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10 A FORTIORI LOGIC

PART I ‐ FORMALITIES

1. The standard forms

The present treatise on a fortiori logic has three purposes: (a) to present recent innovations I have

made in the theory of a fortiori argument; (b) to retrace, as much as I can till now, the history of use

and discussion of such argument; and (c) to review and evaluate (praise or criticize) ideas concerning

such argument by other commentators or logicians. In comparison with the original theory of a fortiori

argument presented in my book Judaic Logic over 15 years ago, the updated theory in the present

work contains many significant improvements and enlargements. As this updated theory will,

naturally, be the standard of judgment of all use and discussion of the argument throughout the present

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work, the reader is well advised to get acquainted with its main features before proceeding further .

1. Copulative a fortiori arguments

Based on close analysis of a large number of Biblical and Talmudic examples (some known to Jewish

tradition and some newly identified by me), as well as examples from everyday discourse, I discovered

and proposed in my book Judaic Logic the four valid moods of copulative a fortiori argument listed

below.

An a fortiori argument consists of three propositions called the major premise, the minor premise and

the conclusion. A copulative such argument is one involving terms. It comprises four terms, which are

always symbolized in the same way. The four terms are called the major, the minor, the middle and the

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subsidiary; and the symbols for them are respectively P, Q, R and S . Other terminology used will be

clarified as we proceed.

a. The positive subjectal {+s} mood:

1 Those who have already read my Judaic Logic ought still to read the present treatise, because there are

very many significant new insights and findings in it, and even some corrections.

2 Notice that the symbols R and S, respectively, happen to match the words “Range” (the middle item

always refers to a range) and Subsidiary.