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Why does the CPC want to remove the expression that the President and Vice-President of the People's Republic of China "shall serve no more than two consecutive terms" from the country's Constitution?

Why is China lifting the two-term limit for Xi? The answer can be found by reading the amendment itself (and remembering a little history):
1. In the seventh paragraph of the Preamble to the Constitution, "the guidance of Marxism-Leninism, Mao Zedong Thought, Deng Xiaoping Theory and the important thought of Three Represents" is amended to read "the guidance of Marxism-Leninism, Mao Zedong Thought, Deng Xiaoping Theory, the important thought of Three Represents, the Scientific Outlook on Development, and the Xi Jinping Thought on Socialism with Chinese Characteristics for a New Era"; "improve the socialist legal system" is amended to read "improve the socialist rule of law"; before "work hard and self-reliantly" is inserted "apply a new vision of development"; and "promote the coordinated development of the material, political and spiritual civilizations, to turn China into a socialist country that is prosperous, powerful, democratic and culturally advanced" is amended to read "promote the coordinated development of the material, political, spiritual, social and ecological civilizations, to turn China into a strong modern socialist country that is prosperous, democratic, culturally advanced, harmonious, and beautiful, and to realize the great rejuvenation for the Chinese nation." This paragraph is accordingly amended to read: "The victory in China's New-Democratic Revolution and the successes in its socialist cause have been achieved by the Chinese people of all nationalities, under the leadership of the Communist Party of China and the guidance of Marxism-Leninism and Mao Zedong Thought, by upholding truth, correcting errors and surmounting numerous difficulties and hardships. China will be in the primary stage of socialism for a long time to come. The basic task of the nation is to concentrate its effort on socialist modernization along the road of Chinese-style socialism. Under the leadership of the Communist Party of China and the guidance of Marxism-Leninism, Mao Zedong Thought, Deng Xiaoping Theory, the important thought of Three Represents, the Scientific Outlook on Development, and the Xi Jinping Thought on Socialism with Chinese Characteristics for a New Era, the Chinese people of all nationalities will continue to adhere to the people's democratic dictatorship and the socialist road, persevere in reform and opening to the outside world, steadily improve socialist institutions, develop the socialist market economy, develop socialist democracy, improve the socialist rule of law, apply a new vision of development, and work hard and self-reliantly to modernize the country's industry, agriculture, national defense and science and technology step by step and promote the coordinated development of the material, political, spiritual, social and ecological civilizations, to turn China into a strong modern socialist country that is prosperous, democratic, culturally advanced, harmonious, and beautiful, and to realize the great rejuvenation for the Chinese nation."

[This article, among other changes, adds Presidents Hu Jintao's and Xi Jinping's political ideologies to the Preamble; replaces "legal system" (法制) with "rule of law" (法治; which is effectively rule bylaw, one could argue); and modifies the goal of the Chinese people's endeavors in accordance with the phrase used in Xi's report to the Party's 19th Congress.] [NPC Observer]
A little history: In 1980, Deng Xiaoping challenged China to provide a basic xiaokang society by 2020, 'a society in which no one is poor and everyone receives an education, has paid employment, more than enough food and clothing, access to medical services, old-age support, a home and a comfortable life'.

That goal will be 100% achieved in 2020, so it's time to set new goals that will take China in the direction Mao set for it: a harmonious dàtóng society*. Since, as Mao observed, it will probably require 100 years to reach dàtóng and since Reform and Opening has achieved its purpose, it's time to set China back on the Communist road again. That is, after all, the overall job of the Communist Party! Duh!

The only people who will be surprised by Xi's return to (more) Communism is those who thought that Reform and Opening represented China's capitulation to Capitalism, the Western media and Western Chinese 'experts'. The Chinese people will not be. 90% of them greatly enjoyed their earlier experiments with Communism, despite their problems and shortcomings. Today, 75% of them feel nostalgic about the Cultural Revolution and President Xi called it 'a dream that could not be realized at the time'.

Why could not the dream of the Cultural Revolution be realized in the 1960s? Because the West placed China under crushing embargoes and constantly threatened it with nuclear attacks, so Deng decided to get strong before permitting any more communist progress - for which he was much criticized by Maoists, though he was probably correct (the USA only stopped bombing China in 1989).

2021 will begin a new era, in which China is strong enough to do whatever it chooses so Xi is responsible for coming up with his own thought on Socialism with Chinese Characteristics for the New Era.

