The Limits of Empiricism?

In the March 21 issue of The New Yorker magazine, Harvard historian Jill Lepore writes about the traumatic shift in jurisprudence from "trial by combat" to "trial by jury," which occurred at the same time that The Magna Carta was being imposed on King John of England, and "required a new doctrines of evidence and a new method of inquiry...". Trial by combat "place[s] judgment in the hands of God", whereas trial by jury "places judgment in the hands of men."
    This watershed event signaled an empiricist consensus that "between the thirteenth century and the nineteenth...spread from law outward to science, history, and journalism." Lepore observes that "empiricists believed they had deduced a method by which they could discover a universe of truth: impartial, verifiable knowledge."
      "Somewhere in the middle of the twentieth century, fundamentalism and post-modernism, the religious right and the academic left, met up: either the only truth is the truth of the divine or there is no truth; for both, empiricism is an error."
    For Lepore, this shift away from an empiricist consensus contributes to the "epistemological havoc" of the current presidential campaign in the U.S.A. . The debate "has a lot more in common with trial by combat than with trial by jury, which is what people are talking about when they say these debates seem 'childish'; the outcome is the evidence."
     Lepore cites writings by " by Michael P. Lynch, which have "identified three sources of skepticism about reason: the suspicion that all reasoning is rationalization; the idea that science is just another faith; and the notion that objectivity is an illusion." As a result, Lynch believes, " we won't be.able to agree on the facts, let alone values." Both these writers are concerned for the future of American politics, because our system is "wholly dependent on the empiricism of the Enlightenment, as answerable to evidence."
      With regard to the current campaign, Lenore writes that "Trump doesn't reason...he wants combat. Cruz's appeal is to the judgment of God... Rubio's appeal is to Google." Lenore goes on to say, "People who care about civil society have two choices: find some epistemic principles other than empiricism on which every one can agree; or else find some method other than reason with which to defend empiricism... Lynch thinks the best defense of reason is a common practical and ethical commitment."

    Are Lynch and Lenore correct when they say that "reason can't defend itself without resort to reason?" While rational discourse must have a place, it seems to me that science, religion, and politics are all subject to the requirement that their products "work" to enhance the human community in one way or another. Is that not the ultimate test of empirical observations? And are not all scientific discoveries "provisional", and in need of constant revival? In this sense even the most empirical experiments are subject to the test of harsh reality. The problem is that, given the vast power of weapons of mass destruction, we don't have a lot of room for experimentation.