
requires not only sustained observation but also accurate tools for

“There is a small discrepancy between the true length of the solar
year and that used as the basis of the calendar calculation (namely, 4 min. 21
sec.). This discrepancy, as small as it is, has added up in the course of 1500
years to approximately 4-1/2 days. This causes some difficulties with regard to
the compliance of our calculated calendar with other requirements of the halakhah.”

“According to the practice of halakhah,
the circumference of a circle is to be taken as three times its diameter”,
instead of

“Another example is the classical problem of the length of the
diagonal of a square”, which is taken as “1-2/5 times the side of the
square”, instead of
(=1.414…). “This specifies the practical procedure for determining this
length if required by the halakhah.”

These examples are given by Hugo Mandelbaum in Torah,
Facts and Conclusions
, who there gives relevant Talmud references.
He argues that these were never meant to be anything more than approximations
for practical purposes, and therefore that the discovery of inaccuracy does not
affect the law. But one might well wonder, if the Sages had known them, why they
would have ignored them, not even acknowledging the correct figures. And if they
did not know them, why continue to rely on them in the issues concerned.
Admittedly, these examples are relatively innocuous (though one might imagine
situations where they have, say, financial implications): but there are matters
of the sort which affect people’s lives more radically, e.g. in the field of

A purely empiricist/rationalistic approach to such matters does not, by
definition, take into account the factor of
. The basic issue is ultimately always the reliability of oral
transmission. Not only the Written Torah, but also the Oral Torah is claimed to
be Divinely revealed. Just as an act of faith is possible and required in the
former case, so in the latter case; the empirical-rational difficulties are not
much different in the two cases. The written document might be a work of
fiction, whether authored by Moses or others, and even if not so, it might over
time have been tampered with. Similarly, the oral tradition might be an
invention, the accretion of centuries of naivety or dishonesty, or again it
might not. Such things are difficult to prove
one way of the other.

One might point to contradictions within the written text or its bloopers
concerning nature or history, as proofs of its human origins; or one might
attribute other significances to such events. One might point to the fact that
the Sages were not always in agreement with regard to the tradition, as proof
that there was originally no monolithic tradition. Or, with more nuance, regard
situations where they were unanimous as signs of faultless transmission and
cases where they differed as so much evidence that confusions occurred somewhere
along the line. The reply that the Torah has seventy facets could seem like a
lame excuse, or one could be satisfied by the explanation that it was Gd’s will
to promote Rabbinic discussion and arbitration. At
every stage, skepticism is possible and faith is required
. What matters to
religion is that acceptance remains possible.

Another difficulty, which applies equally to written and oral revelation,
is that faith is a shaky foundation for law, since faith implies uncertainty
(the faith is intended to buttress a position) and uncertainty about the law
would seem to exempt one from responsibility for breaking it. It is true that
secular legislation is subject to similar queries (at least when we try to base
it on a concept of natural justice, as against pragmatic collective coercion),
but law based non-secular considerations often additionally goes against common
sense, or the ‘sense of justice’ (which, admittedly, is often a cultural
rather than innate phenomenon).

Ultimately, the choice of faith or skepticism has to be a personal one, not
imposed from the outside by social pressures or, worse still, by threats of
violence (except, of course, where the same rights, of others, are at stake).
Religion requires it, since ethics, which is one of the main purposes of
religion, is impossible without freedom of the will. Science requires it,
because knowledge, its principal goal, cannot be achieved under conditions of
intimidation or coercion. The individual gambles either way: opting for faith
and its promised benefits, one may waste one’s life on fanciful nonsense; opting
for skepticism to enjoy life more, one may lose Divine support and a delightful
afterlife. It is a dilemma, and who can claim to know the answer for sure? What
is evident is that once one is locked onto one course or the other, it is very
difficult (though not impossible) to escape its relentless “logic”.
And fence-sitting and indecisive swings one way and the other also have their

the side of science
, where human fallibility and the inductive basis of
knowledge are more freely admitted at all levels, calls to objectivity,
tolerance and flexibility would seem redundant. However, in practise there is a
considerable antipathy towards religion, since many if not most people do not
admit “faith” as a legitimate basis of knowledge. Those who take a
more nuanced position, would accept blind trust as a temporary way-station or
working hypothesis, in cases where experience and reason have so far not managed
to establish fact or theory of high probability, or in metaphysical issues where
science is constitutionally unable to make a judgement satisfactory to its own
standards, so that arbitrary choice (to the extent that it is necessary for
practical purposes) is inevitable anyway. But in cases where inductive logic
leans heavily in a direction contrary to the dictates of faith (alleged to be
revealed or traditional), they would refuse them. All the more so, in cases
where the issue under consideration seems definitely resolved by empirical
observation or logical analysis in a manner clearly contrary to the faith’s

It may in this context be pointed out, to begin with, that science and
religion are not in conflict in all matters, just some. There are a number of
items in apparent conflict (for example, Gen. 1:10 and 1:14-18 suggest that
Earth was created before Sun and Moon); there are many items in apparent
agreement (for examples, Gen. 1:11-12 suggests that vegetable life came first;
Gen. 1:20, that the first animal life was aquatic); and there are large areas
where neither side seemingly impinges upon the other, for one reason or another
(as suggested in the previous paragraph). Where there are conflicts, they are
not always radical; there are often areas of doubt on one side or the other or
both, which make a standoff possible and an eventual compromise conceivable. All
this means that general conclusions one way or the other are unjustified, and
issues have to be dealt with item by item, with full knowledge of the details
and conditions set on both sides.

