Cheng–Zhu school

The Cheng–Zhu school, 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. It is also referred to as the Rationalistic School.

Metaphysics
Zhu Xi's formulation of the Neo-Confucian world view is as follows. He believed that the Dao of Tian  is expressed in principle or li, but that it is sheathed in matter or qi. In this, his system is based on Buddhist systems of the time that divided things into principle (again, li), and shi.

In contrast to Buddhists and Daoists, 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.

Human nature and rationality
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.

Different Neo-Confucians had differing ideas for how to do so. Zhu Xi believed in gewu, the 'investigation of things', essentially an academic form of observational science, based on the idea that li lies within the world.