Final answer:
Ministers of the Great Awakening and philosophers of the Enlightenment shared the idea of promoting rationalism and reason.
Step-by-step explanation:
The idea that ministers of the Great Awakening and philosophers of the Enlightenment shared was promotion of rationalism and reason. Both movements emphasized the importance of using reason and logic to understand and interpret the world. The Enlightenment thinkers valued reason as the primary source of authority and sought to apply it to all aspects of life, including religion. Similarly, the ministers of the Great Awakening emphasized the importance of personal experience and individual understanding of religious beliefs, rejecting formal modes of worship.