Lineal Combinatoric of Ploucquet
Armahedi Mahzar (c) 2015

Gottfried Ploucquet
(1716-1790)

In the last blog it has been shown that the literal combinatoric of Ploucquet can be used as a tool to seek the conclusion of a valid syllogism, simpler than the Boolean, Peircean or Sommersian arithmologic. The secret is that we replace the arithmetic operations with combinatoric operations, while elimination of the oppositely signed variables is replaced by the deletion of capital lower-case letters. Literal combinatoric method of  Ploucquet is indeed simple, but if writing letters are replaced with drawings colored lines, then the syllogism becomes more visual and the method can be easily taught in a pre-schooler who can not read letters.  

Therefore, in a method visualizing the literal combinatoric of  Ploucquet we can:

• Replacing the lowercase letters with short lines
• Replacing the capital letters with long lines
• Changing the names of the letters with the colors of the lines

 
Thus, in this method of lineal combinatoric

• variables are represented by short lines
• negation of variables are represented  by long lines
• conjunction is expressed by the juxtaposition 

Fundamental Categorical Propositions of Aristotle

 

If a = and b = , then the fundamental categorical propositions of Aristotle is described as follows 

 

The premises and conclusion of a syllogism are one of these four statements.

Proving the vadity of syllogism

With line images in this notation we can prove the validity of syllogism. For example, proving the validity of the syllogism Barbara in the lineal combinatoric methods color line is as follows
Abc AND Aab =

Leibniz-Ploucquet table of valid Syllogism

 = Aac

Proving the validity of the other syllogism can be seen in the table below Leibniz

 

Concluding Remarks

1. Actually, the colored lines in the above method is a simplification of the following line method of Ploucquet 

where universality replaced with negativity and the two-dimensional arrangement (from the bottom to the top / from left to right) is replaced with a one-dimensional linear array (from left to right) of upright lines.


2. Game of colored lines with different length as a simulation logical deduction can be simplified by playing a one-sized colored sticks with different orientations. This game of logic is what we will be discussed in the next blog.