Which term best describes is a way of acquiring knowledge that cannot be obtained by inference, deduction, observation, reason, analysis or experience?

The answer is intuition. It is a way of having to understanding an information, fact or something in a more fast phase without having to provide any reasoning  or obtaining any experience, analysis or observation to be done in order to learn or know it.

the old way of life was represented by superstition, an angry god, and absolute submission to authority. the thinkers of the age of reason ushered in a new way of thinking. this new way championed the accomplishments of humankind. individuals did not have to accept despair. science and reason could bring happiness and progress. kings did not rule by divine right. they had an obligation to their subjects. europeans pondered the implications for nearly a century. americans put them into practice first.