www.TheLogician.net © Avi Sion - all rights reserved
© Avi Sion
All rights reserved
© Avi Sion, 1995. All rights reserved.
In this chapter, we shall make some preliminary, general comparisons
between some of the propositional forms and logical processes used in Biblical,
Talmudic and Rabbinic literature, and those found in modern, secular scientific
But note well that these initial reflections were written before engaging
in formal analysis of hermeneutic principles. The latter analysis, as we shall
see in subsequent chapters, considerably changes our perspective.
The present study relates primarily to issues of method, and not to issues of content. Our focus is not
philosophical, in the sense of metaphysical, nor scientific, in the sense of
relating to special sciences like cosmology, biology or history. Our approach is
rather epistemological, to compare the
methodological aspects of religion and science, and take note of similarities
The traditional view of the development of Jewish law, which we traced
briefly in the opening chapter, suggests that it is mainly a deductive enterprise. The laws were derived from the Torah, which
was revealed by Gd through Moses to the Children of Israel at Sinai. These laws
were either explicitly given in the revelation, mostly in writing, partly
orally, and then faithfully transmitted; or later inferred in accordance with
strict hermeneutic rules, by the religious authorities charged with this
responsibility in direct line since Moses.
We are not (to my knowledge) told by Jewish tradition precisely how the first Sefer Torah (physical scroll of the Law) was written.
Did Gd orally dictate it all word by word to Moses, and if so, out loud or in his head? Or did Gd visually display text for Moses to copy down, and if so, externally or internally? Or did Gd take control of Moses' hand directly, without passing the message through his mind and asking him to transcribe it? The latter hypothesis seems more likely, at least in certain passages about Moses, such as those which declare him the humblest of men. The hypotheses of dictation are suggested by Biblical passages like Exod. 17:14, "write this... in the book," though one may wonder why such orders would have been given in specific cases if they were the general rule; video display is suggested by, e.g., Exod. 25:40.
In any case, the Torah must be entirely from Gd, to be authoritative; we cannot suspect some unspecified parts of it to have been authored by humans, whether Moses or any other(s), without Divine origin and control.
With regard to the issue of the writing of the Torah, a distinction ought to be drawn between the time of events and the time of narrating of the events. Reading the stories, one is normally too absorbed to reflect that they were probably not written at the time they occurred. Obviously, there were action situations during which Moses was too busy to write reports; he must have written them later, under some sort of Divine control (preferably - since human memory is always selective). Even where we read that Gd spoke to Moses to communicate laws (e.g. Lev. 1:1), we may wonder whether Moses was writing that down as it was happening or he wrote it ex post facto.
An attempt at epistemological rationale of Jewish law would run as
follows. What is Divinely revealed is indubitably true, because Gd is
omnipotent, omniscient and saintly; and what is tightly inferred from such data
by holy and wholly committed men, such as the Jewish Sages, is also without
doubt true. Such laws are therefore immutable, not open to doubt or review by
later religious authorities or lay thinkers. Let us now briefly consider the
strengths and weaknesses of such a rationale.
First, some comments in defense of the concept of revelation.
What in principle gives revealed truth its 'apodictic', absolutely certain,
character, is that it is proposed to us by a Being, Gd, who is the Creator of
all reality (including objective values, as well as neutral facts), and
therefore all-knowing (having created whatever He wished to, consciously,
knowing exactly what He was doing and why He did it), and who is perfect in
morality (having freely invented it and desired it), and therefore completely
honest and trustworthy (wanting to persuade us, not manipulate us). These are,
to be sure, not arguments, but concepts included in or implied by the Torah
revelation itself, to be taken on faith; however, their significance is their
ability to fit into the concept of logical necessity.
As we saw in the opening chapter, a proposition is logically necessary,
if it appears as true in all knowledge contexts. There are only two conceivable
ways that such modality may occur: either by its having a contradictory which is
immediately evidently self-contradictory; or by being apprehended as evident
within every knowledge context which can ever arise. The former kind of
insight is in the power of all human beings, although their cognitive faculties
have natural limits; and it makes possible the firm foundation of secular
knowledge (science). The latter kind of insight is obviously not within our
grasp, but it would be accessible to an all-encompassing consciousness, such as
Gd's; whence the significance of the omniscience of Gd to revealed religion. The
difficulty in this rationale is that we humans have no prior knowledge of Gd,
except through the revelation, and therefore we cannot logically justify the
revelation without circularity, but must always ultimately rely on faith.
As for the second part of the rationale of Jewish status quo, namely the implied infallibility of the Talmudic Sages
and later religious authorities, the justification given is essentially that, by
virtue of their unswerving obedience of the law in practise, these people were
favoured by Gd with special help in their pursuit of truth, help which very few
since then have deserved; hence, no review of their conclusions by anyone is
ever possible. Reflecting on the miraculous wonder of consciousness as such, and
acknowledging the existence of Providence, it is easy to realize that all
knowledge is a gift from Gd. In this perspective, when even the scientific
knower is a passive recipient, the idea that some people might be subject to
additional grace, and receive special inspiration in their pursuit of religious
knowledge, does not seem far-fetched. Nevertheless, here again, there are
logical circularities, and we must view the statements made as expressions of
faith, rather than pure reasoning. The difficulty is of course that similar
claims can be, and indeed historically have been, made by other people, even
people in other religions.
In contrast to religion, natural science is primarily an inductive enterprise. That is, it relies heavily on empirical evidence, from which it derives general statements by 'trial and error' methods, like generalization and particularization, and adduction, making imaginative theories and testing them - methods in which the role of deduction, though very important, is still relatively secondary. Faced with a world of appearances, which often conflict with each other and change, the scientist is simply a human being trying his or her best to understand and make sense of things. Not having been made privy to any whispered game plan, even the methodological tools scientists rely on, have had to be evolved inductively, starting from intuitive notions which gradually in an ever larger context have demonstrated their reliability.
