Mitigated skepticism is a philosophical approach that attempts to provide a level of caution in human reasoning. The term was made popular by the 18th-century philosopher David Hume in his essay, "An Enquiry Concerning Human Understanding."
In his essay, Hume analyzes the concept of human belief. He begins by dividing mental concepts into impressions and ideas. Impressions are mental connections that are based on direct experiences. For example, if an individual looks at a piece of paper with the color blue on it, he is likely to have an impression of the color blue. An idea is a mental connection that doesn't arise directly from an immediate experience. For example, revisiting a memory of a blue ocean is an idea.
Hume argues that because humans are unable to observe the connections made between ideas, those ideas are irrational and can't be completely trusted. An example is the belief that the sun will rise tomorrow, based upon the fact that in the past the sun rose. However, Hume argues that it's impossible to predict a future event based on past experiences. The individual may expect the sun to rise tomorrow, however he is incapable of knowing this without a doubt. However, Hume understands that it's extremely difficult to live life in a constant state of complete skepticism. Therefore, mitigated skepticism is Hume's way of allowing human nature and reason to coexist.