A Formal Analysis of Biblical, Talmudic and Rabbinic Logic
Avi Sion, Ph. D.
First published, 1995. Slatkine Edition, 1997.
Judaic logic: A Formal Analysis of Biblical, Talmudic and Rabbinic Logic is an original inquiry into the forms of thought determining Jewish law and belief, from the impartial perspective of a logician.
Judaic Logic attempts to honestly estimate the extent to which the logic employed within Judaism fits into the general norms, and whether it has any contributions to make to them. The author ranges far and wide in Jewish lore, finding clear evidence of both inductive and deductive reasoning in the Torah and other books of the Bible, and analyzing the methodology of the Talmud and other Rabbinic literature by means of formal tools which make possible its objective evaluation with reference to scientific logic. The result is a highly innovative work - incisive and open, free of clichés or manipulation.
Judaic Logic succeeds in translating vague and confusing interpretative principles and examples into formulas with the clarity and precision of Aristotelian syllogism. Among the positive outcomes, for logic in general, are a thorough listing, analysis and validation of the various forms of a-fortiori argument, as well as a clarification of dialectic logic. However, on the negative side, this demystification of Talmudic/Rabbinic modes of thought (hermeneutic and heuristic) reveals most of them to be, contrary to the boasts of orthodox commentators, far from deductive and certain. They are often, legitimately enough, inductive. But they are also often unnatural and arbitrary constructs, supported by unverifiable claims and fallacious techniques.
Many other thought-processes, used but not noticed or discussed by the Rabbis, are identified in this treatise, and subjected to logical review. Various more or less explicit Rabbinic doctrines, which have logical significance, are also examined in it. In particular, this work includes a formal study of the ethical logic (deontology) found in Jewish law, to elicit both its universal aspects and its peculiarities.
With regard to Biblical studies, one notable finding is an explicit formulation (which, however, the Rabbis failed to take note of and stress) of the principles of adduction (the testing, and confirmation or rejection, of hypotheses - i.e. of beliefs, and equally of the reasons or explanations put forward in support of beliefs) in the Torah, written long before the acknowledgement of these principles in Western philosophy and their assimilation in a developed theory of knowledge. Another surprise is that, in contrast to Midrashic claims, the Tanakh (Jewish Bible) contains a lot more than ten instances of qal vachomer (a-fortiori) reasoning.
In sum, Judaic Logic elucidates and evaluates the epistemological assumptions which have generated the Halakhah (Jewish religious jurisprudence) and allied doctrines. Traditional justifications, or rationalizations, concerning Judaic law and belief, are carefully dissected and weighed at the level of logical process and structure, without concern for content. This foundational approach, devoid of any critical or supportive bias, clears the way for a timely reassessment of orthodox Judaism (and incidentally, other religious systems, by means of analogies or contrasts). Judaic Logic ought, therefore, to be read by all Halakhists, as well as Bible and Talmud scholars and students; and also by everyone interested in the theory, practice and history of logic.
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Contents in brief
2. Adductive Logic in the Torah.
3. The Formalities of A-Fortiori Logic.
4. Qal VaChomer.
5. Revised List of Biblical A-Fortiori.
6. The Language of Biblical A-Fortiori.
7. Without Prejudice.
8. Initial Impressions.
9. Traditional Teachings.
10. The Thirteen Midot (I)
11. The Thirteen Midot (II)
12. The Sinai Connection.
13. On the Concept of Mitzvah.
14. Logical Aspects of Emunah.
Contents in detail
- The Development of Jewish Law.
- A Logic Primer.
2. ADDUCTIVE LOGIC IN THE TORAH.
- The Art of Knowing.
- Adduction in Western Philosophy.
- Adducing Prophecies and Prophethood.
- Logic and Mysticism.
3. THE FORMALITIES OF A-FORTIORI LOGIC.
- The Valid Moods.
- Validation Procedures.
- Additional Details.
4. QAL VACHOMER.
- Torah Samples.
- The Dayo Principle.
- Rabbinic Formulations.
5. REVISED LIST OF BIBLICAL A-FORTIORI.
- Problems Encountered.
- The Solution Found.
- The Data and their Analysis.
- Synthesis of Results.
- Talmudic/Rabbinic A-Fortiori.
6. THE LANGUAGE OF BIBLICAL A-FORTIORI.
- Torah Books.
- Historical Books.
- Other Books.
7. WITHOUT PREJUDICE.
- Taking a Dilemma by its Horns.
- About Revision.
- Changes in the Law.
8. INITIAL IMPRESSIONS.
- Methods and Contents.
- Davqa or Lav Davqa?
- Kushya and Terutz.
- Standards of Knowledge.
