To begin with, I cannot recommend this little essay highly enough.  Dr. Leithart cracks the door open on a number of issues that pastors, theologians and others need to think much more seriously and creatively about.  The hegemony of the scientific worldview has not been erased by the advent of post-modernity.  Not even close.  If you doubt that just read some of the comments below the essay and notice how many simply cannot conceive of scientism not functioning as the epistemological ace of spades, and thus fail to even understand what it is that Leithart is saying.  It's as if he'd written his article in a foreign language.

However, I would offer one small quibble.  Dr. Leithart states in his essay, "Though it often buttresses its authority by empirical appeals, science secured its hegemony by inculcating skepticism about everyday experience."  But I wonder if science actually inculcated this skepticism, or if they just picked up on something that was in the air, so to speak, and used it to secure an exalted place among those who traffic in truth and confidence.  Remember Galileo was a contemporary of Descartes. And who can even mention skepticism about everyday experience without thinking of René and his intellectual angst about his own physicality.  But perhaps Leithart is right even so.  While the philosophers had been moving in the direction of skepticism and unbelief for at least a few generations, maybe it was the scientists who "inculcated" it as Leithart has it.  That is, while Descartes and Co. pondered in their dens about whether the ball of wax they thumbed was in fact 'real' or was just an illusion, it was those who would follow in the footsteps of Galileo who would make it a commonplace for the average laymen to quip that it is "super obvious" that the sun doesn't rise.
Posted by Alicia at The Old Mill

"Naturalistic science will usually retort that examination of present materials and processes enables us to extrapolate backwards so as to determine what must have occurred. But here again, forsaking his own basic methods, the scientist is speculating (not observing) on the course of historical development; he assumes (but cannot show experimentally) that not only is nature uniform now but always has been, that processes seen today have always worked as they do now. (The 'theistic evolutionist' likewise assumes that today's processes must be basically similar to God's creative activities. This, in effect, is to say that creation was 'immature,' that God did not finish his creative work at a point in the past.) To pretend to answer questions about origins by extrapolating the observable present into the unobservable past is to reason in a circle; it is to forsake the proper descriptive role of science and to make it an arbitrary determiner of the past instead."

Greg Bahnsen, "Revelation, Speculation, and Science"