A FORTIORI LOGIC:
Innovations, History
and Assessments.
Avi Sion, Ph. D.
First published, 2013.
Abstract
A Fortiori Logic: Innovations, History and Assessments is a wide-ranging and in-depth study of a fortiori reasoning, comprising
a great many new theoretical insights
into such argument, a history of its
use and discussion from antiquity to the present day, and critical analyses of the main attempts at its elucidation. Its
purpose is nothing less than to lay the foundations for a new branch of logic
and greatly develop it; and thus to once and for all dispel the many fallacious
ideas circulating regarding the nature of a fortiori reasoning.
The work is divided into three parts. The first part, Formalities, presents the author’s
largely original theory of a fortiori argument, in all its forms and varieties.
Its four (or eight) principal moods are analyzed in great detail and formally
validated, and secondary moods are derived from them. A crescendo argument is
distinguished from purely a fortiori argument, and similarly analyzed and
validated. These argument forms are clearly distinguished from the pro rata and
analogical forms of argument. Moreover, we examine the wide range of a fortiori
argument; the possibilities of quantifying it; the formal interrelationships of
its various moods; and their relationships to syllogistic and analogical
reasoning. Although a fortiori argument is shown to be deductive, inductive
forms of it are acknowledged and explained. Although a fortiori argument is
essentially ontical in character, more specifically logical-epistemic and
ethical-legal variants of it are acknowledged.
The second part of the work, Ancient and Medieval History, looks into use and discussion of a
fortiori argument in Greece and Rome, in the Talmud, among post-Talmudic
rabbis, and in Christian, Moslem, Chinese and Indian sources. Aristotle’s
approach to a fortiori argument is described and evaluated. There is a thorough
analysis of the Mishnaic qal vachomer
argument, and a reassessment of the dayo
principle relating to it, as well as of the Gemara’s later take on these
topics. The valuable contribution, much later, by Moshe Chaim Luzzatto is duly
acknowledged. Lists are drawn up of the use of a fortiori argument in the
Jewish Bible, the Mishna, the works of Plato and Aristotle, the Christian Bible
and the Koran; and the specific moods used are identified. Moreover, there is a
pilot study of the use of a fortiori argument in the Gemara, with reference to
Rodkinson’s partial edition of the Babylonian Talmud, setting detailed
methodological guidelines for a fuller study. There is also a novel, detailed
study of logic in general in the Torah.
The third part of the present work, Modern and Contemporary Authors, describes and evaluates the work
of numerous (some thirty) recent contributors to a fortiori logic, as well as
the articles on the subject in certain lexicons. Here, we discover that whereas
a few authors in the last century or so made some significant contributions to
the field, most of them shot woefully off-target in various ways. The work of
each author, whether famous or unknown, is examined in detail in a dedicated
chapter, or at least in a section; and his ideas on the subject are carefully weighed.
The variety of theories that have been proposed is impressive, and stands
witness to the complexity and elusiveness of the subject, and to the crying
need for the present critical and integrative study. But whatever the intrinsic
value of each work, it must be realized that even errors and lacunae are
interesting because they teach us how not
to proceed.
This book also contains, in a final appendix, some valuable
contributions to general logic, including new analyses of symbolization and
axiomatization, existential import, the tetralemma, the Liar paradox and the
Russell paradox.
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 Google Books and other Internet locations. They are also available in many
university and public libraries.
Contents in brief
Foreword
PART I - FORMALITIES
1.
The standard forms
2.
More formalities
3.
Still more formalities
4.
Apparently variant forms
5.
Comparisons and correlations
PART II – ANCIENT AND MEDIEVAL HISTORY
6.
A fortiori in Greece and Rome
7.
A fortiori in the Talmud
8.
In the Talmud, continued
9.
Post-Talmudic rabbis
10. A
fortiori in the Christian Bible
11. Islamic
‘logic’
12. A
fortiori in China and India
PART III – MODERN AND CONTEMPORARY AUTHORS
13. Moses
Mielziner
14. Adolf
Schwarz
15. Saul
Lieberman
16. Louis
Jacobs
17. Heinrich
Guggenheimer
18. Adin
Steinsaltz
19. Jonathan
Cohen
20. Michael
Avraham
21. Gabriel
Abitbol
22. Hyam
Maccoby
23. Alexander
Samely
24. Lenartowicz
and Koszteyn
25. Abraham,
Gabbay and Schild
26. Stefan
Goltzberg
27. Andrew
Schumann
28. Allen
Wiseman
29. Yisrael
Ury
30. Hubert
Marraud
31. Various
other commentaries
32. A
fortiori in various lexicons
33. Conclusions
and prospects
APPENDICES
1.
