Now there’s an ambitious blog entry title! What Muller is dealing with on pp. 67-73 of Post-Reformation Reformed Dogmatics, is the place of philosophy among the Reformed scholastics.
He says, “The understanding of the relationship of philosophy to theology propounded in the Reformed prolegomena and in various apologetic works of the era of orthodoxy assumes a view of philosophy as ancilla and subordinate both in a purely hierarchical sense among the forms o knowing and in a historical sense, regarding it as a derivative form of knowing” (pg. 70). This is a fairly comprehensive way of looking at the relationship. On the one hand, the Reformed scholastics recognized (in general) the dangers of rationalism, and usually tried to avoid it. On the other hand, philosophy could be useful in theology, though in a derivative manner.
Actually, “the rise of modern science and modern rationalism did not profoundly affect Protestant orthodox theology until the latter half of the seventeenth century” (71). In fact, “Christianized Aristotelianism remain(ed) the dominant philosophical perspective thoughout the era of orthodoxy” (71). This must not be misunderstood, however. Christian Aristotelianism did not substantively affect doctrine until the later half of the 17th century. One suspects that it was the logic of Aristotle, more than any other strand of philosophy, that had the largest impact on Protestant Scholasticism.