Timothy Williamson, the Wykeham Professor of Logic at Oxford University, addresses the basic argument (put forth by Alex Rosenberg in a post, “Why I Am a Naturalist") that science is (as Rosenberg insists) "our most reliable source of knowledge and scientific method as the most effective route to knowledge", writing:
For Professor Rosenberg, it may turn out that “reality contains only the kinds of things that hard science recognizes.” By “hard science” he seems to mean something like physics. He doesn’t explain how that could turn out. How could physics show that reality contains only the kinds of things that physics recognizes? It sounds embarrassingly like physics acting as judge and jury in its own case. That physics does not show that there is such a thing as a debt crisis does not mean that physics shows that there is no such thing as a debt crisis: physics simply does not address the question. That is no criticism of physics; it has other work to do. For it to turn out that reality contains only the kinds of things that hard science recognizes, where they exclude things like debt crises, it would have to turn out that a radically reductionist metaphysical theory is true. That in turn would require industrial-scale argument at a characteristically philosophical level of reasoning. But I doubt that Professor Rosenberg counts philosophy as hard science.
We can formulate the underlying worry as a sharp argument against the extreme naturalist claim that all truths are discoverable by hard science. If it is true that all truths are discoverable by hard science, then it is discoverable by hard science that all truths are discoverable by hard science. But it is not discoverable by hard science that all truths are discoverable by hard science. “Are all truths discoverable by hard science?” is not a question of hard science. Therefore the extreme naturalist claim is not true.
Such problems pose far less threat to more moderate forms of naturalism, based on a broader conception of science that includes mathematics, history, much of philosophy, and the sensible parts of literary criticism, as well as the natural and social sciences. But we should not take for granted that reality contains only the kinds of things that science even in the broad sense recognizes. My caution comes not from any sympathy for mysterious kinds of cognition alien to science in the broad sense, but simply from the difficulty of establishing in any remotely scientific way that reality contains only the kinds of thing that we are capable of recognizing at all. In any case, Professor Rosenberg does not rest content with some moderate form of naturalism. He goes for something far more extreme, in the process lapsing into hard scientism.
See his entire post, "On Ducking Challenges to Naturalism", in the New York Times. Much could be said about different aspects of this debate, but in reading Williamson's post I was reminded of several different passages from the writings of Walker Percy (a former naturalist/positivist who became Catholic) and C. S. Lewis (a former atheist who became Anglo-Catholic). Here are a couple of sections from an essay about Percy that I wrote years ago that contain some of his thoughts on scientism:
"What did at last dawn on me as a medical student and intern, a practitioner, I thought, of the scientific method, was that there was a huge gap in the scientific view of the world. This sector of the world about which science could not utter a single word was nothing less than this: what it is like to be an individual living in the United States in the twentieth century." ("Diagnosing The Modern Malaise," p. 213) ...
Percy rightly dismissed the notion that people can live without an anthropological vision, that is, a specific understanding of who man is and what he meant for. "Everyone has an anthropology," he wrote in the essay, "Rediscovering A Canticle For Leibowitz." "There is no not having one. If a man says he does not, all he is saying is that his anthropology is implicit, a set of assumptions which he has not thought to call into question." His own conversion was due, in large part, to the realization that scientism –– the belief that the scientific method and the technology it produces can provide answers to man’s deepest questions and longings –– was untenable and, in fact, was a lie. As a trained physician, Percy had respect for science when properly practiced and understood. But he saw many theories making claims to being "scientific," but in reality were ideological positions based on a subjective and self-serving view of reality. In the essay "Culture, The Church, And Evangelization," Percy wrote,
"The distinction which must be kept in mind is that between science and what can only be called ‘scientism.’ . . . [Scientism] can be considered only as an ideology, a kind of quasi-religion––not as a valid method of investigating and theorizing which comprises science proper––a cast of mind all the more pervasive for not being recognized as such and, accordingly, one of the most potent forces which inform, almost automatically and unconsciously, the minds of most denizens of modern industrial societies like the United States." ("Culture, The Church, And Evangelization," p. 297).
Percy traced scientism back to Continental philosopher René Descartes, believing the Cartesian distinction between the thinking mind and the rest of the physical world had finally produced its evil fruit in the twentieth century. This radical dualism shaped the ideologies of Communism and Naziism, the sexual revolution of the 1960s, and secular humanism. Each of these belief systems, however well or poorly articulated, rejected God and set up man as the ultimate reference point for all of human activity, whether that activity was political, social, or sexual. Now freed from the confines of the supernatural order and objective truth, man could create and customize his own reality: totalitarian, egalitarian, hedonistic, or consumer-oriented.
