Mirror Logic and the Algebra of Abstract Groups | |

All of this runs head on into the algebra of abstract groups. All of this forces a certain kind of behavior on the logic alphabet. The flip-mate-flip and flip rules will become Now we have it! Table I is the new multiplication table. Akin to Arabic numerals and the use of zero, the 4-tuple (OOOO) is acting both as the rule-free condition and as a combinatory identity element. The 16 combinations of the four rules along the side (N, N, N, C), which line up with the 16 combinations of the An easy way to learn about Table I is to notice that Arabic numerals encourage the use of models, such as an abacus and a slide rule. The Romans, in spite of their numerals, did use an abacus; they did not, however, have a slide rule. Modern logic, even more limited than the Romans, does not use hand-held models with which to make logical calculations. In contrast, the logic alphabet is a notation that stumbles all over itself, so many are the models. | |

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