Combinatoric Logic Game of Marbles and Cards

Combinatoric Logic Game of Marbles and Cards

Armahedi Mahzar (c) 2015

In my previous blog it has been shown that the arrangement and disposal of pairs of colorful cards with two orientation can prove any valid syllogism tabulated by Leibniz. The combinatoric verification process is simulated by the game of arranging and disposing colored cards  with two orientations.

In the following it will be shown that we can also make the game arranging and disposing anything with the help of a piece of paper. The secret is the fact that we can replace the changing the card orientation to represent the opposite concept in the last game with the changing of the thing position relative to the paper in the new game. In this blog we will use marbles and a piece of card as the pieces of the new logic game.

Fundamental Categorical Proposition of Aristotle

If concept a is representing by a marble   , the its opposite NOT a is represented by the the same marble inside the border of a card 

 .

If the subject is represented by a red marble and predicate b represented by green marble , then the fundamental categorical statement of Aristotle is represented by pairs of marbles will be shown in the following table

The premises and conclusion of a syllogism 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 marbles with different positions
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 by disposing pair(s) of 
colored marbles in opposite positions in the  Leibniz’s  table below:

End notes

1.  The colored marbles can be replaced with anything that has duplicates and the card can be replaced with any sheet of paper.

2. The rules of forming the premises can be reversed. Thing outside the border of the paper is representing a universal or negative variable and the inside one is representing particular and positive variable.