JUDAIC LOGIC:
A Formal Analysis of Biblical,
Talmudic and Rabbinic Logic
Avi Sion, Ph. D.
First published, 1995. Slatkine Edition, 1997.
Abstract
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.
Buy it or read it online
All of Avi Sion’s published books can be purchased at Amazon.com
(in paperback or kindle/.mobi form), and at Lulu.com (in
hardcover, paperback or e-book/.epub form), as well as other online stores.
They can also be read online free of charge, chapter by chapter,
at www.TheLogician.net and, in '3D
flipbook' format, at www.AviSionBooks.com,
as well as in GoogleBooks and other Internet locations. They are also available in many
university and public libraries.
Contents in brief
1. Introduction.
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.
15. Epilogue.
Appendices
Addenda
Diagrams
References
Contents in detail
1. INTRODUCTION.
- 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.
- Background.
- Torah Samples.
- The Dayo Principle.
- Objections!
- 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.
- Rejects.
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.
- Hermeneutics.
- Heuristics.
- A Methodical Approach.
10. THE
THIRTEEN MIDOT (I).
- Exposition and
Evaluation.
- Inference of
Information.
- Scope of Terms.
11. THE THIRTEEN MIDOT
(II).
- Harmonization.
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.
15. EPILOGUE.
- Motives of the Present
Research.
- Conclusions of our
Study.
APPENDICES
Appendix 1. Further
Notes on A-Fortiori Argument.
Appendix 2. Notions
of Time.
Appendix 3. Gematria.
Appendix 4.
- 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.
ADDENDA.
- 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.
- Judgment-Calls.
- 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.
DIAGRAMS
REFERENCES
Further Description
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.
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