What does the village physician most likely represent in The Minister's Black Veil?

The village physician seems to represent the voice of empirical reason and rationality.  Physicians deal with the tangible, what can be seen with the eyes and touched with the hands, but the minister is dealing with an issue that cannot be understood or helped in the same way that a doctor can assist someone with a physical ailment.  Mr. Hooper's illness is a spiritual one.  We cannot, then, expect the doctor (as a symbol) to understand the minister's spiritual illness.

The doctor says,

Something must surely be amiss with Mr. Hooper's intellects [...]. But the strangest part of the affair is the effect of this vagary, even on a sober-minded man like myself.  The black veil, though it covers only our pastor's face, throws its influence over his whole person, and makes him ghostlike from head to foot.

He, thus, identifies himself as a "sober-minded man" who one would not expect to be affected by this veil in any kind of irrational or fanciful way, and, yet, he is.  He feels as though the minister has become "ghostlike" as a result of covering his face.  As the town's voice of reason then, it should strike us as unusual that the doctor, a man of science, is so affected.  The effects of the veil are so extreme that they even bother a man like this (it doesn't just bother the old or the young, or the superstitious, for example).