Peirce as the Primary Precursor of the Logic Alphabet 
 
In passing realize that in 1902 Charles Sanders Peirce (18391914), 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 shapevalue 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 boxX notation for all of the 16binary connectives. Logic for Peirce was strong in the logic of relations and, likewise, what follows will be relationstheory 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 4by4 pattern shown above is one representation of the logic alphabet. The 16 signs in this shapevalue notation, which could also be called a positionvalue notation, are placed in a standard configuration that is called a ClockCompass. 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 dletter is always at 11 o'clock and the hletter is always at 5 o'clock, both of which are located symmetrically across the center of the clockcompass. Note that Peirce used just the compass image when he described his own 4by4 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 boxX notation in 1902.
previous page  next page 

 



 



