BLACK AND WHITE LOGIC OF THE
The Greek philosopher Aristotle (384-322 BC) developed the principles of logical thinking at the School of Athens in Greece. This is known as the Logic of the West. In order to foster clarity and distinction in logical thinking, Aristotle formulated two axiomatic principles as its sine qua non. The first one was the Principle of Excluded Middle (PEM), which requires that every claim must be either “True” or “False”, with no other options existing. In Latin, this principle is called, tertium non datur, which literally means, ‘a third is not given’. The claim must be either “Black” or “White” and never “Grey”! The grey regions that could lie between the black and white extreme points are conveniently excluded, in the interest of clarity and distinction of thought. Thus Aristotle defines a binary logic, with just two truth values, “True” or “False”. There is no clear justification for why should it be so. It is rather taken for granted in the interest of avoiding fuzziness in thinking. In fact, the fast growth of the Western science and technology owes much to this single axiom of the underlying logic.
The second axiom of Western logic is the Principle of Non- Contradiction (PNC). According to it, a statement can either be “True” or “False”, and not both at the same time. Here “True” means 100% true and “False” means 100% false. “True” and “False” cannot coexist. The Persian philosopher Ibn Sina alias Avicenna (c.980 -1037), logician of the Islamic Golden Age once declared: “Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned.”
These axioms made Western logic compatible to critical thinking. The analysis of the nature in science, technology and even religion was rendered rigorous and without an iota of ambiguity surrounding it. The Aristotelian logic was further developed by idealists like Rene Descartes (1596- 1650) and logical empiricists like John Locke (1632–1704), and a host of other rationalists, who initiated Renaissance in the West. The logic of the West is also known as Boolean logic after George Boole (1815–1864), the English mathematician and logician. Boole is best known as the author of The Laws of Thought (1854), which describes the fundamentals of Boolean algebra. Binary logic finds application in all spheres of life including mathematical, judicial, scientific and religious discourses of the day and is considered one of the important intellectual accomplishments of Western culture.
WEAKNESS OF THE BINARY LOGIC
The inherent potential of binary logic to polarize mind is enormous. Uncompromising personal and political stands resulting from conflicting ideologies could easily turn pharisaic and arrogant, giving birth to polemics of hate philosophies. Binary logic inculcated intolerance into the philosophical, ideological or religious discourses, one excommunicating the other! Binary logic also paved the way for the emergence of absolute truths, which could only be fully endorsed or fully rejected. It practically annulled possibilities of dialogues and reconciliation of opposite views. It sowed lot of hatred on the face of earth!
However, imaginative minds soon identified situations where binary logic cannot be applied. A host of philosophical paradoxes revealed the folly of binary logic. The Liar’s Paradox (Eubulides of Miletus) was an important one among them. Consider, for example, the statement: “This statement is false.” It is an example for a Liar’s Paradox. If the statement is true, then it is indeed false. But if it is false, well, then it is true. The statement seems to be both true and false at the same time, which is vehemently opposed by the Principle of Non-Contradiction! Do these paradoxes shoot down Aristotelian binary logic? By no means! However, they posited the incompleteness of Aristotelian logic and highlighted the need to transcend the inherent dualism of the Western logic.
Modern science has further exposed the weakness of binary logic. The Theory of Relativity due to Albert Einstein necessitated a shift from absolute description of the Space and Time towards a relativist Space-Time Continuum. Emergence of Quantum Mechanics necessitated description of the subatomic world in terms of Probability Theory! Subatomic matter could be either particle or wave at the same time, depending on the observation made over it. A concept even Einstein could not easily digest as he quipped: “God does not play dice!”
The inherent incompleteness of the binary logic of Aristotle and requirements of the modern science called for a paradigm shift in modern logic: A shift from blackand- white logic to grey logic, a shift from bivalent logic to multivalent logic, a shift from absolute logic to a relative logic, which could accommodate the uncertainties and probabilities of the phenomena. Such logic was invented ahead of Aristotelian logic, during the times of Lao-tze and Sri Buddha, the so called Logic of the East.
THE GREY LOGIC OF THE EAST
This logic propagated by Sri Buddha is called “catuskoti”, which means “four corners”. According to this concept, any statement has four possibilities attached to it.
1) It could be “True”,
2) It could be “False”,
3) It could be “Both True and False” or
4) It could be neither “Neither True nor False”.
A similar concept is described in Chinese Philosophy (Taoism) with the help of Yin-Yang symbol. Yin and Yang are parts of the Oneness that is also equated with the Tao, the Chinese Concept of the path, the religion. Yin is considered as negative/passive/female principle in nature and Yang, positive/active/male principle in nature. Yin-Yang describes how seemingly opposite or contrary forces may actually be complementary, interconnected and interdependent in the natural world, and how they may give rise to each other as they interrelate to one another.
The Buddhist monk Nagarjuna presents a fifth dimension to the Truth Values. This is encountered when one handles statements about the ultimate reality. This reality may be experienced directly in meditation, which one may not be in a position to describe, something which could be called “Ineffable”. Only silence (Mauna) is the language in such contexts. They are simply “indescribable” or “unspeakable”!
Eastern logic is poly-valent. It bypasses or surpasses both the Principle of Excluded Middle, and the Principle of Non-Contradiction. It is also open to the Logic of the Ineffable. It is a grey logic, to which Aristotelian logic is only an approximation.
FUZZY LOGIC OF MODERN TIMES
In recent times, Lotfi Aliasker Zadeh, an Iranian origin professor at the University of California, pioneered fresh studies in fuzzy logic. He initiated the concepts of fuzzy mathematics. Fuzzy logic has already built inroads to various disciplines including science and technology. Here the “Truth Values” are not restricted to “True” and “False”, or “1” and “0”. Fuzzy logic allows for shades of grey. Truth values are made compatible and relative to the variations happening to the ambient. In this way mathematical description of the world takes an analogical path than digital one. It has once again become compatible to the working pattern of human brain, which operates in a fuzzy manner based on multi-valued inputs.
The surge of changes occurring in the mathematical arena gets reflected on the technological front too. In this paradigm shift in technology, as expected, the nations of the East take lead. Japanese engineers have successfully developed a large number of commercial products based on fuzzy logic assisted by smart technologies.
The first successful application of fuzzy logic was on the high-speed train in Sendai, in which fuzzy logic improved the economy, comfort, and precision of the ride. Fuzzy controls were applied to washing machines to gauge each load to determine how much soap to use, and to air conditioning to constantly adjust the cooling strength based on room temperature. Fuzzy controlled microwave ovens, camcorders, carburetors, train controllers, nuclear reactor and hundreds of other smart products followed. It took no time for fuzzy controls to become state-of-the art technology that gels well with artificial intelligence.
Fuzziness has turned the rule of the day! Creative minds shall acknowledge the fuzziness of contemporary logic, accommodate to the spectrum of truth values, appreciate the shades of grey and appropriate the absolute Truth bit per bit with extreme humility. That is an attitude, modern enough!