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INFORMATION TECHNOLOGY AND ANCIENT GREEK LOGIC

By Demosthenes Kyriazis.

 

 

"Logic is the science the purpose of which is the study of correct intellect; the laws of cognitive processes, the principles of validity of arguments, the methods of inferring conclusions, and the control of their correctness." [1]

From the above definition it follows that Logic is the basis for the development of any other science. Who and when did they develop the science of Logic? What is the cradle of Logic?

The answer to the above questions is: Cradle of Logic is the Ancient Greece. The science of Logic was born in the same place and in the same time that was born, Democracy and an unprecedented, in principles, ideas and humanistic conquests, civilization.

In Ancient Greek Logic, the basic tool for "correct intellect" is the reasoning, like those we once learned in Gymnasium, eg:

- All dogs are animals

 - Jack is a dog

 ..............................

- Conclusion / decision: Jack is an animal.

These reasoning, in which the conclusion taking process moves from the general to the particular, are called productive reasoning. On the contrary, those in whom the process moves from the particular to the general are called inductive reasoning. Note that, this fundamental and clear distinction was made by Aristotle, two and a half thousand years ago.

It is not in our intentions, nor in our capabilities, to say more about the Ancient Greek Logic and Logic developed in the past two and a half thousand years. Our intention is to say our view on the relationship between the Ancient Greek Logic and the Information Technology.

 

From the logic of Ancient Greeks to the logic of Algebra of Boole

Over the centuries the simple, understandable and transparent reasoning of Ancient Greeks were degenerated. The reasoning from a 100% logical process that led to knowledge with vehicle the "correct intellect", became an emotional process that, with the vehicle the "right feelings", led to faith; to faith in all kind of power establishment; of political, economic, spiritual, religious power. So the logic changed. From the logic of knowledge, it became the «logic" of faith.  

In the new logic, the simple and transparent reasoning of ancient Greek logic are now despised and rejected. On the contrary, the pompous, complex and opaque reasoning are appreciated and highly accepted.

In order to free the reasoning from opacity and verbalization and to make them a tool of knowledge, the German Mathematician, Physicist and Philosopher Leibnitz (1646-1716) attempted to present the elements of ancient Greek  thoughts (hypotheses - conclusion) with symbols and transform the reasoning into a mathematical management of symbols.

Leibnitz did not succeed in realizing his vision. But it left us an important legacy. This is his vision.

Attempts to transform ancient Greek Logic into mathematical management were also undertaken by others, such as Morgan (1806-1876).  

But he who completed these efforts was the English Mathematician and scholar of the ancient Greek Philosophers George Boole 1814 - 1864.

Boole managed to create a complete mathematical tool for conclusions and decisions making, called the Algebra of Boole.  A basic feature of his philosophy is - in our view - the return to the simple, understandable and transparent reasoning of Ancient Greek Logic.

Boole in his algebra has officially assigned only three logical operations, only three basic reasoning: (1) the logical addition or OR operation, (2) the logical multiplication or AND operation and (3) the logical refusal or NOR operation. Every other logical presentation was a set of these three basic operations, of these three basic reasoning.

In the Algebra of the Boole, the variables (the unknowns we learned at the Algebra of the Gymnasium) can only get two prices;  1 (the right) and 0 (the wrong). So, all actions of the Boole algebra were much easier to do in the binary system, because it has only two digits. The  1 and 0. Let us remember that the decimal system has ten digits of 0.1, 2, ... 9.

The binary system, due to its small number of digits, is the simplest but also the most “chatter” (great multiplicity) system. His philosophy reminds a bit of the Golden Rule of the levers we once learned in Gymnasium: "Whatever we gain in strength we lose it in road length." And in the Boole’s Algebra happens something similar:  “What we gain in simplicity we lose .... in chatter". 

 The use of the Boole’s Algebra from the people themselves was of no practical interest. People arrived at conclusions and decisions much faster in their own way, than with the methodical, transparent, but the chatter and tedious way of Boole

Until 1938 the Boole algebra had a theoretical but not a practical value.

In 1938, an American student of MIT, Claude Shannon (1916 - 2001), had the amazing idea to use the Boole algebra not in mans’ affairs but to switches of electrical circuits.

The use of the switches became possible due to the simplicity of the binary system, which, as mentioned, is mathematical management, of two digits only. 1 and 0. As we all know, switches have only two states: 1 (switch closed) and 0 (switch open).

The simple but “chatter” actions of Boole’s algebra could now be carried out from technical elements that had no intelligence, but they could work fast, without time limits, without getting tired and hurt.

This idea of Shannon gave great practical value to the Algebra of Boole and led to today's Science and Technology of Information. [2]

 

Information Technology and Democracy

The relationship between Information / Digital Technology and Democracy at the practical level is well known. It ensures excellent and accessible communication conditions for all people; rich and poor, of high and elementary education. At the theoretical level however, this relationship is not as obvious. But we can approach it from the following two facts and historical conclusions:

a. Democracy functioned in countries where there was a sensible mentality and alphabetical writing. On the contrary, in countries where there was dogmatic mentality and symbolic writing, monarchic / theocratic states functioned. (see Citizens’ intelligence and political regimes  http://www.dd-democracy.gr/article.asp?Id=160  .  Digital technology, therefore, as a tool for the development and service of logic is a vehicle for the development of Democracy too

.b. The philosophy of digital technology is the same as the philosophy of alphabetical scripts, with an extra great advantage. The "digital alphabet" uses only two letters (1 and 0) and has a worldwide usage. The other alphabets have more than 23 letters and are limited to a group of people.

This view therefore that information/digital technology can become the vehicle for the renaissance of Democracy is not only a humanistic and noble idea; it is a rational and practicable idea.

 

………………………………………………………………………………………………………………………..

[1] Dictionary of the Modern Greek Language G. Babiniotis.

[2] In the beginning for the execution of logical operations, switches with moving elements (relays) were used; later they were used "static switches" (switches without moving elements) from electronic bulbs at the beginning and later by transistors and integrated circuits

 

 

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