What it is . . .
Let me first give a simple working definition of philosophical theology. If philosophy is an attempt at a rational interpretation of reality, and if theology is the study of God, then philosophical theology is an attempt to arrive at rational conclusions concerning the question of God. It is the study of how philosophical theologians have come to conclusions about the existence of God and how they have answered all of the impending questions attached to various responses to that ontological question.
Why it matters . . .
So, what is the inherent value in a study of philosophical theology? A significant outlay of time and dedication is required in order to properly address its various issues and subjects. Is it worth it? I have determined that it is for the following reasons:
1) A great shift away from God happened as a result of what some have referred to as “the modern ‘turn to the subject’.”
It was, however, the modern “turn to the subject” that proved decisive. Kant’s call for “autonomy,” for the individual’s “release from a self-incurred tutelage” to such heteronomous [external] authorities as the Bible and the Church, embodied the spirit of the Enlightenment. Increasingly, individual reason and conscience became the arbiters of religious truth. Although the Romantics rejected the appeal to autonomous “reason alone,” they nevertheless shifted the source of spiritual authority to the “religious self-consciousness,” that is, to religious experience. The entire nineteenth century can be viewed as an effort to resolve the increasingly problematic issue of authority (emphasis mine).
This “shift away from God” did not begin with Kant; he merely codified and canonized it. The shift began in the decades prior to the Reformation. Even the Reformation itself can be seen in the light of self-focus and rebellion against authority. As the discoveries and assertions of Kepler, Copernicus, and Galileo brought about a mechanistic view of the universe, God began to drift into the background, being replaced by self in the foreground.
2) Western culture is still in the throes of Enlightenment, mechanistic thinking and is particularly focused on the self. Understanding the roots of our present frame of mind gives insight into the issues of Christ and culture thus making this type of study potentially relevant to the Church.
Rene Descartes in his Rule for the Direction of the Mind, Rule III, wrote:
In the subjects we propose to investigate, our inquiries should be directed, not to what others have thought, nor to what we ourselves conjecture, but to what we can clearly and perspicuously behold and with certainty deduce; for knowledge is not won in any other way.
He goes on to endorse the study of what “the ancients” have taught while warning us not to “become infected with their errors.” He advocates for intuition and induction as the only two ways to “arrive at the knowledge of things.” And yet, he allows (Paschal would say grudgingly) for the belief of matters “divinely revealed” though he expects those truth to be discernible through the two ways he prescribes.
 Livingston, Fiorenza, Coakley, and Evans, Jr., Modern Christian Thought: Twentieth Century, Second Edition, Vol. 2, (Fortress Press, 2006), 2.
 See Paschal, Pensees, Section II, no. 77.