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Here Hume was not challenging a particular school of thought; he was challenging a whole style of thinking. Let's get specific: he was actually challenging the view that there could be fixed, knowable answers to some of the most basic questions about the nature of reality. In short, Hume was a skeptic. Many of his most memorable conclusions showed the doubtful nature of our most familiar concepts: causality, the existence of the external world, the existence of God, the existence of the self, the existence of girlfriends for shy, awkward teenage boys.
And, not surprisingly, raising doubt about such notions made a lot of people—not only philosophers, but normal people, too—quite angry.