We are already familiar with many rational processes which are simply beyond the capability of the human mind to undertake, perhaps not in principle, but as a practical matter. The simplest example might be those intrinsically trivial but highly interative or repetitive calculations we rely on numerical approximations or mechanical devices to perform for us.
If there are mental processes we cannot perform at all which are essential in order to solve certain problems, then it is unlikely that we will stumble on to those problems and identify them in the first place. Historically, we have seen the failure of human abilities to visualize certain physical realities which could only be dealt with by the use of mathematics, but which became amenable to attack once we developed the appropriate techniques. For example, it is very difficult to talk about physics in any detail without applying the methods of real and complex analysis: calculus and differential equations.
There may very well be natural processes which are not describable using mathematics or language. We certainly are aware of many psychological and social realities like this, which we still deal with, however imperfectly, but routinely. And even though it may be premature to know with any certainty that we can never systematize these processes, neither can we rule out the fact that someday we may.
Most of all, we should always keep in mind that using scientific methodologies where they are not appropriate can get us into lots of trouble. After all, it is not our reason which makes the final decision, but our emotions. Our brains tell us how things work, our hearts are what tell us whether or not they are right.