But this is similar to saying what is real is what corresponds to reality. Do you see the circularity here?
The philosophers who engage in questioning the "real" are not doing it for the reasons scientists engage in discovering "correct" phenomena. The longing for a deeper meaning and clarity beyond scientific inquiry is a spiritual longing. These philosophers are trying to describe ways in which human beings fit in the world, how we can deal with the groundlessness of our existence, what choices we have in light of the anguish that comes from our mortality.
The problem is that many people view this as a competition against science or "exact" thinking. It is not.
I think this quote from Leo Strauss sums up my point:
"Men are constantly attracted and deluded by two opposite charms: the charm of competence which is engendered by mathematics and everything akin to mathematics, and the charm of humble awe, which is engendered by meditation on the human soul and its experiences. Philosophy is characterized by the gentle, if firm, refusal to succumb to either charm. It is the highest form of the mating of courage and moderation. In spite of its highness or nobility, it could appear as Sisyphean or ugly, when one contrasts its achievement with its goal. Yet it is necessarily accompanied, sustained and elevated by eros. It is graced by nature's grace."