Combinatoric Logic Game of Cards

Combinatoric Logic Game of Cards

Armahedi Mahzar (c) 2015

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

In the following it will be shown that we can also make the game arranging and disposing colorful cards with only two orientation. The secret is the fact that we can replace the changing the marble positions to represent the opposite concept in the last gamewith the changing of the card orientation in the new game.

Fundamental Categorical Proposition of Aristotle

 ed the card , the its opposite NOT a is represented by the horizontally oriented card  .

If the subject is represented by a red card and predicate b represented by green card , then the fundamental categorical statement of Aristotle is represented by pairs of cards  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 card pairs which represent both premises of a syllogism
2. disposing the pair of same colored cards with different orientation
3. putting the card which represent the subject of the second premise as the card 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 opposite orientated card of the same color  in the  Leibniz’s  table below:

End notes

1. Apparently, the game is very simple using colored cards that it can be taught to kindergartners. The game can also be seen as a Sommersian arithmologic game.
2. The cards can be replaced with anything that have duplicates with the help of one sheet of paper.