A fortiori discourse in the Jewish Bible
2.
A fortiori discourse in the Mishna
3.
A fortiori discourse in the two Talmuds
4.
A fortiori discourse by Plato and Aristotle
5.
A fortiori discourse in other world literature
6.
Logic in the Torah
7.
Some logic topics of general interest
Main References / Bibliography
Contents in detail
FOREWORD
1.
Innovations
2.
History
3.
Assessments
Part I - Formalities
1. THE STANDARD
FORMS
1.
Copulative a fortiori arguments
2.
Implicational a fortiori arguments
3.
Validations
4.
Ranging from zero or less
5.
Secondary moods
2. MORE
FORMALITIES
1.
Species and Genera
2.
Proportionality
3.
A crescendo argument
4.
Hermeneutics
5.
Relative middle terms
3. STILL MORE
FORMALITIES
1.
Understanding the laws of thought
2.
Quantification
3.
A fortiori through induction
4.
Antithetical items
5.
Traductions
4. APPARENTLY
VARIANT FORMS
1.
Variations in form and content
2.
Logical-epistemic a fortiori
3.
Ethical-legal a fortiori
4.
There are no really hybrid forms
5.
Probable inferences
6.
Correlating ontical and probabilistic forms
5. COMPARISONS
AND CORRELATIONS
1.
Analogical argument
2.
Is a fortiori argument syllogism?
3.
Correlating arguments
4.
Structural comparisons
5.
From syllogism to a fortiori argument
6.
From a fortiori argument to syllogism
7.
Reiterating translations
8.
Lessons learned
Part II – Ancient and Medieval History
6. A FORTIORI
IN GREECE AND ROME
1.
Aristotle’s observations
2.
The Kneales’ list
3.
Aristotle in practice
4.
Relation to syllogism
5.
Cicero
6.
Alexander of Aphrodisias
7.
Historical questions
7. A FORTIORI
IN THE TALMUD
1.
Brief history of a fortiori
2.
A brief course in the relevant logic
3.
A fresh analysis of the Mishna Baba Qama 2:5
4.
A logician’s reading of Numbers 12:14-15
5.
A critique of the Gemara in Baba Qama 25a
6.
A slightly different reading of the Gemara
8. IN THE
TALMUD, CONTINUED
1.
Natural, conventional or revealed?
2.
Measure for measure
3.
The dayo principle in formal terms
4.
The human element
5.
Qal vachomer without dayo
6.
Three additional Gemara arguments
7.
Assessment of the Talmud’s logic
8.
The syllogistic Midot
9.
Historical questions
9. POST-TALMUDIC
RABBIS
1.
Logic and history issues
2.
Philo of Alexandria
3.
Sifra
4.
The Korach arguments
5.
Saadia Gaon
6.
Rashi and Tosafot
7.
Kol zeh assim
8.
Maimonides
9.
More on medieval authors
10. Moshe
Chaim Luzzatto
11. More
research is needed
10. A FORTIORI IN
THE CHRISTIAN BIBLE
1.
In the Christian Bible
2.
Jesus of Nazareth
3.
Paul of Tarsus
4.
In later Christian discourse
5.
Additional findings
11. ISLAMIC
‘LOGIC’
1.
Logic in the Koran
2.
About the Koran
3.
Logic in the hadiths
4.
A fortiori in fiqh, based on Hallaq
5.
Other presentations and issues
6.
The dayo principle and more
7.
The essence of Islamic discourse
12. A FORTIORI IN
CHINA AND INDIA
1.
Zen logic in general
2.
A fortiori use in Zen
3.
The Indian kaimutika
Part III – Modern and Contemporary Authors
13. MOSES
MIELZINER
1.
Description of the argument
2.
Structural analyses
3.
Concerning the jus talionis
4.
Restrictions and refutations
14. ADOLF SCHWARZ
1.
Equation to syllogism
2.
Jacobs’
critique
3.
Kunst’s
critique
4.
Wiseman
on Schwarz
5.