9. TRADITIONAL TEACHINGS.
- A Methodical Approach.
10. THE THIRTEEN MIDOT (I).
- Exposition and Evaluation.
- Inference of Information.
- Scope of Terms.
11. THE THIRTEEN MIDOT (II).
12. THE SINAI CONNECTION.
- Verdict on Rabbinic Hermeneutics.
- Artificial Blocks to Natural Development of the Law.
- How "Tradition" Keeps Growing.
13. ON THE CONCEPT OF MITZVAH.
- Basic Properties.
- Complementary Factors.
- How to Count Mitzvot.
- Commanded vs. Personal Morality.
14. LOGICAL ASPECTS OF EMUNAH.
- On Natural Proofs of Religion.
- Theodicy and the Believer's Wager.
- Faith and Justice.
- Legislated Belief.
- Motives of the Present Research.
- Conclusions of our Study.
Appendix 1. Further Notes on A-Fortiori Argument.
Appendix 2. Notions of Time.
Appendix 3. Gematria.
- Feigenbaum's Understanding the Talmud.
- Rabinowich's Talmudic Terminology.
- The Ramchal's Ways of Reason.
Appendix 5. The Hebrew Language.
Appendix 6. Further Notes on Harmonization Rules.
- Concerning Adductive Reasoning Relative to Prophecy.
- A Note on Astronomy.
- An Example of Secondary A-Fortiori in the Talmud.
- One More Example of A-Fortiori in the Tanakh.
- A Note Concerning Anachronisms.
- Inferences from Context.
- Post Hoc Ergo Propter Hoc.
- Tolerance of Contradictions.
- Proof of Gd by Analogy?
- Disproofs of Gd?
- Neither Certainty Nor Faith are Essential to Religious Ethics.
- The Rabbis' Antipathy to Philosophy.
Judaic logic: A Formal Analysis of Biblical, Talmudic and Rabbinic Logic is an original inquiry into the forms of thought determining Jewish law and belief, from the objective perspective of a logician. The author's previous treatise, Future Logic: Categorical and Conditional Deduction and Induction of the Natural, Temporal, Extensional and Logical Modalities, was a large-scale study of formal logic and epistemology; in the present work, his purpose is to consider the logic employed within his religion, Judaism, and honestly estimate the extent to which it fits into the general norms and whether it has any contributions to make to them. It covers a wide range of topics:
· A brief overview of the sources of Jewish law (the Halakhah), and a quick introduction to generic logic theory (induction and deduction), for the uninitiated.
· The new discovery of an explicit formulation of the principles of adduction in the Torah (the Pentateuch), written long before their acknowledgement in Western philosophy and their assimilation in a developed theory of knowledge (epistemology).
· An original and thorough formal analysis of a-fortiori logic (the qal vachomer type of argument, the most deductive of Judaism's interpretative processes), together with a detailed investigation of its use in the Tanakh (the Jewish Bible) which reveals it to be much more widespread than traditionally supposed.
· A reflection on the psychological and social factors affecting both religious and secular thought, which may cause people to deviate from openness and objectivity, whether within one of these domains or in relation to the other.
· An examination of some of the main similarities and differences between the methods and databases of religious and secular pursuits of knowledge, which shows the overwhelmingly inductive (rather than, as traditionally assumed, deductive) methodology of Talmudic and Rabbinic thought.
· A presentation, in considerable detail, of traditional teachings of Judaic logic, including principles of interpretation (hermeneutics) and organization (heuristics); and suggestions for methodical study.
· A detailed and incisive formalization and evaluation of the 13 Midot of R. Ishmael and other fundamental principles of exegesis of Jewish law - a completely novel research effort (which may be considered as the central motive of the work), revealing impartially the strengths and weaknesses of Talmudic and Rabbinic modes of thought.
· A formal study of the ethical logic (deontology) found in Jewish law, to elicit its universal aspects and its peculiarities.
· Finally, an examination of possible bases and motives of belief in G-d, and, more broadly, in the religious tradition; and a critical assessment of some of the less formal legal generalities adopted by the Rabbinic tradition.
Judaic Logic is of both theoretical and practical value, to students of Bible and Talmud and to students of Logic and Philosophy alike. The work's universality lies in its efforts both (a) to bring Judaic logic into the general fold, demystifying it and showing the extent to which its processes are, or are not, commonplace; and (b) to draw from it any lessons of value to logic theory and practise in general. In fulfilling the first of those tasks, this work incidentally provides Bible and Talmud students, and more specifically the deciders of Jewish law, with wider methodological perspectives and powerful new technical tools. In fulfilling the second, it provides the secular layperson, the scientist or philosopher, and in particular the logician, with novel historical insights and formal instruments.