In such an approach to knowledge, all appeal to Divine inspiration has been eschewed, and all researchers are therefore on equal footing with respect to the need to provide convincing evidence and arguments for their claims. No one has unshakable authority, however deservedly respected in his or her time for great discoveries and ideas of genius. There is no good old wine, or rather origin and age are beside the point. Newer truths are more reliable than older ones, insofar as they take into consideration not only the data on which preceding beliefs were based, but also more recent discoveries and insights. We are not attached to some perfect past, but on the contrary, full knowledge is projected to be in a distant future, something to which we can only tend but which we can never expect to fully reach.
Since the data base of experience is constantly changing and growing, and new insights and ideas are always conceivable, we must always in principle be ready and willing to review our beliefs and belief-systems, however certain they seem at any given time. This does not imply anarchy or working in a vacuum; there is intellectual and cultural continuity and changes are achieved over time and through collective efforts. Still, every proposition is ultimately no more than a theory, a working hypothesis, valid only so long as it is not overturned by another, more informative and consistent proposition. A scientific world-view might be abandoned in one swoop, if only and as soon as another has been found which is reasonably more convincing and fruitful - and this has occurred often enough.
As we shall see, the above contrast of the methods of religion and
science, as respectively deductive and inductive, has some truth and
justification; but it emphasizes differences, some of which are superficial,
without paying due attention to many similarities.
But, before going further with the issues of method, a few comments are
worth making with respect to issues of content. A comparison of the specific contents
of Torah and Science is not our subject-matter, here; readers interested in that
are referred to specialized literature. Much has been written and continues to be written, comparing the claims
of the Jewish religion and those of natural science. Such comparisons usually
refer to cosmogony, cosmography, biology or history.
Such comparative studies will, according to the ideology and information
of the writer - either seek to contrast religion and science, and reject the one
or resist the other; or to reconcile the two, by means of some reinterpretation
in more metaphoric terms of certain claims of religion, or by showing the
essential compatibility of specific religious claims with current scientific
views, or by demonstrating the continuing uncertainties in the scientific
positions under scrutiny.
The Torah itself contains various 'factual' information; some of it
concerns human history, some is about nature, and some is more metaphysical. With regard to history - for instances, the common
origin of all peoples (the Adam and Eve story), their subdivision into
linguistic groups (the Tower of Babel story), the time and circumstances of the
Exodus from Egypt and entry of the Children of Israel into the Holy Land, and so
on. With regard to nature - for instances, the age of the world or data on the
physiology of certain animals or the psychology of human beings. With regard to
metaphysics - we may mention information like the existence of Gd, His names,
His attributes, powers and acts, like His unity, primacy, supremacy, His justice
and mercy, His authorship of the universe and open or hidden providential
interference in human affairs, and so forth.
Similarly, for the rest of the Bible, the Talmud and other Rabbinic
writings. In the legal debates of the Talmud, the Rabbis often make factual
claims, which may be historical or natural as well as metaphysical, to justify
their positions. For instance, in Yom Tov
2b, Rabbah claims that an egg is always 'fully developed' a day before it is
laid; for him this is obvious, because it is required as a logical precondition
of the law he defends. In effect, laws handed down by a tradition may be
certain enough to infer even plainly physical or biological 'fact' from them.
It should be noted in passing that much of the Jewish religion's view of the world, 'natural' and 'supernatural', is built on this mode of thought: i.e. projecting attributes of the world from laws (or even, eventually, just traditions). The latter serve effectively as 'empirical data' from which a world-view is cumulatively developed; they constitute springboards and boundaries for non-legal theories. But such theories must be considered speculative, to the extent that they ignore, or contradict, the data of natural cognition.
Now, in the event of disagreements between religion and science with
regard to natural or historical facts, we are of course faced with a problem,
which must eventually somehow or other be solved, if we want to have a
consistent body of knowledge. It would be dishonest to ignore such
discrepancies; but on the other hand, it would be naive to expect to resolve
them all convincingly or to make overly severe judgements when they cannot be.
We must leave room for doubt and even mystery. With regard to metaphysical facts, like the supreme
sovereignty of Gd, these are to a large extent inaccessible to normal empirical
evaluation; we can only speculate concerning them, if we have not been gifted
with special states of consciousness or Divine revelation.
In any event, the traditional view is that the Torah, as its name
attests, is essentially a legal document. Factual data in it, concerning history
or nature, is incidental, providing a context for the understanding of the law.
As for information about Gd, it provides a justification and rationale for the
law, suggesting the existence of a "moral order" in the universe. But
the essential message is the law. Thus, the content of such a religious document
is primarily normative,
rather than descriptive. Its role is to prescribe or proscribe, or allow and
exempt, or leave to individual choice, specific acts of human behaviour. Within such a perspective, it may matter little what
the date of Creation might be, or whether humans evolved from animals, and
Biblical passages relating to such matters need not be taken literally.
In contrast, the content of science is overwhelmingly descriptive; it tends to deliberately avoid normative issues. Its goal is to "get at the facts" - to provide humankind with a neutral database, allowing us to make informed choices and providing us with intellectual and material tools to carry them out effectively. Judgements of value are regarded as a separate problem, the concern of ethical philosophy or religion. The ambition of science is only to know the way things "are" (or at least, how they appear to us to be), which includes certain forms of explanation (our answers to "why" things are as they are, are themselves further descriptions, with reference to wider or deeper abstractions or yet more removed causal factors). With regard to the way things "should be", science is modestly silent.
Furthermore, the founders of modern science deliberately chose to bypass metaphysical issues. The idea of Gd was, as it were, put between parentheses. There were political reasons for this: the Church a few hundred years ago had the power to persecute those with ideas it considered threatening, and often used that power. The interests of the scientists were in any case secular and material; they did not mind leaving religious and spiritual issues to "specialists". But also, they realized that such issues were ultimately unresolvable, and they did not want to get bogged down in them, but preferred to move on and deal with phenomena more accessible to empirical testing and rational scrutiny.
