The meaning of "a gentleman is cautious in his independence" is that when a person is alone, unsupervised, and has many possibilities to do bad things without being discovered, he can still firmly believe in his moral beliefs and act consciously. Act according to certain moral principles without doing anything bad.
Source: "Book of Rites·The Doctrine of the Mean"——Warring States Period·Zisi
Destiny is called nature, willfulness is called Tao, and cultivating Tao is called teaching. The Tao cannot be separated for a moment; it can be separated, but it is not the Tao. Therefore, a gentleman should be cautious about what he does not see and be afraid of what he does not hear. Don't see what's hidden, don't show what's subtle, so a gentleman should be cautious about being alone.
Translation The most fundamental principles given by God that govern the operation of all things are called laws. Acting in compliance with the laws is called correct principles. Practicing correct principles is education. Any correct principle cannot be deviated from for even a moment; if it can be deviated even slightly without guilt, it is not a truly correct principle.
Therefore, people who understand the Way still maintain a state of caution and fear at all times in places where they are not heard or seen, and do not allow the most subtle behaviors that violate correct principles to appear and take effect. Therefore, they practice to the ultimate level. A good gentleman will be very careful about his every thought and word.
Extended information
1. The creative background of "The Book of Rites·The Doctrine of the Mean"
"The Doctrine of the Mean" comes from the "Book of Rites" and was originally the fortieth chapter of the "Book of Rites" Chapter 31 of nine. "Book of Rites" was originally called "Book of Rites of Xiao Dai", also known as "Ji of Xiao Dai". It was compiled by Dai Sheng, a man of Emperor Xuan of the Han Dynasty, based on a group of anonymous Confucian works left over from history.
Before the Song Dynasty, scholars all believed that "The Doctrine of the Mean" was written by Zisi during the Spring and Autumn Period and the Warring States Period. Sima Qian's "Historical Records: The Family of Confucius": "Zisi wrote "The Doctrine of the Mean"." Li Ao's "Collection of Li Wengong·Fu Xing Shu": "Ziusi wrote forty-seven chapters of "The Doctrine of the Mean" and passed it down to Meng Ke." Zhu Xi's "The Doctrine of the Mean" Chapter · Preface: "Why was the Doctrine of the Mean written? Zisi wrote it because he was worried about the loss of Taoism."
Since the Song Dynasty, some scholars have argued that "The Doctrine of the Mean" is the work of Zisi and the Qin and Han Dynasties. It is composed of miscellaneous accounts by contemporary Confucian scholars. Ouyang Xiu's "Asking Jinshi Strategies": "Question: The books on ritual and music are scattered, and they are mixed with the theories of Confucianism. Only "The Doctrine of the Mean" comes from Zisi. Zisi is a descendant of the saints, so what he preaches should be true, and Why is his statement different from that of a saint?"
The above two views have their own basis. The current academic circles generally believe that "The Doctrine of the Mean" was written by Zisi and many of his disciples.
2. Appreciation of "The Book of Rites·The Doctrine of the Mean"
"The Doctrine of the Mean" is a prose that discusses the cultivation of Confucian human nature. It was originally the 31st chapter of the "Book of Rites" and is said to be Zisi's work is a classic treatise on Confucianism. Cheng Hao and Cheng Yi of the Northern Song Dynasty strongly respected it, and Zhu Xi of the Southern Song Dynasty wrote the "Commentary on the Doctrine of the Mean", which was eventually called the "Four Books" together with "The Great Learning", "The Analects of Confucius" and "Mencius".
After the Song and Yuan Dynasties, "The Doctrine of the Mean" became an official school textbook and a required reading for imperial examinations, which had a great impact on ancient Chinese education. "The Doctrine of the Mean" puts forward the "Five Ways", "Three Virtues", "Cultivation with caution", "Sincerity and perfection" and other contents, which have an important impact on how to deal with people and cultivate human nature.