Understanding and philosophical methodology

According to Conceptualism, philosophy is an independent discipline that can be pursued from the armchair because philosophy seeks truths that can be discovered purely on the basis of our understanding of expressions and the concepts they express. In his recent book, The Philosophy of Philosophy, Timothy Williamson argues that while philosophy can indeed be pursued from the armchair, we should reject any form of Conceptualism. In this paper, we show that Williamson's arguments against Conceptualism are not successful, and we sketch a way to understand understanding that shows that there is a clear sense in which we can indeed come to know the answers to (many) philosophical questions purely on the basis of understanding.