Such fractionalizing of the pursuit of knowledge did not necessarily reflect a negative attitude towards religion, but represented a legitimate strategy. The idea of Gd was not intended to be permanently ignored or rejected, but was merely put on hold. Often the difficult problems we encounter are shunted aside, and we concentrate on the easier ones, hopefully at least temporarily, waiting for new insights and gathering more data in the interim. As the achievements of science increased, ecclesiastics gradually came to accept, even if reluctantly, the narrowing of their domain. In practise, the division of labor has not always been maintained - on either side. Many believers in Gd and the Bible continue to have dissident opinions concerning nature and history, and some scientists occasionally claim their theories or findings have metaphysical or normative implications.
From the logical point of view, the setting of norms has always been a
problem difficult to solve. There have of course been attempts to derive ethical
propositions from emotional, psychological or sociological facts, but invariably
close scrutiny reveals the element of arbitrariness involved, the subjectivity
and cultural bias underlying the suggested norms. Many people, including many
capable philosophers, conclude that objective norms are impossible. The Jewish
religion suggests that, in the normative domain, the human faculties of
cognition are inadequate because the answers to our questions are not inscribed
and made manifest in nature: there has to be an external impulse, a credible
message from Gd, to settle issues and provide us with standards. Gd, it seems,
wished to reserve access to this domain, and transmit moral guidance to us
through the words of Torah.
section, we shall demonstrate, through a technical peculiarity of Talmudic
logic, that in contrast to other kinds of discourse, it is inherently oriented
towards deduction. However, we shall also begin to unveil, with reference to the
exceptions to this very same peculiarity, the strong inductive currents
underlying Talmudic thought processes.
When one compares the logical pronouncements in Talmudic and other
Rabbinic discourse to the logic apparent in common and scientific thought and
discussion, an immediately noticeable practical distinction is the different interpretation each
gives to particular propositions. This
refers to sentences which are introduced by the quantifier "some", as
in "some swans are white".
Normally, in everyday discourse or in science, we understand the
expression "some" as meaning "at least some" - it is indefinite
about the exact quantity. Such a statement is left
open, to give us time for further investigation, which will determine
whether we may assume, for the subject-matter at hand, that the universal
"all" is applicable or we must assert that the contingent "only
some" (meaning "some, but not all", or "some yes and some
no") is the case. These latter quantities are relatively
more definite (with regard to
proportion, though not to number). In
contrast, in Talmudic and related discussions, the word "some"
has usually got a prima facie value of
"only some", which excludes the option "all". It is only
after much debate that sometimes, in rare
cases, the initial "some" is concluded to have been intended as an
indefinite particular, which admits of interpretation as "all".
Particular statements taken to be contingent are said to be davqa particular; whereas
indefinite particulars, which allow for a universal as well as contingent
interpretation, are said to be lav
davqa. Davqa is Aramaic, and means 'thusly', or 'precisely
thus', or 'exclusively thus'; lav
signifies 'not'. These expressions are not, of course, limited to the quantifier
"some", but may be applied to any quantity variously interpretable;
for instance, does "10" mean exactly ten, or ten or more, or up to
ten, or about ten?
Now, this difference in approach has a deep and interesting reason; it is
not accidental or merely conventional. When, say, an Amora (a Rabbi in the
Gemara) encounters a particular statement by a Tana (a Mishnaic Rabbi), or in
the Torah itself, it is a matter of course for him to interpret it, at least to
begin with, as intended as davqa
"some", that is, "some, but not all". For it is a statement made by an intelligent being (a Tana, in the
case of the Mishnah, or Gd, in the case of the Torah). So he (the Amora) can
argue: "Nu? if the author meant
'all', he would have said so!" Thus, the statement may reasonably be
assumed to mean no more than what it says - that is, only "some", or
In Talmudic logic, then, "some X are Y" (I) is taken to imply and be
implied by "some X are not Y" (O), because both mean no less than IO; i.e. there is here no I
or O other than in IO.
This deductive rule holds in the large majority of cases,
as the lekhatechila (initial) position. It does happen comparatively
infrequently that, after a thorough analysis of the situation, such an ab
initio assumption is found untenable, because it leads to internal
contradictions or acute disagreements between different Rabbis. In such case,
the particular, which was first taken as davqa,
is bedi'eved (as a last
resort) downgraded to a lav davqa
status (making it compatible with a corresponding general proposition, in which
case I and O are subcontrary). Here, the indefinite particular is the result of
an inductive process, an attempt to reconcile conflicting theses, to
resolve a difficulty. However, it does not retain this status long, since the
whole purpose of the process is to arrive at the corresponding general
The above explains why Talmudic logic is regarded as essentially
deductive. The Talmud is built on a number of ready-made
(written or oral) propositions considered to be of Divine origin. In such a
situation, a proposition of the indefinite form I or O is merely a
shorthand expression of the definite compound IO, because that is the expected inductive result in, say (this is a
wild guess), 95% of the cases to be dealt with. The raw data on which such
knowledge is based is already verbalized; the epistemological processes used are
directed towards the interpretation
of this verbal raw data (expressing it in other words, drawing inferences from
it), through its internal and external integration
(that is, checking the mutual consistencies of the parts of the revelation, and
its coherence with the wider context of empirico-rational knowledge, including
In contrast, in ordinary or scientific thought, there are no verbal givens, other than those impinging on individuals from the rest of society. Verbal knowledge is ultimately built-up from experience, by labeling groups of similar and distinct phenomena (be they sensory or mental, concrete or abstract). In such a framework, there are virtually no absolutes which can serve as top principles from which the rest of knowledge may be derived; apart from a very small number of logically self-evident axioms (whose denials would be paradoxical, that is, self-contradictory), we have to develop knowledge very tentatively and gradually. Here, the indefinite particular forms I and O are pressingly needed for efficient discourse, as way-stations and stepping-stones to fuller knowledge, as already explained.
