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A FORTIORI LOGIC

© Avi Sion, 2013 All rights reserved.

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A FORTIORI LOGIC

TABLE OF CONTENTS.

Contents in brief:

Abstract

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

Contents in detail:

Abstract

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

Addendum to chapter 25

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



Please note that the Appendices are integral parts of the present work, to be studied in conjunction with the chapters in which they are mentioned. Also, the footnotes throughout this volume are intended to be read; they often contain important additional information or reflection.

As regards the spelling of foreign words, no great effort has been made here to harmonize it. The same word may have different spellings in different contexts. Very often, the spelling used depends on the spelling others prefer, who are discussed in the given context. The reader is asked to be indulgent in this matter.

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2016-06-13T13:00:51+00:00