Why a fortiori is not syllogism
15. SAUL
LIEBERMAN
1.
Hermogenes
2.
Influences on rabbis
3.
Reassessment
4.
Cicero
16. LOUIS JACOBS
1.
The simple and complex types
2.
Deficiencies in Jacobs’ forms
3.
More comments on Jacobs’ work
4.
A more recent contribution
17. HEINRICH
GUGGENHEIMER
1.
Tout un programme
2.
Theory of a fortiori
3.
A faulty approach
18. ADIN
STEINSALTZ
1.
Qal vachomer and dayo
2.
A recurrent fallacy
3.
Lack of formalism
19. JONATHAN
COHEN
1.
Formula for a fortiori
2.
Fallacy of diverse weights
3.
No effort of validation
20. MICHAEL
AVRAHAM
1.
Model of a fortiori
2.
Outlook on a fortiori
3.
On Baba Qama 2:5
21. GABRIEL
ABITBOL
1.
Name and functioning
2.
Tabular representation
3.
Treatment of dayo
4.
Refutations
5.
Closing remarks
22. HYAM MACCOBY
1.
Purely a fortiori argument
2.
A crescendo argument
3.
Baba Qama 25a
4.
Faulty qal vachomer
23. ALEXANDER
SAMELY
1.
General definition
2.
Descriptive formula
3.
Three alleged techniques
4.
Bava Kamma 25a-b
5.
Samely’s online database
6.
My critical researches
24. LENARTOWICZ
AND KOSZTEYN
1.
The form of the argument
2.
The dayo principle
3.
Epistemic substitution
25. ABRAHAM,
GABBAY AND SCHILD
1.
Their opinion of past work
2.
Their erroneous basic premise
3.
Some errors of logic
4.
Mixing apples and oranges
5.
Quid pro quo
26. STEFAN
GOLTZBERG
1.
Source of his definition
2.
Soundness of the argument
3.
The dayo principle
4.
His “two-dimensional” theory
27. ANDREW
SCHUMANN
1.
Interpretation of Baba Qama 25a
2.
Syllogism as a fortiori
3.
Grandiosity without substance
4.
Logic custom-made
5.
Not logic, but lunacy
28. ALLEN WISEMAN
1.
Definition and Moods
2.
Inductive a fortiori
3.
Abduction and conduction
4.
Proportional a fortiori
5.
The dayo principle
6.
The scope of dayo
7.
Miriam and Aaron
8.
Summing up
29. YISRAEL URY
1.
An ingenious idea
2.
Diagrams for a fortiori argument
3.
No a crescendo or dayo
4.
Kol zeh achnis
30. HUBERT
MARRAUD
1.
Warrants and premises
2.
The main form of a fortiori
3.
So-called meta-arguments
4.
Paulo minor argument
5.
Legal a fortiori argument
31. VARIOUS OTHER
COMMENTARIES
1.
H. S. Hirschfeld
2.
H.W.B. Joseph
3.
Moshe
Ostrovsky
4.
Pierre
André Lalande
5.
David
Daube
6.
Meir Zvi Bergman
7.
Strack and Stemberger
8.
Meir Brachfeld
9.
Gary G. Porton
10. Mordechai
Torczyner
11. Ron
Villanova
12. Giovanni
Sartor
13. And
others still
32. A FORTIORI IN
VARIOUS LEXICONS
1.
The Jewish Encyclopedia
2.
Encyclopaedia Judaica
3.
Encyclopedia Talmudit
4.
How to define a fortiori
5.
Various dictionaries and encyclopedias
6.
Wikipedia
33. CONCLUSIONS
AND PROSPECTS
1.
My past errors and present improvements
2.
Historical research into logic
3.
Assessing contemporaries
4.
Perspectives
APPENDICES
1.
A fortiori discourse in the Jewish Bible
2.
A fortiori discourse in the Mishna
3.
A fortiori discourse in the two Talmuds
4.
A fortiori discourse by Plato and Aristotle
1.
Plato
2.
Aristotle
5.
A fortiori discourse in other world literature
1.
Ancient literature
2.
More recent literature
6.
Logic in the Torah
7.
Some logic topics of general interest
1.
About modern symbolic logic
2.
The triviality of the existential import
doctrine
3.
The vanity of the tetralemma
4.
The Liar paradox (redux)
5.
The Russell paradox (redux)
Main References / Bibliography
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