Also, “science,” the secular pursuit of knowledge, is a broad
concept, including not only the study of the natural world (the various physical
and biological sciences, mathematics), but also the study of humans (history,
psychology, sociology, politics and economics, etc., all of which relate to the
will), and of course philosophy (epistemology and ontology, logic, which are the
sciences of science). The concerns of these disciplines intersect with that of
religion in only some areas, as already stated. But furthermore, their levels of
certainty are very varied. While the results of the natural sciences on the
whole seem most certain, there are significant variations from one specific
field or topic to the other. The human sciences, though often well documented
and tightly argued, are just as often almost conventional in their wisdoms,
products of widely accepted imagination. As for philosophy, there are many
conflicting schools of thought; and relatively few areas of agreement, let alone
solid grounds. These factors have to be taken into consideration when making

Secondly, we may linger on the methodological, rather than material,
aspects of the two domains, and take note of the similarities as well as of
differences in their approaches. Similarities include a wide range of inductive
and deductive techniques (which, to be sure, may be occasionally misused). As
for differences, some are technical, some relatively ideological or attitudinal.
Certain more ‘literary’ than logical techniques used by religious exegetes would
seem dubious to scientists; some aspects of some of the hermeneutic principles
used by Rabbis are indubitably sophistic. The reliance on faith, in cases of
scientific doubt and more so in cases where science has reached conclusions
contrary to religion, and the willingness to submit to authority, may be
considered radical divergences.

Suspending one’s own judgement, under the guise of ‘humility’ or ‘piety’,
is unacceptable to science: it is ultimately arrogance. Karl Popper has rightly
stressed the distinction between science and religion in the possibility of
“falsifiability”: science, ideally, remains flexible, open to real
change in the face of new observation or insight, whereas religion, at least in
its more fundamentalist forms, refuses to budge from certain positions, whatever
the evidence or criticism leveled against it. To be sure, the defenses of
religious apologists often seem contrived, at best appeals to very distant and
improbable possibilities, designed only to maintain their idées

Nevertheless, science is bound to remain tolerant, not merely because
religion (at its best) is one expression of the profundities of the human spirit
and the reduction of knowledge to a narrower perspective would be a loss to all
of us, but precisely because the virtue of science, in its own terms, is its
open-mindedness. We sometimes see in the media scientific discoveries and ideas
presented as final fact; but actual scientists, who are acquainted with the
wider philosophical issues surrounding the scientific enterprise, are not so
definite and exclusive. At the core of science are perceptual phenomena
(such as a flash of light in an electron microscope or a sound emitted by a
meter); from these, under certain conceptual assumptions and by means of
generalizations, natural “facts” and “laws” of considerable
reliability are constructed; and beyond those, through imagination and
hypothesis, larger “theories” are postulated and continually checked
and adjusted. At all transitions, we
depend on our logical intuitions (or ‘common sense’, which relies on
conceptual phenomena) to guide us to
appropriate results.
This always leaves a “window of opportunity”,
however remote, which religion can appeal to, and science, to remain science
(that is, true to itself), must nobly concede.

In conclusion, it is hoped that, while this work has certainly not
finally resolved all the issues, it has enriched and advanced their discussion

in Geneva, Switzerland,

November 1991 to July 1995.

With gratitude to the




That analysis constitutes the only bit of really fundamental
research, of value to generic logic, in the present work.

Needless to say, the term ethical is used here with reference to a
mode of modality, which covers legal statements as well as others.

In the way of a “rogues’ gallery” in a museum of logic!
Such exhibits are still interesting to logicians, for the reflections they

Individually is bad enough. Though collective review provides a
corrective mechanism, the fact of individual error demonstrates the
fallibility of the participants, and therefore the possibility that the
mechanism is not invariably fool-proof.

That the Rabbis sensed their thought forms to be shaky, was implicit
in their interdicting use of these forms without authoritative license, as
well as in their need to appeal to a Deus
ex machina
for support.

Finally ordering and clarifying, if not simplifying, their arguments,
so as to verify them.

Looking at the past couple of hundred years. As for the Baal Teshuvah (Returnees) movement of my generation and after, it
has been highly overrated and seems, to my prejudiced eyes, anyway to have
peaked and be pettering out. I was part of it myself, and can report my
disappointment. Expectations of higher consciousness and of moral and social
improvement were not fulfilled. Much more could be said on this, but it is
irrelevant to our discussion.

Saying, for examples, “this is a conversion, of A to I“, “this
is a syllogism, 2/EAE“,
“this is a simple constructive dilemma “, “this is an
a-fortiori argument, and here is its major premise, and that is its middle
term, etc.” , “this is a generalization, from O to E“.

This is not a gratuitous statement; I have often enough (mostly on
Sabbaths, however, when note-taking was impossible!) come across arguments
in Talmud study sessions which I could not consider valid.

For instance: a general statement might be made in a given context,
because it ‘proves’ a point; while, elsewhere, that very same general
statement might be denied, without trying to render the two sides

Sing. apikorsus. The
expression presumably derives from ‘Epicurean’, and is taken to imply that
the person so afflicted yearns only for debauchery and such. But this
accusation more deeply suggests the person concerned to lack objectivity,
truth-orientation, honesty, etc. (unlike the accuser, supposedly). That is
an inconsistency in it!

Hopefully, and more likely than not, such revisions would tend
towards leniency rather than severity, since many of the severities which
have accumulated over time stemmed, it is easy to suspect, from cultural or
subcultural superstition and fanaticism, rather than truly legal

Moreh, 3:14. Quoted by
Azriel Rosenfeld in Torah in the Space
, Proceedings of the Associations of Orthodox Jewish Scientists,
Volume 2.

Proceedings of the Associations of Orthodox Jewish Scientists, Volume