History of logic

While many cultures employ intricate systems of reasoning, it is generally agreed that logic as an explicit analysis of the methods of reasoning was independently developed by only three traditions: China, India and Greece. Although exact dates are uncertain, especially in the case of India, it is possible that logic emerged in all three societies in the 4th. Century BCE.

In China, a contemporary of Confucius, Mo Zi, "Master Mo", is credited with founding the Mohist school, whose canons dealt with issues relating to valid inference and the conditions of correct conclusions. In particular, one of the schools that grew out of Mohism, the Logicians, are credited by some scholars for their early investigation of formal logic. Unfortunately, due to the harsh rule of Legalism in the subsequent Qin Dynasty, this line of investigation disappeared in China until the introduction of Indian philosophy by Buddhists.

The "Nyayasutras" of Gautama represent the basic texts of one of the six orthodox schools of Indian philosophy. This realist, one might say materialist, school worked out a rigid five-member schema of inference involving an initial premise, a reason, an example, an application and a conclusion. The idealist Buddhist philosophy became the chief opponent to the Naiyayikas. Nagarjuna, the founder of the Madhyamika "Middle Way" developed an analysis known as the "catuskoti" or tetralemma. This four-cornered argumentation systematically examined and rejected the affirmation of a proposition, its denial, the joint affirmation and denial, and finally, the rejection of its affirmation and denial. But it was with Dignaga and his successor Dharmakirti that Buddhist logic reached its height. Their analysis centered on the definition of necessary logical entailment, "vyapti", also known as invariable concomittance or pervasion. To this end a doctrine known as "apoha" or differentiation was developed. This involved what might be called inclusion and exclusion of defining properties. The difficulties involved in this enterprise, in part, stimulated the neo-scholastic school of Navya-Nyaya.

In Greece, Aristotle's collection of works known as the "Organon" or instrument almost ex nihilo created the discipline known as logic. Aristotle's examination of the syllogism bears interesting comparison with the Indian schema of inference and the less rigid Chinese discussion. Through Latin in Western Europe, and disparate languages more to the East, such as Arabic, Armenian and Georgian, the Aristotelian tradition was considered to pre-eminently codify the laws of reasoning. It was only in the Nineteenth Century that acquaintance with the classical literature of India and deeper knowledge of China brought about a change in this viewpoint.