Nonetheless, our above observation does not signify that there is an
unbridgeable epistemological gap between the two "logics", that of the
Talmud and the common. It should be clear from the preceding that the two
systems use by and large one and the same logic, only their givens differ in format. That is, were they faced with equally
formatted data, their way of development would indeed be identical; but one
depends largely on verbal givens, while the other is limited to non-verbal data.
It is true that their givens also differ
in source, being Divinely revealed (to some people) in one case and
naturally apparent (to everyone) in the other; but this issue affects the
credibility of the initial data, rather than the subsequent mental processes
relating to assimilation of the information.
In any case, note, the two bodies of knowledge are not mutually
exclusive. For a start, religious knowledge is never totally independent of
secular data; a religion may explain the material world away, as a big illusion,
but it may not completely ignore it - the language used by religion is
understood only because it is reducible to common experience. And since religion
(certainly, the Jewish religion) admits of secular data, it also acknowledges
the inductive method which assimilates such data. But furthermore, as we shall
see, the method by which religion (at least, the Jewish) ultimately assimilates
its own peculiar data is very similar to the secular.
Secular knowledge without religious data might seem conceivable, but only if one turned a blind eye to various otherwise burning questions - in the limit, religion is unavoidable, except by silence, because even negative answers to such questions may be counted as effectively 'religious' in their own way. With regard to methodology, the secular sciences certainly, to some degree, use techniques found in religious study, like textual analysis, since the sciences generate texts to communicate their results, and these texts while being written or read are subject to analysis. Textual analysis is also used in secular contexts in relation to historical documents (literary or legal documents, including the Bible itself). So scientists cannot object to hermeneutics as such (though they may look askance at specific interpretative techniques).
We have seen that Talmudic logic, being more deductive than inductive,
has a preference for the davqa
interpretation of particular propositions. However, we will now show that formal
logic cannot ultimately avoid recourse to lav-davqa particulars,
and so demonstrate that Talmudic logic must at least implicitly acknowledge
them. The situations implied by the forms I and O, of partial
ignorance or deficient knowledge, arise again and again in the course of all
human thought - not only within inductive processes of gathering and judging
empirical data, but just as much within
purely deductive processes. Indefinite particulars are therefore
indispensable if we want to be articulate.
We could, in truth, construct a formal logic with a propositional arsenal
devoid of indefinite particulars, simply by explicitly expressing our position
in such cases by the disjunction of definite forms (general and contingent).
Instead of I, we would always say
"either A or IO"; and instead of O,
"either E or IO".
But this would be artificial. Why deprive our thinking of valuable tools, and
not take as given what ordinary language has provided? Ordinary language surely
satisfies the needs of our cognitive faculties. A certain degree of linguistic
brevity is necessary to reason clearly, otherwise language may become a source
of confusion. The forms I and O make such simplification possible (even though having them
slightly increases the size of our propositional arsenal).
To show that Talmudists need indefinite particulars as much as anyone, to
reason clearly beyond the ab initio
stage, we need not go into a systematic and exhaustive listing and analysis of
logical processes. It suffices for us to consider some arguments whose conclusions are quantitatively more indefinite than
their premises. In eduction, we may illustrate what we mean with reference
to certain conversions:
(A) All X are Y, is
convertible to (I) Some Y are X.
(IO) Some X are Y and some X
are not Y, converts to (I) Some Y are
Whether we start off with a general affirmative or contingent
proposition, we can by conversion only arrive at an indefinite particular; so
that in fact it is only the I element
in these forms which is convertible. In contrast, on the negative side,
an O proposition is inconvertible,
and only the E form may be converted
(but that fully, to an E). Thus, given A, or given IO, inference
by conversion will only yield a conclusion of less definite quantity, namely an I.
We could, of course, reword the conclusion as "either all Y are X, or some
Y are X and some Y are not X", but its correctness might seem less
immediately evident. Other eductions display similar results, though in
With regard to syllogistic reasoning, particular conclusions are almost
always indefinite. Only in the third figure (by conjoining the valid moods 3/IAI
and 3/OAO, which have the same minor premise) is it possible to
construct an argument with a contingent (major) premise, which yields a
contingent, and therefore just as definite, conclusion. We get the following
Some Y are Z and some Y are not Z (IO);
and all Y are X (A);
therefore, some X are Z and some X are not Z (IO).
In all other cases, even if we start with a contingent proposition as one
of our premises, the conclusion as such can only be an indefinite particular.
For in the first and third figures, the valid moods AII and EIO cannot be
combined, since their major premises are contrary, and there are no valid moods
with a negative minor premise; and in the second figure, only negative
conclusions may be drawn (see AOO and
EIO), anyway. This shows that anyone
reasoning syllogistically from contingent premises is sooner or later bound to encounter indefinite particular conclusions.
Thus, deductive logic requires a language with lav
davqa particulars, as surely as inductive logic does. This incidentally
confirms that Aristotelean-type logic is indeed generic, as applicable to the
world-view of the Talmud (with its preponderance of deduction), as to that of
people concerned with cognition of non-revelational phenomena (who rely more on
The reading of (indefinite) particular
propositions as contingent is the paradigm of davqa interpretation; a similar movement of thought is used in
relation to general propositions, as
we shall now explain. When we read a particular proposition 'Some X are Y' as davqa,
we are producing new information, because we are supposing that 'Some (other)
X are not Y'. The latter proposition concerns instances of X other
than those subsumed by the former; and it assigns the opposite predicate to them (i.e. not Y, instead of Y).
