Combinatoric Logic Game of Things

Armahedi Mahzar (c) 2015

In my sequence  of blogs I have presented variety games of things with different rules of arranging things, but single rule of disposing pair of things, all simulates the proving of valid categorical syllogisms in the table of Leibniz. In fact, all games that being discussed can simulate the proof of hypothetical and disjunctive syllogisms of the Stoic. It even can prove all tautologies of the Boolean algebra of logic.

The simplest game of logic is purely combinatoric that simulating Ploucquet method of proving syllogism which has two premises. The premises consist  of two state letters. The conclusion can be derived by disposing paired letters of similar sound but different case in the combination of premises.  The capital letters are representing universal  subject and negative predicate. The lower case letters are representing particular subject or positive predicate they represent.

Let me show you how can we play the general combinatoric game with tin soldiers used as representation of concepts or variables and a sheet of paper to differentiate the universality / negativity or particularity / positivity of the concepts by positioning the tin soldiers outside or inside the paper borders.  This convention is the reversal of the convention held in my last blog. But the new convention seems more natural.

Categorical proposition of Aristoteles

In Ploucqetian combinatoric “all a is b” is represented by Ab, “no a is b”  is represented by AB, “ some a are b” is represented by ab and “some a are not b” is represented by aB.  In the tin soldiers combinatorics game of logic They represented by the following picture

Proving Aristotlean Syllogism Validity

The simulation of the proof of the validity of Barbara syllogism by playing the tin soldiers game is shown by the following picture:

Proving Stoic Syllogism validity

The game can be used to prove the validity of the hypothetical and disjunctive syllogisms of the Stoic logicians: modus ponens, modus tollens and modus tollendo ponens.

Afternotes

The game In this blog is based on the Sommersian arithmologic. However more complex games can also be created based on Boolean and Peircean arithmologic.  As a tool such games is too complex, however  it shows that all arithmologic systems can be simulated with combinatorics games of thing.