My story of Logic.

My Story of Logic
Armahedi Mahzar (c) 2015

When I was a secondary school student, my uncle always said that I was illogical in our discussions. While I was in high school, I found a book for introductory logic in my uncle's library. That's because my uncle is a law student. Reading this book I have a perception of logic as branch of philosophy like ethics and aesthetics. So it is just a meaningful strings of words.

When I was a physics student in ITB, in the university library I found out that Aristotle , the founder of the science of logic describe his science all in words and some times with single alphabet. So I really could not comprehend it. However, when I read logical positivist books, I knew that logic is now formulated in  symbols like propositional calculus in Russell -Whitehead   book Principia Mathematica. I read it, still I could not comprehend it.

In my student years in ITB my other uncle came from United States brought a wonderful game WFF'N PROOF, but I could not play it and I could not comprehend the goal and the rules of game. Later in the internet, I knew that in the past Lewis Carroll , the famous author of Alice in Wonderland,  had designed another board game of logic, but, as for me, it is also hard to understand. :(

Later, when I started lecturing physics in ITB, I learned to program the mainframe computer in Fortran as the programming language. There I knew that beside NOT, AND and OR there is another logical operation called IF THEN. I knew then, that computers operation is based on logical algebra called Boolean algebra which is very easy to be studied because its arithmetic base is only involving two numbers: 1 and 0.

When I read George Boole original book, it is very difficult book to be read especially when he related his mathematically formulated logic to the verbally described syllogisms of Aristotle. However when I read George Spencer-Brown book, which is recommended by Bertrand Russell "Not since Euclid's Elements have we seen anything like it", in his appendix I knew that the 24 Aristotle-Leibniz syllogisms can be proved easily with his method. However I can not comprehend his strange symbolism using cross and void as fundamental operation and constant.

When I retired, I can access the internet through the campus computer and I can download a book Laws of Form by Louis Kauffman  . In this book I understood that the primary algebra in GSB book is nothing but a simplified axiomatization of Boolean algebra. But I am not interested in logic until I have found another logic operation XOR in the formulation of imaginary units of 16 dimensional number called sedenion.

That's why after 10 years studied the hyperdimensional numbers in the hypernumber mailing list as a class in the internet as a cyber-university, five years ago I joined another class lawsofform@yahoogroups.com. So I start my quest to simplify the axiomatization of Boolean algebra until finally found the most simple axiomatization using easy arithmetical identities as inference rules. I called the system as arithmologic.

Unfortunately, there are no respond to my discovery. So I was just continuing to report my journey in the Boolean subspace of the mathematical Platonic space of numbers and forms in my blogs. The surprise is that finally I discovered the game of things as the simulation of the algebra of logic that it is so simple so it can be taught to a kindergartener.

Fortunately it was reponded by me fellow student in hypercomplex mailing list that I had left five years ago. So to discuss more seriously my logical discoveries in new mailing list that I call holologics@yahoogroups.com. If you are also interested in the topic, please join me in my new new yahoogroups which try to discuss logic in wider base than binary values and its representations in formulas, diagrams, games, poems and rythms.

Thanks for your attentions.
Arma