History of logic

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The history of logic is the study of the development of the science of valid inference (logic). While many cultures have employed intricate systems of reasoning, and logical methods are evident in all human thought, an explicit analysis of the principles of reasoning was developed only in three traditions: those of China, India, and Greece. Of these, only the treatment of logic descending from the Greek tradition, particularly Aristotelian logic, found wide application and acceptance in science and mathematics. Logic was known as dialectic or analytic in Ancient Greece.

Aristotle's logic was further developed by Islamic and then medieval European logicians, reaching a high point in the mid-fourteenth century. The period between the fourteenth century and the beginning of the nineteenth century was largely one of decline and neglect, and is generally regarded as barren by historians of logic.[1]

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.[2]

Progress in mathematical logic in the first few decades of the twentieth century, particularly arising from the work of Gödel and Tarski, had a significant impact on analytic philosophy and philosophical logic, particularly from the 1950s onwards, in subjects such as modal logic, temporal logic, deontic logic, and relevance logic.

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