Page 15 - A Fortiori Logic: Innovations, History and Assessments
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The present work also contains, in a final appendix, valuable innovations relating to certain
topics in general logic; namely, symbolization and axiomatization, existential import, the
tetralemma, the Liar paradox and the Russell paradox.

2. History

Logic science, properly conceived, is not just a theoretical enterprise, but also an investigation into the
historical roots of the forms of human discourse. The present work on a fortiori logic constitutes an
excellent case study of how a particular form of thought is rooted deep in antiquity (in history), and
probably much earlier, in language itself (in prehistory), and then gradually develops as awareness of
it dawns, expands and intensifies. There is ample evidence that a fortiori discourse existed in very
ancient times and in very diverse cultures. A fortiori reasoning was present in early Greek literature
(Homer, Aesop), long before Aristotle first discussed it (in his Rhetoric and Topics); and it was present
before that in Jewish literature (the Torah and other Biblical books). Aristotle did not invent the a
fortiori argument, any more than he invented the syllogism; he ‘merely’ observed, described and
explained them, as a botanist might notice and catalogue interesting plants.
‘Ancient and Medieval History’, part two of the present volume, 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.

3. Assessments
When I started to study a fortiori logic, I was little aware of the number of people who have since the
late 19 century attempted to describe and explain this common form of reasoning. The field seemed
nearly empty of contributors, a desert yet to be explored. Only little by little did I realize that many
people have indeed tried their hand at solving the enigma of a fortiori argument – some, to be sure,
more competently than others. It gradually became clear that a survey of existing contributors needed
to be made, and their work had to be carefully studied and assessed. Such assessment depended, of
course, on the theoretical and historiographical work undertaken earlier. It was interesting to see how
many of the contributors studied past work very little before proposing their own ideas. Each
apparently thought he was one of the first explorers.
‘Modern and Contemporary Authors’, part three of the present work, 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 astonishing, 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

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