I came across this article discussing the the importance of formal methods, i.e., higher-order logic and mathematics, in solving certain philosophical questions. The author argued, however, that while such methods are in increasingly becoming popular, they cannot replace the traditional philosophical methods used in answering the "what-is" type of questions. In his own words:

"It is one thing to have a logic of justification or of epistemic possibility but just what does knowledge or justification itself consist in? In response to such ‘what is ... ?’ questions, my feeling is that the response of the formal philosopher should be modest. In formal epistemology, for example, we should not expect a logic to reveal the nature of knowledge of justification itself."

If higher-order logic and mathematics are the methods used in formal philosophy, what are the methods used in traditional philosophy? Is conceptual analysis among them?