Zhu Xi & the Cheng Brothers
The Synthesis of the Neo-Confucian Tradition

Cheng Yi
Zhu Xi
All things under Heaven can be understood by their principle. As there are things, there must be specific principles of their being. ... Due to the interaction of the two material forces [yin and yang] and the Five Phases, things vary as weak and strong in thousands of ways. ...
 What the sage follows, however, is the one principle. People must return to their original nature [which is one with principle]. [Sources of Chinese Tradition, 690]
The mind of each human being is one with the mind of Heaven and Earth. The principle of each thing is one with the principle of all things. … There is only one principle in the world. You may extend it over the four seas and it is everywhere true. It is the unchangeable principle that “can be laid before heaven and Earth” and is “tested by the experience of the three kings.” Therefore to be serious (reverent, jing) is to be serious with this principle. To be humane is to be humane according to this principle. And to be truthful is to be truthful to this principle. [Sources of Chinese Tradition, 690]
Fa-zang builds up from the interpenetration of multiple worlds to expound his view of the interconnectedness of multiple things within each world. He uses the gold lion example to illustrate that the whole phenomenal world, the Realm of Things, is like one single object, each part of which is inseparable from the other parts. Without any of the multiple parts of the lion, the whole lion cannot exist; without the whole lion, no part of the lion could possibly exist. By the same token, with any single thing lacking in the phenomenal world, the whole world would not exist; without the whole world, no single thing can exist. There is thus mutual entailment between the whole and its parts. This kind of view is now considered a form of holism, the thesis that any single item within a particular system is part of the whole system and cannot be considered independently of the whole. [An Introduction to Chinese Philosophy, 258]

What's so important about a unified theory?

The nature [i.e. the “principle” of a human being] comes from Heaven, whereas capacity comes from material-force. When material-force is clear, capacity is clear. On the other hand, when material-force is turbid, capacity is turbid. ... Human nature is universally good. In cases where there is evil it is because of one’s capacity. The nature is the same as principle, and principle is the same whether in the sage emperors Yao and Shun or in the common man in the street. Material-force, which may be either clear or turbid, is the source of capacity. Men endowed with clear material-force are wise, while those endowed with turbid material-force are stupid.
       Further Question: Can stupidity be changed?
       Answer: Yes. ... Since all have the same basic nature, who cannot be changed? Because they ruin and cast themselves away and are not willing to learn, people are unable to change. In principle, if they are willing to learn, they could change. [Sources of Chinese Tradition, 691]

Zhu Xi (Chu Hsi)

Zhu Xi’s understanding of the relationship between principle and material-force (a.k.a. “psychophysical stuff”) is clearly explained in the following passage by Daniel Gardner:
According to Chu, all things in the universe possessed principle, which as defined by him and the Ch’eng brothers before him was both the reason why a thing was as it was and the rule to which a thing should conform. In Chu’s view principle in the world was one, it simply had many manifestations. So although different things manifested it in different ways, the rule to which those things conformed was ultimately one, as was the reason those things were as they were. Perhaps “principle,” a translation that on its own has little meaning, should be understood as something like a blueprint or pattern for the cosmos, a blueprint or pattern that underlies everything and every affair in that cosmos. Man, too, naturally possessed principle. And in man this principle, Chu argued, was identical with the human nature (hsing) heaven had endowed in him at birth. As reason here would suggest, this human nature was in each and every person the same. And in every person it was morally good, constituted as it was of the four cardinal virtues, benevolence, righteousness, propriety, and wisdom, as Mencius earlier had argued.
But every thing — and thus every person — was also born with an endowment of psychophysical stuff. The quality as well as the quantity of the psychophysical stuff differed from one thing and one individual to another. Some psychophysical stuff was clearer than others, some more refined than others, some less dense than others. This endowment of psychophysical stuff gave each thing or person its peculiar form and individual characteristics. As to the relationship between principle and psychophysical stuff, Chu was very clear: “There has never been any psychophysical stuff without principle nor any principle without psychophysical stuff.” The two entities simply could not exist independently of each other: without principle the psychophysical stuff had no ontological reason for being, and without psychophysical stuff principle had nothing in which to inhere. [Chu Hsi: Learning to be a Sage, 49-50]
The Interdependence of
Li and Qi
Despite the interdependence of principle and psychophysical stuff (i.e. material-force), Zhu insists that there is some sense in which principle is “prior,” for one can imagine the “pattern” of the universe apart from its manifestation, whereas one can never imagine the manifest universe without the pattern through which it is manifest:
Question:  Which exists first, principle or material-force?
Answer:  Principle has never been separated from material-force. However, principle is above the realm of corporeality, whereas material-force is within the realm of corporeality. Hence when spoken of as being above or within the realm of corporeality, is there not a difference of priority and posteriority? Principle has no corporeal form, but material-force is coarse and contains impurities.
       Fundamentally, principle and material-force cannot be spoken of as prior or posterior. But if we must trace their origin, we are obliged to say that principle is prior. However, principle is not a separate entity. It exists right in material-force. Without material-force, principle would have nothing to adhere to. Material-force consists of the Five Phases of metal, wood, water, fire, and earth, while principle includes humaneness, rightness, ritual decorum, and wisdom. [Sources of Chinese Tradition, 699-700]
Although principle is identical in each and every “thing,” the diversity of the universe is explained by the suggestion that the material-force through which principle is manifest comes in many different forms, from the most dense (the earth) to the most rarefied (heaven). In the following passage, Zhu Xi explains the difference between humans and beasts; the point is that only humans begin with sufficiently clear material-force (manifest as human nature within the heart/mind) to realize the “moral” dimension of universal principle:

Nature is similar to water. If it flows through a clear channel, it remains clear; if it flows through a filthy channel, it becomes turbid. [Nature] that acquires clear and balanced psychophysical stuff will remain whole — this is what happens to man. [Nature] that acquires turbid and unbalanced psychophysical stuff will become obscured. This is what happens to beasts. Psychophysical stuff is both clear and turbid. Men acquire the clear stuff, beasts acquire the turbid stuff. Men, for the most part, are fundamentally clear and thus different from beasts. But there are also those who are turbid and so not very different from beasts. [Chu Hsi: Learning to be a Sage, 98]
After exerting himself for a long time, he will one day experience a breakthrough to integral comprehension. Then the qualities of all things, whether internal or external, refined or coarse, will all be apprehended and the mind, in its whole substance and great functioning, will all be clearly manifested. [Sources of Chinese Tradition, 729]