Hume formulated and applied, over a large range of subjects, two main principles. First, all of our knowledge is the result of either sense impressions or reflections on the workings of our own mind. Second, no matter of fact can be proved a priori, or before experience. As Hume put it: “All the perceptions of the human mind resolve themselves into two distinct kinds, which I shall call impressions and ideas.”

He held that the sciences of the natural world and beliefs about human society are the result of empirical investigation. The truths of mathematics and logic are known without investigating the world. For this reason, they are not about the world, but about the workings of human minds. Our sensory information, which gives us immediate factual knowledge, is more compelling than our ideas. As Hume stated: “The most lively thought is still inferior to the dullest sensation.”

Hume had no use for past philosophical projects that contained a priori speculation about the workings of this world or the next. Here is how he summed up this doctrine: