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The Cheng-Zhu school, known in Chinese as Chéngzhūlĭxué 程朱理學, is one of the major philosophical schools of Neo-Confucianism, based on the ideas of the Neo-Confucian philosophers Cheng Yi, Cheng Hao, and Zhu Xi.
Zhu Xi's formulation of the Neo-Confucian world view is as follows. He believed that the Tao (Chinese: 道; pinyin: dào; literally "way") of Tian (Chinese: 天; pinyin: tiān; literally "heaven") is expressed in principle or li (Chinese: 理; pinyin: lǐ), but that it is sheathed in matter or qi (Chinese: 氣; pinyin: qì). In this, his system is based on Buddhist systems of the time that divided things into principle (again, li), and shi (Chinese: 事; pinyin: shì). In the Neo-Confucian formulation, li in itself is pure and almost-perfect, but with the addition of qi, base emotions and conflicts arise. Human nature is originally good, the Neo-Confucians argued (following Mencius), but not pure unless action is taken to purify it. The imperative is then to purify one's li. However, in contrast to Buddhists and Taoists, neo-Confucians did not believe in an external world unconnected with the world of matter. In addition, Neo-Confucians in general rejected the idea of reincarnation and the associated idea of karma.
Different Neo-Confucians had differing ideas for how to do so. Zhu Xi believed in gewu (Chinese: 格物; pinyin: géwù), the Investigation of Things, essentially an academic form of observational science, based on the idea that li lies within the world.
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