Confucianism employs four meanings for the term 'Heaven.'
According to Duan Yucai (段玉裁, 1735-1815), a famous philologist in the Qing Dynasty, the character for 'Heaven', 天, is ideographic. The lower part is 大, meaning 'great'; the upper part is 一 , meaning 'one.' Therefore, 天 refers to 'the one which is the greatest,' viz., something greater than which nothing can be imagined (其大無二). This corresponds to the philosophical understanding of 'Heaven' in Confucianism.
The first connotation for 'Heaven' thus refers to the one and only ontological domain in which all possible cosmic events take place. Correspondingly, it also connotes an all-encompassing, constantly creative cosmic power which permeates this domain. After Einstein, we know that it is not necessary to differentiate a space-time framework from the matter-energies flowing and interacting within that framework: they are each interconnected with the others. Hence, I would say, quite straightforwardly, that the first connotation of 'Heaven' in Confucianism is to an all-encompassing, constantly creative cosmic power which permeates everything.
From my previous article 'A Catechism of Confucianism: the Absolute Good (至善),' we know that Heaven can create a condition of dynamic harmony in any place and at any time within the cosmic process. In Confucianism, this indescribable sublimity of the Heavenly creation becomes the transcendent 'ideal' which Confucian practitioners try to emulate in their personal moral self-cultivation.
However, although 'Heaven' can be taken to be the ideal of Confucian self-cultivation, the Heavenly creation (understood in this first meaning) may have nothing to do with human beings. Even if the whole of human civilization didn't exist at all, Heaven would still be creating, spontaneously, naturally, and without cease. Accordingly, the dynamic harmony which Heaven creates at each moment of the cosmic process can only be understood in this most mysterious sense: everything created in the past, in the present and in the future is-and-changes together in the one and only ontological domain: 'Heaven.' All things thus enjoy the being-and-becoming of their togetherness eternally! This sense of 'dynamic harmony' is not anthropomorphic. Neither is it anthropocentric. It is benevolent, but also wild, awesome, beyond values according to human standards, and thus possesses its own ineffable beauty. When Confucius insisted upon keeping silent (予欲無言, The Analects 17.19), what he felt was this ineffable beauty of the Heavenly creation (四時行焉 , 百物生焉).
The second reading of 'Heaven' connotes the all-encompassing constantly creative cosmic power with which a Confucian mystic feels united in his or her ecstatic life-moments (天人合一）. As I argued in the same earlier article, humans are finite. The dynamic harmony which humans try to achieve is always situational and contextual. In other words, humans try to live and grow together within the human-human and human-cosmic continuum, defined primarily from the perspective of humanity. Understood this way, though global warming, drought, and flooding are all 'harmonious' from the mysterious point of view of Heaven, they are not harmonious from the point of view of human beings. Accordingly, when a Confucian ritual performer (musician, dancer, calligrapher, meditator, technician, etc.) tries hard to discipline every movement of his or her body and mind at one moment, he or she would ideally feel a 'flow' and feel united with everything he or she is engaging. The mystical union felt at this ecstatic moment results from a concrete energy equilibrium which a human individual accomplishes in relation to his or her environment but one in which he or she does not lose his or her genuine self. In other words, the harmony in process is a graded harmony according to human standards, and is potentially a gradually expansive harmony in accordance with its cosmic values.
Because this shift of meanings between the 'Heaven' per se and the 'Heaven' united with humans, a new connotation of 'Heaven' is engendered. The term can also refer to non-human nature （天人之別）. From a Confucian viewpoint, nature is indeed benevolent and graceful. It shines with the sun, the rains fall, and the crops grow. Nevertheless, distinct from nature, only human beings are able to furrow the fields, build terraces, and establish granaries to charitably feed the hungry in case of a poor harvest. In other words, human beings have the obligation to add something uniquely human to nature itself in order to achieve a specific manifestation of dynamic harmony with nature. In terms of creation, humans assist in the cosmic creation which has been left unfinished by nature. Therefore, the ancient text, Zhong Yong (中庸), describes the religious calling of human beings as, "to assist in the creating and nurturing of Heaven and Earth, to form a triad with Heaven and Earth" ( 贊天地之化育, 與天地參).
In this quotation, the phrase 'Heaven and Earth' refers to the whole realm of non-human nature. In this case, 'Heaven' in its first meaning is composed of three parts: Heaven, Earth and Human Beings. Accordingly, in this fourth connotation, 'Heaven' refers to the Yang (陽) powers of cosmic creation in the realm of nature. In the Confucian understanding of nature, Heaven is proactive, while Earth is receptive; Heaven is explorative, while Earth is supportive. Life on earth evolved by means of a combination of the descending Yang powers of Heaven and the ascending Yin (陰) powers of Earth. As a result, the dynamic balance between Yin and Yang is what creates the myriad of living things under Heaven. In Confucian moral-self cultivation, this co-operation of Heaven and Earth in producing life is read as representing a virtuous person's (君子) moral behavior. A virtuous person can establish him or herself (by means of his or her Yang power) while establishing others (through his or her Yin power). By the same token, a virtuous person may achieve something (through the Yang power) while simultaneously helping others to also achieve it (through the Yin power) (己欲立而立人, 己欲達而達人）.
In a word, Confucianism teaches human beings to manifest the transcendent 'One' principle of the Heavenly creation in a specifically humane (仁) way. Understanding the union but also the distinction between Heaven and Human Beings is key to parsing out the varying meanings of 'Heaven' in the context of Confucianism.