Continuity of method between sciences and epistemology means that the methods of inquiry followed in the sciences and in epistemology are continuous with each other. This view is opposed to the old idea of epistemology being the foundational discipline for sciences.
At the heart of methodological continuity lies the reflexivity of the knowing process. It begins with the assumption that we already have some knowledge. We examine that knowledge with a view to discovering the cannons and principles through which we have come to acquire it. In other words, by examining what we already know, we come to understand the method of knowing. And by applying that method we can learn more about the world.
But what we have learned about the method of knowing can be applied not only for knowing more about the world; it can also be applied to the process of knowing itself. It is for this reason that Quine’s description of naturalized epistemology as “science self-applied” is a good one. The idea of epistemology as self-application of method is very important in the light of the second crisis of epistemology namely the internal conflicts in epistemology.