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A Fortiori Logic: Innovations, History and Assessments, by Avi Sion, 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.

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