For this reason, the allegedly derived proposition is sometimes, in Latin, said to be the a-contrario of the original. I hesitate to use this expression too freely, however, because it might be misinterpreted. It is important to note that the original proposition and the one derived from it by a davqa reading are not contrary; they are compatible, since they can be and are conjoined. Thus, a-contrario does not mean 'on the contrary,' but assigns, to the remainder of a subject-class, the negation of a predicate.
Thus, the essence of davqa
interpretation is to limit a statement, by means of an exclusion.
In the case of particulars, the movement of thought is from 'Some X are Y' to
'Only some X are Y' (or, needless to say, from 'Some X are not Y' to 'Only some
X are not Y'). Similarly, in the case of generals, the davqa
reading of 'All X are Y' is the exclusive 'Only X's are Y', implying 'Every nonX
is not Y' - that is, 'No nonX is Y' (or, likewise, the davqa
reading of 'No X is Y' is 'All nonX are Y').
Note well that, by mere eduction,
we can only infer from 'All X are Y' that 'Some nonX are nonY' (the process is
called inversion, and is validated in this instance by contraposition, then
conversion); to get to the inference 'All nonX
are nonY', we must generalize the
inverse. From the point of view of ordinary logic, therefore, the davqa
reading of a general proposition involves an inductive factor. Just as in the
case of particulars, new information is produced, so in the case of generals.
The parallelism of the davqa
interpretations of general and particular propositions can be further brought
out as follows. Consider a subject S (for species), which is subsumed under a
larger subject G (for genus); and let P refer to a predicate. The general 'All S
are P' implies the particular 'Some G (namely those S) are P', and the former's davqa
implication 'All nonS are nonP' parallels the latter's 'Some G (namely those not
S) are not P'.
Similar readings may be made with respect to (normal) conditional
propositions. For instance, when 'if P, then Q' is understood as davqa, it implies 'if not P, then not Q'; although lav
davqa, it only (normally) implies 'if not P, not-then Q'.
the methodologies of the Talmud (and cognate investigations) and science (and
everyday discourse), so far, we have stressed certain overall differences. We
noted, firstly, their different data bases. And, secondly, we presented religion
as a predominantly deductive system, and secular science as an essentially
inductive one, and indicated some of the reasons for this contrast. But we need
now to consider certain similarities between these disciplines, to obtain a more
balanced appraisal, for further scrutiny makes clear that they converge in many
With regard to raw data, though in theory our religion is based on
mystical experiences (mainly the Revelation at Sinai, which was partly
collective, though in large measure the privilege of prophets, especially Moses,
to which we must add later events, like the prophecies of Isaiah, for instance),
which included both non-verbal and verbal components - in practise, today, only
the verbal components remain, so that our religion depends on very ordinary
sense-data, namely words read in books or
heard from the mouth of others, as well as some personal intuitions, and
some imaginations and emotions.
With regard to logic, though the starting posture of Jewish law is
theoretically deductive, if we pay close attention to the way such law is
actually developed in Talmudic and
Rabbinic texts, and the way it is taught
and studied in practise, we see that they are manifestly inductive.
The Talmud develops in large part dialectically,
by uncovering a kushya (literally, a difficulty - a logical problem) in the
midst of received texts and related data, and searching for and usually finding
(a solution) for it. This is also the way the Talmud is taught and studied,
retracing the steps of the original debate.
The kushya in question may be
an outright contradiction, or it may be a less obvious tension between two or
more statements. Two or more propositions may be said to be in a state of tension
- of possible incompatibility - if there are conceivable logical or natural
qualifications under which they would be contradictory, or there are conceivable
interpretations of their terms which would result in an untenable antinomy.
Also, the difficulty may not be a conflict between explicit statements, but
relate to implicit factors, such as a perplexing silence concerning some topic
or a surprisingly superfluous comment. However, once the tacit source of
discomfort is brought out in the open, the difficulty is verbalized and can be
Conflicting propositions may come from the same or different sources. The
relevant sources are, as we have seen, the written Torah, the Nakh, the Mishnah
and allied documents (e.g. Baraitot), the Jerusalem and Babylonian Gemarot and
allied documents (e.g. later Midrashim), oral traditions carried by
authoritative Rabbis, and later various Rabbinical Responsa and codes of law. Thus, for examples, a Mishnah may
seem to conflict with some Torah sentence; or two Gemarot, even two having the
same author, may seemingly conflict; and so forth (in every combination). In
rare cases, the difficulty may be an apparent conflict between the teaching of
some Rabbi and some teaching of science (e.g. agronomy or medicine).
The role of the terutz is to
reconcile such real or imagined differences. This might be achieved in a variety
of ways. Sometimes, the Rabbis admit not knowing how to solve a problem, and
they leave the issue open (teku) "for the prophet Elijah" to deal with when he
returns. Meanwhile, they may use their prerogative to arbitrate, and simply
reject, through a majority vote, one of the conflicting theses, which
is thus reclassified as "a theoretical tradition without practical
appeal". But preferably, the conflict is
dissolved by showing that the propositions involved concern distinct
assumptions, or refer to different cases, or are applicable to different
circumstances or times, or mean different things. At first sight, the conflict seems insurmountable, but after
careful verbal or conceptual analysis the propositions are shown to be more
harmonious than previously thought.
Such resolutions of paradox are often, after a long-winded debate, disappointingly anti-climactic: a statement which seemed at first general, turns out to have been of more limited applicability; or a statement initially made unconditionally, is finally inferred to have been intended as conditional; or some word(s) that were apparently identical end up having dissonant senses in different contexts. One wonders why the people involved did not from the start take the trouble to express themselves clearly and unequivocally, if what they meant was the same as what they are later taken to have meant. In some cases, one is tempted to suspect an ex post facto forcing of reconciliation! To a newcomer, or an unsympathetic outsider, the process may at times seem downright dishonest, a come-on, a time-wasting weaving and unweaving of illusions. But evidently, or apparently, there is progress, since a reasonably consistent and meaningful doctrine does gradually emerge. From a didactic point of view, the succession of confusion and relief serves to create and maintain interest. In any case, what concerns us here is the inductive role of the dialectic.
