Historically logic was developed during ancient times in China, India and Greece.
In China logic was unique due to the country’s issues of repression and abandonment compared to the strong ancient adoption and continued development of the study of logic in Europe, India, and the Islamic world.
Classical China’s semantic theory is a bridge discipline between linguistics and philosophy, with no logic. But the Mohist school of Chinese philosophy offered an approach to logic, stressing rhetorical analogies over mathematical reasoning, based on the methods of drawing distinctions between kinds of things.
Out of this came the Logicians, another school that credited by some scholars for their early investigation of formal logic.
Logic was revived in the mid-nineteenth century, at the beginning of a revolutionary period when the subject developed into a rigorous and formalistic discipline whose exemplar was the exact method of proof used in mathematics. The development of the modern so-called “symbolic” or “mathematical” logic during this period is the most significant in the two-thousand-year history of logic, and is arguably one of the most important and remarkable events in human intellectual history.
Greek Aristotelian logic was widely accepted in the studies of mathematics and science. Further developed by Christian and Islamic philosophers during the Middle Ages, Aristotle’s logic reached its peak during the mid-fourteenth century, and his theory of the syllogism had a major influence on the history of Western thought.
During this same period modern “symbolic” or “mathematical” logic came about and was the most significant of the 2,000 year history of logic. In actuality, it has been touted as the most important events in human intellectual history.
There was progress in mathematical logic during the first few decades of the twentieth century. This made a significant impact on analytic philosophy and philosophical logic, during and after the 1950s. We can give credit to the work of Gödel and Tarski for this.