Page 14 - A Fortiori Logic: Innovations, History and Assessments
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When I started writing the present work, in late 2010, I thought it would take a dozen pages and a
couple of weeks at most to say what I felt the need to say. I had, I believed, said most of what needed
to be said in my previous foray in the field of a fortiori logic, in my 1995 study of Judaic logic. But
having noticed that some people were still writing on the subject without reference to my work, and to
boot were making serious mistakes, I felt the need to show them the errors of their ways. However, as
I proceeded in this set task, I found myself more and more involved in its intricacies.
For a start, to be fair the critiques had to be detailed, and show exactly what had been said and where
lay the errors and lacunae. Secondly, I kept discovering more and more commentaries which needed to
be similarly reviewed and evaluated. Thirdly, it became obvious that I needed to expand my
theoretical investigations, to be able to answer various questions these commentaries brought up,
consciously or unconsciously. Eventually, I realized that I had to aim for a history of the subject and a
survey of more recent contributions to it, to be able to demonstrate precisely who said what first.
Thus, the work ended up taking me three years to complete. Three parts emerged. The first presented
my new, much more detailed theory of a fortiori argument. The second part traced the early history of
use and discussion of such argument, so far as I could make it out with the resources available to me.
The third focused on modern commentaries on the subject. However, these parts did not emerge
separately, but repeatedly impinged on each other, so that many chapters or sections had to be written
more than once to be adapted to new findings. For this reason, it was impossible to publish any part of
the work before it was all done.
It should be stressed that the work did not proceed in the order that the chapters are now set out.
Whereas now all commentators are ordered chronologically, I did not comment on their work in their
order of appearance in history. It was all a matter of chance encounter and personal mood. Moreover,
my theoretical baggage at each stage was different. For this reason, some earlier chapters may appear
more perspicacious or analytically cutting than some later ones. I tried, of course, to harmonize things
as much as I could; but as the book grew in size, it became more and more unwieldy. No doubt my
memory in these later years is not what it was once; so I may have missed some things.

1. Innovations
The present work is replete with valuable innovations in the field of a fortiori logic, and in other,
related subjects. The present, wider ranging research confirms that my past work in this field, in my
1995 book Judaic Logic, was novel and important. But moreover, the present work corrects some
inaccuracies in that past work, and greatly enlarges and sharpens our theory of a fortiori argument, so
that it may be said to address almost every nook and cranny of the subject. There is not a single topic
that I worked on here that did not yield some new insight or new theoretical development in a fortiori
logic. This means that the research was certainly worthwhile and interesting; it is not a mere collection
and rehashing of old material.
‘Formalities’, part one of the present volume, 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.
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