An underlying problem is the telegraphic style used in Talmudic
discourse. A seemingly simple word is often a mere catchword for a very
complex thesis, and there is no way for us to know what's what except through
the dialectic. Theses
and counter-theses are not from the start clearly defined, but receive their
final form only through the final synthesis, which shows that they were
not quite so antithetical as they appeared.
Examples abound. For instance, in Baba
Qama 84b, which debates the payment of damages in the event of burning
(causing pain) or bruising (wounding) - for one party, the term
"burning" is interpreted as excluding
"bruising" by definition, and the term "bruising" is taken
as including "burning"; for
another party, the term "burning" is interpreted as "burning and
bruising" by definition, and the term "bruising" (funnily enough,
if I am not mistaken) is taken to mean "burning without
bruising"; and so on. We see here that "X" need not mean "X,
whether or not Y", but may mean "X and Y", or "X but not
Y", or even "notX and Y", or "notX and notY". A term is
merely an abridged title (techila)
for a more complicated expression, in which it may even have negative value!
Now, the dialectical process of correlating divergent answers to a legal
question cannot be considered part of deductive logic, but has to be classified
as inductive, for several related reasons. Firstly, the process of finding
answers to the questions posed is more creative than mechanical; it is
essentially a process of adduction -
proposing new terms or conditions, which will reestablish internal or external
consistency in one's knowledge base. Secondly, alternative solutions may usually
be offered to the problem at hand, and often are. Thirdly, the final decision,
if any, is rarely arrived at immediately, but rather through a gradual trial and
error process. The Sages make various suggestions as to how the conflicting
theses might conceivably be
harmonized, and these proposals are be successively eliminated for some reason
or another, until a proposal is found which is obviously acceptable to everyone
or withstands all criticism leveled against it.
Notice that we have two superimposed levels of discussion: at the core,
there is a conflict relating to textual matters and/or authoritative opinions
about such matters; but next, there may be contending opinions as to how the
core conflict may be remedied. Yet further levels of discussion may be
identified, when we consider all subsequent commentaries and supercommentaries
across the centuries! All that is additional evidence of the inductive character
of large segments of Talmudic discourse.
Similarly, by the way, the mental operations of anyone who teaches or
studies the Talmud are of necessity inductive. All the more so, since the Talmud
does not set out its results in an orderly, organized fashion, but leaves its
researches in their brute form. The reader is required to retrace the course of
the discussion, as if a participant in it, using trial and error. For this
reason, the Talmud remains forever a peculiarly living document, free of the dry
finality of more modern codifications of law.
The radicalness and importance of our classification of much of Talmudic
logic under the heading of inductive logic must be emphasized, for it is
contrary to the views of certain past commentators who (it must be said, without
intending disrespect) did not always have a very advanced knowledge and
understanding of the science of Logic.
conclusion (so far in our research), the thought-processes involved in and
generated by the Talmud largely resemble those of science. Like the scientist,
the Talmudist must repeatedly make hypotheses and test them on the given data
which specifically concerns him, as well as pursue logical consistency.
For the scientist, the data-base consists ultimately of non-verbal
sensory impressions of natural phenomena (which are ideally reproducible in
public, though not always so). For the Talmudist, as we saw, the data-base
consists of the (written or oral) verbal leftovers of long past mystical
experiences. But apart from these essential differences in empirical context,
the two display a uniform mental response,
the same array of methodological tools - inductive and deductive arguments used
in various combinations and orders. Which is to be expected - we are all
people, similarly constituted, having the same cognitive faculties, subject to
the same epistemic facilities and constraints.
Epistemology is the philosophical discipline concerned with understanding
how knowledge is obtained and how it may be justified. That discipline, through
the work of formal logicians, has made clear that the justification of any
content of knowledge, or of any change from one content to another, is a
formal issue. Prior to any scientific or Talmudic inference, be it inductive
or deductive, there is the
need to examine the logical validity of that method of inference independently
of its content. No reasoning process, be it by a pious Talmudist, a
professional scientist, or a common man or woman, is exempt from such formal
However, it must be emphasized that (contrary to the views of certain
philosophers and logicians) the validation of a logic is a very prosaic
achievement of "common sense", and not at all the special privilege of
some transcendental method. Just as our everyday reasoning proceeds by logical
intuitions - our common conceptual insights that, say, some thesis is compatible
or incompatible with another, or implies or does not imply it - so it is with
the reasoning processes of logicians intent on formal validations. The ultimate
test of any reasoning process, material or formal, is its ability to convince
us. If, sincerely, however informed and intelligent we be and however hard we
try, we are not convinced - then, we are not convinced. An argument must carry
within itself the power to change our minds.
Some logicians think that we can, following the model of Euclidean
geometry, in advance posit standards of reasoning, by means of
"axioms" standing outside of the totality of knowledge. But they fail
to realize that such "axioms" would themselves remain unproved, and
therefore be unable to prove anything. Other logicians, finding this circularity
problematic, try to avoid it by rejecting all conceptual knowledge and
considering only purely perceptual knowledge as valid. However, such a position
cannot be consistently sustained, being itself a conceptual proposal. A balanced
and practical viewpoint is only possible, through honest introspection and
acknowledgement of the ways we actually reason, and reason about reasoning.
Talmudic reasoning, like secular reasoning, could not proceed if we did
not have the same logical reactions to the stimuli of received doctrines. An
esoteric "logic", like the incomprehensible mental acrobatics of the
Zen koan, has little credibility. It
is only to the extent that a "logic" causes a universal reaction of
understanding and conviction that it qualifies as a real logic. The goal of the koan
is not to convince by appeal to evidence and rational processes, but to assist
those who meditate on it to overcome such ordinary mental patterns and break
through to another kind of consciousness; in that case, assuming even that it
works and produces the desired result, the koan
is not a logic, but at best a psychological tool.