He will fill in the details on June 1, 2021, the centenary of Mao's founding of the CCP but Xi told the 19th Party Plenum in 2017:
  1. China's GINI under Mao was the best in the world but, as Deng warned, some grew richer than others during Reform and Opening and China became almost as unequal as the USA. So, until 2039, we must devote ourselves to re-creating a society in which wealth and income are so equitably distributed that the world will envy us.
  2. Once our GINI is fixed, until by 2049, we must complete the job of making China, once again, the envy of the world: the richest, most beautiful, most powerful, most harmonious society on earth: a prosperous, modern, Socialist society.
Since Xi is the architect of this program and since his first term was so successful, it makes sense for him to stay for a third term, just as it did for America's greatest President, Franklin Delano Roosevelt.
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* In the early twentieth century, the great Chinese thinker and reformer Kang Youwei wrote a book entitled Dàtóng shu (Book on the Great Community) in which he advanced an original and radical interpretation of datong, drawing mainly on both Liyun and another of the Confucian classics - the Gongyang Commentary to the Spring and Autumn Annals, which propounds a theory of progress in human history from the Age of Disorder to the Age of Ascending Peace and finally to the Age of Universal Peace, the idea of the common good in traditional Chinese social and political philosophy. The Chinese Communist Party's current ideology, including the "preliminary stage of socialism" and the "xiaokang society," are best understood in light of the concept of "datong" (Mao constantly advocated datong).

Datong is where the Great Way prevails. It is usually interpreted to refer to a Golden Age in prehistoric times, that the ideal society that has subsequently declined. In the datong society "the world was shared by all alike. The worthy and the able were promoted to office and men practiced good faith and lived in affection. Therefore they did not regard as parents only their own parents, or as sons only their own sons."

Although this has never been officially recognized, there is in fact a surprising degree of convergence between some important ingredients of Kang Youwei's datong thought and the official ideology currently propagated by the Chinese Communist Party. According to this ideology, the Marxist vision of the communist society is still the highest ideal pursued by the Party and the Chinese people. However, this ideal can only be realized after socialist society has reached a high level of development. "The development and perfection of socialism is a long historical process." China is, and will remain for a long time, in the "preliminary stage of socialism," because China, as an "economically and culturally backward" nation, needs to undergo "socialist modernization." The theory of the preliminary stage of socialism implies that full socialism cannot be practiced yet, and China may legitimately borrow capitalist techniques from the West. Not all means of production will be socialized and subject to public ownership, and there will still be economic inequality among the Chinese people. The idea that the ideals of socialism and communism will be realized, and will only be realized, in the course of a long process of historical development and social evolution thus converges with Kang's idea of historical progress and his vision of the datong world in which socialist or communist principles will be applicable in economic life.

The official view of the current level of economic development in Chinese society is that it has just reached the xiaokang level. It is hoped that by the centenary of the founding of the Chinese Communist Party (2021), China will have reached a "higher level of xiaokang society," and by the centenary of the establishment of the People's Republic of China (2049), it will have reached the level of a middle-level developed country and will have "basically completed its modernization". Thus the term xiaokang, which dates back more than two millennia ago to Liyun, is still being used today to refer to the second-best level of development. The concept of "harmonious society" advocated in recent years by the Chinese Communist Party also draws on traditional Chinese thought, particularly the Confucian vision of social harmony and amicable social relationships.

In the final analysis, the datong philosophy in Liyun and in Datong shu speaks not only to the Chinese people but to the whole of humankind. It is a philosophy that is universalist in nature rather than particularistic and dependent on a particular culture or religion. As a philosophy of the common good, it is a valuable contribution to the common heritage of mankind. Though ancient in origin, it still speaks to the needs, circumstances, and challenges faced by the contemporary world. Though Chinese in origin, datong is capable, as Kang Youwei has demonstrated, of entering into dialogue with the utilitarian, socialist, and liberal traditions of the West. It is to be hoped that datong thinking will continue to develop and contribute to the Chinese social and political philosophy of the twenty first century.

The Concept of "Datong" in Chinese Philosophy as an Expression of the Idea of the Common Good. Albert H.Y. Chen. The Common Good: Chinese and American Perspectives
SPECIAL EDITOR for Asian Affairs Godfree Roberts (Ed.D. Education & Geopolitics, University of Massachusetts, Amherst (1973)), currently resides in Chiang Mai, Thailand. His expertise covers many areas, from history, politics and economics of Asian countries, chiefly China, to questions relating to technology and even retirement in Thailand, a topic of special interests for many would-be Western expats interested in relocating to places where a modest income can still assure a decent standard of living and medical care.