HISTORY OF LOGIC

Several ancient civilizations have employed intricate systems of reasoning and asked questions about logic or propounded logical paradoxes. In India, the Nasadiya Sukta of the Rigveda (RV 10.129) contains ontological speculation in terms of various logical divisions that were later recast formally as the four circles of catuskoti: "A", "not A", "A and not A", and "not A and not not A".^[8] The Chinese philosopher Gongsun Long (ca. 325–250 BC) proposed the paradox "One and one cannot become two, since neither becomes two."^[9] In China, the tradition of scholarly investigation into logic, however, was repressed by the Qin dynasty following the legalist philosophy of Han Feizi.

The earliest sustained work on the subject of logic which has survived was that of Aristotle,^[10] although the Chinese 'School of Names' is recorded as having examined logical puzzles such as "A White Horse is not a Horse" as early as the fifth century BCE.^[11] The formally sophisticated treatment of modern logic descends from the Greek tradition, the latter mainly being informed from the transmission of Aristotelian logic.

Logic in Islamic philosophy also contributed to the development of modern logic, which included the development of "Avicennian logic" as an alternative to Aristotelian logic. Avicenna's system of logic was responsible for the introduction of hypothetical syllogism,^[12] temporal modal logic,^[13][14] and inductive logic.^[15][16] The rise of the Asharite school, however, limited original work on logic in Islamic philosophy, though it did continue into the 15th century and had a significant influence on European logic during the Renaissance.

In India, innovations in the scholastic school, called Nyaya, continued from ancient times into the early 18th century, though it did not survive long into the colonial period. In the 20th century, Western philosophers like Stanislaw Schayer and Klaus Glashoff have tried to explore certain aspects of the Indian tradition of logic.

During the later medieval period, major efforts were made to show that Aristotle's ideas were compatible with Christian faith. During the later period of the Middle Ages, logic became a main focus of philosophers, who would engage in critical logical analyses of philosophical arguments.

In the late 19th and early 20th centuries, there were many attempts by mathematicians such as David Hilbert and Bertrand Russell to express logic mathematically. Today mathematical logic is an important area of mathematics.