Combinatoric Logic Game of Marbles
Armahedi Mahzar (c) 2015

In my previous blog it has been shown that the combination and disposal of parallel colorful sticks with two orientations can prove any valid syllogism tabulated by Leibniz by the lineal combinatoric of Ploucquet. The combinatoric verification process can also be simulated by the game of arranging and disposing colored marbles and pieces of paper.

In the following it will be shown that we can simulate logical proof with the game arranging and disposing  the colorful marbles and pieces of paper. The secret is the fact that we can replace the changing the line length to represent the opposite concept with the changing of the marble’s ground.

Fundamental Categorical Proposition of Aristotle

If the subject a is represented by a red marble   and predicate b represented by green marble  , then NOT a is represented by red marble placed upon small white paper  .

Furthermore, the fundamental categorical statement of Aristotle is represented by pairs of marbles as it is shown in the following table

The premises and conclusion of a syllogism form is one of four such statements.

Proof of the Validity of Syllogism

The game playing that simulate the proving of the validity of a syllogism includes the following steps

1. juxtaposing the marble pairs which represent both premises of a syllogism
2. disposing the pair of same colored marble with different ground
3. putting the marble which represent the subject of the second premise as the marble that represent the subject of the syllogism conclusion.

With a game like this, we can do the proving of valid syllogisms with ease, because the end result of the game is a representation of the syllogism conclusion. The table below is the Leibniz table of the premises of valid syllogisms. 

End notes

1.  Apparently, the game is very simple using colored marbles  can be taught to kindergartners. The game can also be seen as a simulation of Sommersian arithmologic.
2. Unfortunately, this game can only be played with the help of additional pieces of paper.  However, with a set of colored cards without  the help of other pieces of paper, we can simulate the proving of the syllogism validity with a simpler game as I have found it. Hopefully, that will be presented in my next blog.