An initial reaction is: how many closed problems are there in philosophy? But of course philosophy is so tolerant of dissent that even if a philosophical problem is solved, an ingenious philosopher can always challenge an assumption of the solution and still be counted as doing philosophy. Thus, as Austin noted, philosophical progress tends to be constituted by the creation of new disciplines, such as logic and formal semantics, less tolerant of philosophical dissent. I suspect that this gradual hiving off of bits of philosophy once philosophers have brought them under sufficient theoretical control will continue.
Timothy Williamson, In Vincent F. Hendricks and John Symons (eds.), Formal Philosophy, 2005