In Chinese philosophy, the School of Names and Mohism were particularly influential. The School of
Names focused on the use of language and on paradoxes. For example, Gongsun Long proposed the
white horse paradox, which defends the thesis that a white horse is not a horse. The school of Mohism
also acknowledged the importance of language for logic and tried to relate the ideas in these fields to the
realm of ethics.[197]
In India, the study of logic was primarily pursued by the schools of Nyaya, Buddhism, and Jainism. It
was not treated as a separate academic discipline and discussions of its topics usually happened in the
context of epistemology and theories of dialogue or argumentation.[198] In Nyaya, inference is understood
as a source of knowledge (pramā ṇ a). It follows the perception of an object and tries to arrive at
conclusions, for example, about the cause of this object.[199] A similar emphasis on the relation to
epistemology is also found in Buddhist and Jainist schools of logic, where inference is used to expand the
knowledge gained through other sources.[200] Some of the later theories of Nyaya, belonging to the
Navya-Nyāya school, resemble modern forms of logic, such as Gottlob Frege's distinction between sense
and reference and his definition of number.[201]
The syllogistic logic developed by Aristotle predominated in the West until the mid-19th century, when
interest in the foundations of mathematics stimulated the development of modern symbolic logic.[202]
Many see Gottlob Frege's Begriffsschrift as the birthplace of modern logic. Gottfried Wilhelm Leibniz's
idea of a universal formal language is often considered a forerunner. Other pioneers were George Boole,
who invented Boolean algebra as a mathematical system of logic, and Charles Peirce, who developed the
logic of relatives. Alfred North Whitehead and Bertrand Russell, in turn, condensed many of these
insights in their work Principia Mathematica. Modern logic introduced novel concepts, such as functions,
quantifiers, and relational predicates. A hallmark of modern symbolic logic is its use of formal language
to precisely codify its insights. In this regard, it departs from earlier logicians, who relied mainly on
natural language.[203] Of particular influence was the development of first-order logic, which is usually
treated as the standard system of modern logic.[204] Its analytical generality allowed the formalization of
mathematics and drove the investigation of set theory. It also made Alfred Tarski's approach to model
theory possible and provided the foundation of modern mathematical logic.[205]
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See also