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A Top-Down Approach to Sign Factors Engineering
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Why is the logic alphabet doing such a good job when it circulates in the networks of interrelations? Because we are going at this whole thing the other way around. Instead of selecting signs for the parts, such as "vee" for (A or B), and then trying to struggle our way back into the larger system, what we have done is turned around and going in the opposite direction. We went to the larger system first, to the interrelational symmetry properties contained in the square part of square truth tables, and then we designed the parts, namely, a special set of signs in a special notation (connectals), so that they will fit the needs of the larger system. In brief, very much in line with Peirce and 1902, our sign making has a Gestalt bias. In this case, the bias puts the emphasis on the polyhedral and on the crystallographic structures that are generated when a certain set of symmetry transformations is acting on a shape-value notation for the 16 binary connectives. The bias is straight-forward and direct. Let the systemic properties of the whole determine the formation of the parts. This bias cuts a claryifying swath across the full length of the 1900's. We can now say that, breaking with the standard format carried in the traditional mold, any notation that is limited to (and, or, if) is not enough. In effect, this bias exposes a faulty assumption, one that is still carried strong in the conventional wisdom and one that still looks to economy-driven axiomatics to justify notation building for the propositional calculus. Ironically, the counter view started as early as Pierce and his 1902 Box-X notation. Like it or not, all those tables, all those diagrams, all those models introduced by the X-stem Logic Alphabet leaves us walking full stride into the 21st Century. This approach also gives rise to a run of frontline questions. How about an optical computer? What about isomorphisms that lead into crystallography and into quantum physics? What about a specialized computer language? What about another form of Arabic numerals, when the 16 LSs in another font are used as number symbols that are alphanumeric, binary stem-positional, and hexadecimal? What about semiotics and cognitive ergonomics? What about mental development and the psychology of logic education, especially for children? What about the standard presentation of symbolic logic as it continues to appear in the textbooks today? It is easy enough to say, "Let the fingers do the walking." By now it is obvious, we hope, that, when we construct the logic signs with great care, it will be easy to say "Let the mirrors do the thinking and let the people do the reflecting." One more nudge. Suppose that you have lived all of your life back in the age of Roman numerals. Also suppose that one day quite by accident you read a short summary of Arabic numerals. How would you have reacted to the jolt carried in that much change? We suggest that what you now know about the logic alphabet leaves you, and whatever you do in logic, very much in the same position. |
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