Similarly, we must draw a clear line between Talmudic logic and faith;
these bases of belief cannot be confused. When we face an argument, or a form of
argument, used in the Talmud, if we are to grant it the status of logic,
it must be capable of convincing us by itself, independently
of any issue of faith. We may well grant proper respect to faith, but we
cannot do violence to our minds and pretend that there is logic where there is
none. Being convinced by an argument cannot be a test of faith; either we arrive at a conviction through logic, in
which case no forcing of belief is needed or permissible, or through faith, in
which case we simply honestly admit that this is the basis of our belief.
These comments have to be made, here, because it may be that the Talmud
has a koan-like function. Many
positions and processes found in it may seem weird to some people; perhaps
continued study eventually causes a sort of shift in consciousness, after which
everything previously found enigmatic becomes perfectly comprehensible. Be that
as it may, we cannot be swayed by such a consideration; our concern in the
present volume is only with logic. We will as we proceed consider various
patterns of argument found in the Talmud, and related documents, and try to
fairly and frankly assess their credibility, with reference to high standards of
Using the terms "secular" and "scientific", here,
without implying such thought to be at the outset or inevitably
anti-religious (secularist). We may include under the same broad category,
not only the natural sciences and history, but also philosophy at its best
(not all philosophy is well thought out; however, most philosophy has a
contribution to make, however inarticulately expressed), and any aspects of
the humanities which obviously qualify.
The present essay's general conclusions are rather over-optimistic;
but the specifics on which it bases such conclusions are essentially
See Lewittes, p. 35. He quotes the Rambam as saying "... though
exactly by what method is known only to the recipient, Moses." In the
Talmud, Gittin 60a, two
possibilities are floated, one, that Moses wrote the Torah down when it was
communicated to him, another, that he memorized it and wrote it all at the
end of his career.
A. Ibn Ezra suggests this specific order may have referred to the
Book of the Wars of the Lrd, rather than the Book of Torah (Cohen, p. 433).
The ideal scientist, if you prefer.
When we support or reject an idea, only with regard to the person(s)
formulating it, without regard to its coherence and cogency, we are
committing the logical fallacy of ad
hominem. (Some reserve the expression for the negative case, preferring ad
verecundiam for the positive case; but there is no essential difference,
in my view.)
e.g. Comparing the Biblical account of Creation, apparently in 7
days, 5754 years ago, with the Big Bang scenario, 15 billion years ago.
e.g. Comparing the seeming Biblical view of the Earth as the main
theater of the universal drama, and the empirical evidence that our planet
is without centrality in its own solar system, or even galaxy, and a mere
speck of dust in an enormous universe. Actually, this issue seems to have
been a burning issue at the time of Galileo, but today seems irrelevant,
except perhaps to people attached to the qabalistic notions of 'heavenly
spheres' built on the Ptolemaic model of the universe (actually several
hundred years more ancient than Ptolemaeus, being found in Plato and
e.g. What is the nature of life, is it material or spiritual? And
what are the origins, ages, and evolutionary courses, if any, of living
e.g. Comparing the stories and dates given in the Bible and
subsequent tradition, with the findings of archaeology and the scenarios
History is of course an aspect of nature, insofar as we humans belong
to this world; however, what philosophically distinguishes historical
processes from other natural processes, is the role played in the former by
human freewill; methodologically, differences are due to the peculiar
intimacy, singularity and temporal distance of most historical facts, which
makes most accounts of them largely conjectural, whereas natural facts are
generally more easily verifiable. Metaphysics can similarly be analyzed with
regard to its distinctions from the natural sciences.
Namely, the prohibition to eat an egg laid on a holy day.
In the example here given, the concept of full development of an egg
is sufficiently vague and ambiguous to be unverifiable. A better example
should be found.
In any case, as already indicated, such harmonizations are not within
the scope of the present work.
Note that Torah laws are regarded by Judaism as binding on their
subjects, whereas the concept of "norms" is generally understood
more broadly, as including the gentle advice of wisdom.
Difficulty arises due to the reasoning that if the Bible is not
entirely literal, it cannot be strictly-speaking considered true, and
therefore one may doubt its Divine origin. However, it is also conceivable
that Gd wished us to find out certain less relevant or pressing matters for
ourselves, over time, by natural means (science) - and considered it enough
for us to have, until then, easily-grasped token accounts of things, images
and ideas designed to inspire rather than inform.
Of course, the normative data which are the main concern of religion
are ultimately as "factual" and "descriptive", in
enlarged senses of these terms, as the neutral data which interests science.
If objective values exist, decreed by the Creator, they are effectively
"inscribed in nature", as much as other phenomena. Their
ontological status is the same, though they differ constitutionally.
However, their epistemological status may be different: whereas neutral
information is known through its gradual appearance before our perceptual
senses and conceptual insight, Judaism suggests that Gd chose to deliver
normative information to us (mostly, if not exclusively) by special
Belief or disbelief in Gd should have no effect on the descriptive
appearance of the natural world, since one can always claim that, however
the world happens to appear, it may well have been the way He chose to make
it. Conflicts between religion and science arise only in relation to
religious texts or oral traditions; and even then, the flexibility and
intelligence of the beholder count for much.
For examples, speculations about Creation by Big-Bang proponents, or
advice given by psychologists to their clients. But we must not forget that
scientists are people, too; and like all people, need answers to certain
questions right now, to be able to run their lives. People may, even without
religion, have opinions about what is right or wrong, and correct or
incorrect ideas as to how to justify these opinions. Often, secular moral
beliefs historically stem from religion, but after being deeply ingrained in
a person or culture they become independent of the religion.
