The synthesis of Confucian, Taoist, and Buddhist ideas in Neo-Confucianism is significant in several ways. It not only helped to revitalize Confucian thought during the Song dynasty in China but also had a lasting impact on East Asian philosophy and culture.

Firstly, the incorporation of Taoist and Buddhist ideas into Confucianism allowed for a more holistic understanding of the world and human nature. Confucianism, with its emphasis on social and moral values, was often criticized for neglecting the spiritual and metaphysical aspects of life. By integrating Taoist and Buddhist concepts such as the Tao, qi, and karma, Neo-Confucianism provided a more comprehensive understanding of the universe and human existence.

Secondly, the synthesis of these three philosophical traditions helped to bridge the gap between the elite and popular beliefs. Confucianism, with its emphasis on education and moral cultivation, was primarily embraced by the educated elite. On the other hand, Taoism and Buddhism were more popular among the common people due to their emphasis on rituals, superstitions, and salvation. Neo-Confucianism, with its combination of both intellectual and spiritual elements, appealed to both the elite and the masses, making it a more inclusive and widely accepted philosophy.

Moreover, the incorporation of Taoist and Buddhist ideas also helped to address some of the limitations of Confucianism. For instance, Confucianism's strict hierarchical structure and emphasis on filial piety were sometimes criticized for promoting social conformity and stifling individualism. By integrating Taoist and Buddhist concepts of self-cultivation and inner peace, Neo-Confucianism encouraged individuals to find a balance between social responsibilities and personal fulfillment.

The synthesis of Confucian, Taoist, and Buddhist ideas also had a significant impact on East Asian culture and art. Neo-Confucianism's emphasis on the unity of nature and humanity, as well as the pursuit of inner harmony, influenced various forms of artistic expression, including painting, calligraphy, and poetry. These art forms often incorporated Taoist and Buddhist symbols and themes, reflecting the influence of Neo-Confucianism on East Asian aesthetics.

In conclusion, the synthesis of Confucian, Taoist, and Buddhist ideas in Neo-Confucianism was a significant development in the history of East Asian philosophy. It not only helped to revitalize Confucian thought but also had a lasting impact on East Asian culture and art. The integration of these three philosophical traditions allowed for a more holistic understanding of the world and human nature, making Neo-Confucianism a highly influential and enduring philosophy.