Some great logicians and mathematicians (e.g. Gödel) in the past have pointed (perhaps implicitly) to the possibility of formal philosophy (can be referred to as "exact philosophy" as well). I read it to be more of a desire, rather than something that has been actualized. But it's believable, if one considers for example the success of the scientific method, which is a set of rules taken from a larger set of rules (the set of all rules that can be taken) and which lead to more well-defined knowledge.
But what is formal philosophy? Is it different from mathematics (perhaps augmented or extended to natural language)?