Logic in the Talmud

A Thematic Compilation by Avi Sion

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6. Initial Impressions on Method

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 thought[1].

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[2].


1.   Methods and contents

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 and differences.

The traditional view of the development of Jewish law, which we traced briefly in the opening chapter of JL, suggests that it is mainly a deductive enterprise. The laws were derived from the Torah, which was revealed by God 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.[3]

Did God orally dictate it all word by word to Moses, and if so, out loud or in his head? Or did God visually display text for Moses to copy down, and if so, externally or internally? Or did God 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[4]; video display is suggested by, e.g., Exod. 25:40.

In any case, the Torah must be entirely from God, 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 God 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 God 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, God, 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 of JL, 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 God’s; whence the significance of the omniscience of God to revealed religion. The difficulty in this rationale is that we humans have no prior knowledge of God, 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 practice, these people were favoured by God 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 God. 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[5] 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[6]. 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[7]. 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[8], cosmography[9], biology[10] or history[11].

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[12]. 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 God, 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[13]. In effect, laws handed down by a tradition may be certain enough to infer even plainly physical or biological ‘fact’ from them[14].

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 judgments when they cannot be. We must leave room for doubt and even mystery[15]. With regard to metaphysical facts, like the supreme sovereignty of God, 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 God, 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[16]. 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[17].

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. Judgments 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[18].

Furthermore, the founders of modern science deliberately chose to bypass metaphysical issues. The idea of God 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 God 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 practice, the division of labor has not always been maintained – on either side. Many believers in God and the Bible continue to have dissident opinions concerning nature and history[19], and some scientists occasionally claim their theories or findings have metaphysical or normative implications[20].

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 God, to settle issues and provide us with standards. God, it seems, wished to reserve access to this domain, and transmit moral guidance to us through the words of Torah.


2.   Davqa or lav-davqa?

In this 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[21], 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 God, 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 “only some”.

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[22] 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 conclusion![23]

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 linguistic factors).

In contrast, in ordinary or scientific thought, there are no verbal givens, other than those impinging on individuals from the rest of society[24]. 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[25], 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[26]. 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 X.

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[27]. 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)[28]. 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 different cases[29].

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 “double syllogism”:

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 Aristotelian-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 induction).

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.[30]

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’[31] (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[32]); 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.[33]

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’.


3.Kushya and terutz

In comparing 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 respects.

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 practice, 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 practice, 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 terutz (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 dealt with.[34]

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[35]. 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[36], one of the conflicting theses, which is thus reclassified as “a theoretical tradition without practical appeal”[37]. 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[38]. 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 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.[39]

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.


4.Standards of knowledge

Thus, in 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 scrutiny.

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.[40]

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 truth.


Drawn from Judaic Logic (1995), chapter 8.


[1]              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.

[2]              The present essay's general conclusions are rather over-optimistic; but the specifics on which it bases such conclusions are essentially correct.

[3]              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.

[4]              A. Ibn Ezra suggests this specific order may have referred to the Book of the Wars of the Lord, rather than the Book of Torah (Cohen, p. 433).

[5]              The ideal scientist, if you prefer.

[6]              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.)

[7]              For instances, see Schroeder or Kelemen. See also JL. Appendix 2 for additional comments.

[8]              e.g. Comparing the Biblical account of Creation, apparently in 7 days, 5754 years ago, with the Big Bang scenario, 15 billion years ago.

[9]              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 Aristotle).

[10]            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 species?

[11]            e.g. Comparing the stories and dates given in the Bible and subsequent tradition, with the findings of archaeology and the scenarios they suggest.

[12]            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.

[13]            Namely, the prohibition to eat an egg laid on a holy day.

[14]            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.

[15]            In any case, as already indicated, such harmonizations are not within the scope of the present work.

[16]            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.

[17]            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 God 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.

[18]            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 God chose to deliver normative information to us (mostly, if not exclusively) by special proclamation.

[19]            Belief or disbelief in God 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.

[20]            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.

[21]            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, exactly.

[22]            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.

[23]            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.

[24]            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.

[25]            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'.

[26]            In this sense, atheism is also a religion, one which opts for a negative answer to the question of God's existence.

[27]            "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.

[28]            The conversion of E is reducible to that of I, by ad absurdum; or it may be understood independently, in a like manner.

[29]            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".

[30]            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.

[31]            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)'.

[32]            Inversion of "No X is Y" would be done by conversion, then contraposition.

[33]            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).

[34]            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.

[35]            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.

[36]            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.

[37]            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 God 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.

[38]            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 practice in Medieval European universities.

[39]            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 practice, see pp. 62-63 of same.

[40]            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.

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