Peirce as the Primary Precursor of the Logic Alphabet

In passing realize that in 1902 Charles Sanders Peirce (1839-1914), American philosopher and logician, devised a notation that is like the logic alphabet. His manuscripts, the Simplest Mathematics (MSS 430, 431, 429), were published (1933) only in selected parts. This was done in such a way that his notation was desymbolized and recast so that its shape-value properties were lost. Today these manuscripts with few exceptions are totally ignored.

Even though the second author devised the Logic Alphabet a full decade before seeing what Peirce had done, the development of the logic alphabet is best thought of as a direct continuation of Peirce's 1902 box-X notation for all of the 16-binary connectives.

Logic for Peirce was strong in the logic of relations and, likewise, what follows will be relations-theory generated. Logic for Peirce was also centered in what he established as the study of signs and sign action, a study that has been given modern form, now called semiotics (also spelled semeiotics). Looking again at our working analogy, it is obvious that, when we go

from Roman numerals to Arabic numerals, the key step lies in becoming acquainted with the code that goes with the new set of numerals. Such a key step repeats in what follows.

But first, the 4-by-4 pattern shown above is one representation of the logic alphabet. The 16 signs in this shape-value notation, which could also be called a position-value notation, are placed in a standard configuration that is called a Clock-Compass. Twelve positions are placed around the outside and the four directions are in the middle. This means that the same sign will always be placed in the same position. For example, the d-letter is always at 11 o'clock and the h-letter is always at 5 o'clock, both of which are located symmetrically across the center of the clock-compass. Note that Peirce used just the compass image when he described his own 4-by-4 configuration.

As already mentioned, the construction, development, and use of the logic alphabet as a total system is best thought of as a direct continuation of what Peirce accomplished when he devised his box-X notation in 1902.

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