Three-Way Signs that Cofunction as Index, Icon, and Symbol
Let LS stand for Letter Shape and then go directly to (A and B), also written as a pattern of four finger pairs (A TFFF B). Now use this connective as a model for what we have in mind for all of the 16 connectives. This takes a big step. It treats all of the connectives as a total system, with all parts present and no parts inactive. In (1), begin by seeing that (A and B) is equivalent to itself, (A and B). In (2), the pair of fingers in which the Touching takes place puts a T in the upper-right corner. In (3), a
basic square puts an enlarged doT in the same corner. In (4), the LS in (A d B) has a sTem in the same corner. By design, also centered in Peirce and his three-way emphasis on sign making (index, icon, symbol), note especially that (2), (3), and (4) have become the main parts in a triple isomorphism, Sowa (1998) and Shin (2002) come the closest to this analysis. In brief, when the logic alphabet was devised in 1961-62, it became one more logic in an infinite variety of logics, and now it continues to function as a fully developed multi-modal representation system. The "and" in (1) is repeated three times: in (2) as a square truth table, in (3) as a matching coded dot-square, and in (4) as a corresponding square-outlined stem shape. The d-letter is a simple cursive that has enough teamwork built into its carefully selected subareas so that, as needed, it is geometrically capable of being inserted to meet any one of the sign-object conditions in (2), (3), and (4). Consequently, all in one stroke and also in terms of Peirce's three classes of sign-object relations, (i) the d-letter in reference to the square truth table is an index; (ii) in reference to the dot-square, it is an icon; and (iii) in reference the concept called conjunction, it is a symbol. When all three are conjoined and carried in the same multi-modal channel, this indexical, iconic, symbolic d-letter is not only serving as a three-way compound for conjunction (A TFFF B). It also runs head-on into a nmemonic accident. The last letter of the word "and" happens to be the same d-letter that appears in (A d B). The external code (below) puts the finger pairs (TT, TF, FT, FF) at the four corners of the all-common basic square. This ground-form repeats the order in common use for the plus-minus quadrants in Cartesian coordinates. The internal code puts a sTem so that it comes close to Touching a corner, when the finger pair in the same corner is counted as True. See that the h-letter (FTTT) has stem positions that are opposite exactly to where the d-letter (TFFF) does and does not have stems. These opposites (h, d) are at both ends of the word "hand." In (5), by way of a special act of abstraction, like an eagle off to the sky, we come to the asterisk in general. It has become an algebraic symbol. Like an x when it stands for any number, the asterisk stands for any of the 16 binary connectives.
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