Related to the Hebrew 2-letter root DQ,
connoting minuteness, as in daq,
fine dust (Isaiah, 40:15), daqah,
a minute in time, and bediuq,
This form of inference, which is quite common in Talmudic discourse,
might be called, in English, "inference by negation"; in Latin,
its name is, if I am not mistaken, a-contrario.
We must interpret in a similar vein statements like the following, by
Guggenheimer (pp. 179, 193):
The inner logic of the Law (...) is definitely hostile to
modalities... The Talmud avoids all attempts at modal logic. Instead, we
have a set of rules, known as rob (majority) and hazaka
(status quo ante) which serve to transform actual probabilities into
judicial certainties. The result of such transformation may be used in a
universe of discourse in which modalities have no place.
While it is true that lav davqa statements in the Talmud are left indefinite no longer
than it takes to find a davqa finale
to their discussion, it is totally untrue to claim that there is no modality
in the Talmud. The very fact that distinction is made between lekhatechila and bedieved positions
is proof enough that logical modalities are involved in it. The recognition
that some arguments are strong (deductive), and some relatively weak
(inductive), is further proof. But anyway, the "transformations"
mentioned in the above quotation would suffice: before a ruling is decided,
it must have been momentarily uncertain, or else it would not have been open
to debate. As for natural, temporal, extensional and especially ethical
modalities - the Talmud would have been unable to describe different
situations and conditions without use of them, nor been able to make any
legal rulings. We might readily have excused Guggenheimer with reference to
the widespread gap in knowledge concerning modal logic, which he himself
admits, saying: "modal logic is without satisfactory formulation even
today"; but his denial of modality is too extreme even in that context.
We must refer, here, to humanity as a whole since its inception, when
discussing the construction of language and knowledge from scratch;
evidently, individuals today receive a great deal of their knowledge in
already verbalized form from the society around them.
This statement, and similar ones elsewhere in the present chapter,
will have to be considerably revised later on in the book, after formal
analysis of the Rabbinic hermeneutics. For we will thereafter discover
Talmudic thought processes which can only be called 'logical' or 'inductive'
by a very generous concession - but which rather deserve the labels
'pseudo-logical' and 'arbitrary'.
In this sense, atheism is also a religion, one which opts for a
negative answer to the question of Gd's existence.
"Some X are Y" and "Some Y are X" both mean
"some things are both X and Y", in which form the order of the
terms is irrelevant.
The conversion of E is
reducible to that of I, by ad
absurdum; or it may be understood independently, in a like manner.
For instance, in contraposition, it is the E
and I forms which inhibit the process, since "All X are Y" (A)
may be contraposed to "All nonY are nonX", and "Some X are
not Y" (O) to "Some nonY are not nonX".
Note, anyway, that a-contrario is
not really an 'argument' (though used in arguments); it is merely a
'reading', since the result is not formally inferable from the given.
This is usually the case, though note that 'davqa
all X are Y' is often intended to mean: literally
all (and not just most) X are Y. What is negated, in such case, is the
possible assumption that the quantifier 'all' is being used in a hyperbolic
sense, i.e. when what is really meant by it is 'virtually
all' or 'almost all (but not quite all)'.
Inversion of "No X is Y" would be done by conversion, then
Note that modality changes may be involved. For instance, the
Rabbinical reading of Lev. 7:19, which says that the ritually impure are allowed
to eat holy offerings, is that the ritually impure are forbidden to eat holy offerings (see Scherman, p. 51).
The word kushya has originally, within the Talmud, a more specialized sense,
referring especially to textual differences. However, nowadays, in
Talmud-study, the word is used more broadly, much like the English word
'difficulty'. It is in this sense that we will use it here. Note that there
is often a subjective element involved: it is someone
who is perplexed by silence or surprised by repetition, etc. In such case,
there is a need to understand the whys and wherefores of that person's
logical or other expectations, which other people may not share.
Responsa are written answers to questions posed to authoritative
Rabbis concerning the Halakhah; this way of clarifying and explaining the
law has played an important role in Jewish life since Geonic times. The
codes, like Maimonides' Mishneh Torah
and R. Joseph Caro's Shulchan Arukh,
were later developments, but are today of course very authoritative in any
legal decision making.
Regarding the all-important principle that the majority opinion is
Halakhah, its epistemological justification obviously cannot be that the
truth comes to be known through a majority vote. Rather, we may refer to a
shared impression of truth, or a collective memory of a previously known,
but no longer certain, truth, in which cases majority vote establishes a
sort of inductive probability. A still better rationale to offer is
ontological: through a power granted by Divine authority, a potential law is
made actual by majority arbitration.
The epistemological motive of that concept is obvious enough: namely,
to incapacitate the rejected thesis Halakhically, without delegitimizing the
authority of its proponent, i.e. without putting in doubt his infallibility
in other contexts. Ontologically, the concept seems to imply a
transcendental reservoir of previously potential laws which can no longer be
actualized. That idea would be consistent with the remark made previously,
that the legislative power seemingly granted to the Rabbis by Gd must be
viewed as a creative power, since the moment a law is promulgated by them it
becomes an objective value, a normative fact. We may then speak of the
irreversible actualization of a potential law.
It must be pointed out that this kind of reasoning, in which the goal
is to reconcile conflicting authorities, is not confined to Judaism, but was
common practise in Medieval European universities.
See Lewittes pp. 66-68 on Rabbinic disputation; in particular, note
R. Yannai's statement: "If the Torah had been given clear-cut, no
opinions would be countenanced in the halls of learning." On the wide
law-making powers of the Sanhedrin in practise, see pp. 62-63 of same.
What is said here should be obvious, but I have often enough observed
people afraid to admit being unconvinced by an argument, through fear of
being suspected of lack of faith or of disrespect of the Rabbis.