From Roman Numerals to Arabic Numerals

Roman numerals start with some of the number values, such as I, V, X, and then the right combinations are used to express any of the in-between values, such as IV, VII, IX. Modern logic does the same thing when it starts with a few heavy-duty connectives, such as "and" (TFFF), "or" (TTTF), "if" (TFTT), and then "not" (Negation) and "equivalence" (Equivalence) are added to this mix to express the other relations in the special 16-set of (A, B) relations (1 4 6 4 1).

Roman numerals are loaded with difficulties because they do not lay bare, in any transparent way, the interrelations among the number values. Notice, instead, that we use Arabic numerals when we build a multiplication table. When modern logic uses (dot, vee, horseshoe) to express (and, or, if), it does not lay bare the networks of interrelations that are a fundamental part of the 16 binary connectives taken as a total system. Unfortunately, in contrast to what we will see later, the state of the art is such that symbolic logic continues to remain many, many miles away from coming up with its own multiplication table.

Now continue with the comparison. Begin by looking upon Arabic numberals so that they become a primary set of ten distinct and separate abacus settings that have been carried to the mental level (0-9). Likewise, now look upon the X-stem Logic Alphabet (XLA) so that it becomes a primary set of 16 coded, iconic Venn truth tables that have been carried to the mental level (o-x).

What a paradox! The disparity in the extremes could not be more disturbing. It is obvious that we have such high standards for number symbols; in effect, Arabic numerals. But, squirm as we will, wiggle as we may, it is very odd indeed that the standards we are now using for logic signs continue to remain so much lower. The next move is obvious. Take what we already know about Arabic numberals and do no more than repeat it for a new notation for logic.

By now the challenge should be clear. It continues to emphasize the working analogy. Roman numerals are to Arabic numerals as the symbols in common use for the binary connectives, such as (dot, vee, horseshoe) for (and, or, if), are to what? What follows will introduce you to the "X-stem Logic Alphabet." Then comes the part about the mirrors.

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