This paper demonstrates that two signature methodological concepts in Husserl’s transcendental phenomenology, the epoché and the phenomenological reduction, derive from his reflections on the history and significance of epistemological skepticism in the Western tradition. Drawing on his Lectures on Logic and Epistemology (Hua XXIV) from the Winter semester of 1906–07, it is argued that Husserl derives his conception of the fundamental task of transcendental philosophy from his reading of a novel skeptical challenge posed by David Hume’s philosophy—a kind of skeptical (...) challenge that Husserl did not recognize in his earlier treatments of Hume. On Husserl’s revised reading, Hume promotes a certain kind of philosophical “despair” (Verzweiflung) or, as it may be called today, “quietism” as the only possible response to the traditional problems of epistemology stemming back to the ancient skeptics. Husserl’s criticism of Hume’s quietism is presented. And Husserl’s reading of Descartes’s cogito as the first decisive uncovering of the limits of epistemological skepticism in the Western tradition is shown to be the source of two key elements of Husserl’s positive alternative to Humean epistemological quietism, which ultimately become the heart of a novel conception of critical transcendental philosophy. These two key elements are the phenomenological epoché and phenomenological reduction. Husserl’s arguments are presented for the claim that these are essential parts of any epistemological program that can answer traditional skeptical challenges. (shrink)