Percy often noted the paradoxical fact that man can form a perfect scientific theory explaining the material world –- but cannot adequately account for himself in that theory. Man is the round peg never quite fitting into the square hole of scientism. "Our view of the world, which we get consciously or unconsciously from modern science, is radically incoherent," Percy wrote in his essay "The Fateful Rift: The San Andreas Fault in the Modern Mind." Again, science must either recognize its own limits or create confusion: "A corollary of this proposition is that modern science is itself radically incoherent, not when it seeks to understand things and subhuman organisms and the cosmos itself, but when it seeks to understand man, not man’s physiology or neurology or his bloodstream, but man qua man, man when he is peculiarly human. In short, the sciences of man are incoherent." ("The Fateful Rift: The San Andreas Fault In The Modern Mind," p. 271). In a self-interview, "Questions They Never Asked Me," he put the matter more bluntly:
"This life is much too much trouble, far too strange, to arrive at the end of it and then be asked what you make of it and have to answer, ‘Scientific humanism.’ That won’t do. A poor show. Life is a mystery, love is a delight. Therefore, I take it as axiomatic that one should settle for nothing less than the infinite mystery and infinite delight; i.e., God." ("Questions They Never Asked Me," p. 417)
Lewis, in the book, Miracles, made similar points:
All possible knowledge, then, depends on the validity of reasoning. If the feeling of certainty which we express by words like must be and therefore and since is a real perception of how things outside our own minds really 'must' be, well and good. But if this certainty is merely a feeling in our own minds and not a genuine insight into realities beyond them--if it merely represents the way our minds happen to work-then we can have no knowledge. Unless human reasoning is valid no science can be true.
It follows that no account of the universe can be true I unless that account leaves it possible for our thinking to be a real insight. A theory which explained everything else in the whole universe but which made it impossible to believe that our thinking was valid, would be utterly out of court. For that theory would itself have been reached by thinking,  and if thinking is not valid that theory would, of course, be itself demolished. It would have destroyed its own credentials. It would be an argument which proved that no argument was sound--a proof that there are no such things as proofs--which is nonsense.
Thus a strict materialism refutes itself for the reason given long ago by Professor Haldane: 'If my mental processes are determined wholly by the motions of atoms in my brain, I have no reason to suppose that my beliefs are true . . . and hence I have no reason for supposing my brain to be composed of atoms.’ (Possible Worlds, p. 209)
But Naturalism, even if it is not purely materialistic, seems to me to involve the same difficulty, though in a somewhat less obvious form. It discredits our processes of reasoning or at least reduces their credit to such a humble level that it can no longer support Naturalism itself.
Percy put all of this rather succinctly in one of his early (and perhaps most famous) essays, "The Deltra Factor", writing: "The modern began to come to an end when men discovered that they could no longer understand themselves by the theory professed by the age." He wrote at length about the conflict of vision about the nature of truth and man between naturalists/adherents to scientism and artists/novelists, believing that it was the duty of the latter to plumb, describe, and present the mystery of man and existence. This is noteworthy because Rosenberg makes it clear that while literature and such is nice for some people, it can't be taken seriously as a means of real knowledge: "That doesn’t mean anyone should stop doing literary criticism any more than forgoing fiction", he concludes. "Naturalism treats both as fun, but neither as knowledge."
A recent book that responds at length to that basic assertion is Western Culture at the American Crossroads: Conflicts Over the Nature of Science and Reason (ISI, 2011), by art historians Arthur Pontynen and Rod Miller. In the opening chapter, they write:
Scientism takes for granted that knowledge is limited to empirical fact; modernists associate fact with an extrinsic rational clarity, while postmodernists associate fact with experiential power. In neither case is science associated with rational meaningful completion. The foundational premise of this pardigm of knowledge is positivism. But neither a factual and rational clarity, not power can remedy the Enlightenments' denial of wisdom—and therefore its denial of the unity of science and reason. As a consequence, it cannot defend culture as the arena of responsible freedom. At best it defends freedom as self-expession and self-realization in an ultimately purposeless world. As such, the modernist-postmodernist tradition is not only antagnostic to classical-Judeo-Christian culture; it is antagonistic to the very possibility of culture as the realm of responsible freedom. It denies the founational principle that as conscious beings all of humanity has the ability, responsibility, and intrinsic right to try and make good choices grounded to some degree on ontological reality. It denies that we have the right and responsibility to freely and conscientiously attempt to comprehend and pursue what is true, good, and beautiful. ...
If the conversation between culture, science, and reason cannot be resolved, then culture, science, and reason are trivialized and brutalized. As the Medievalists pointed out: ars sine scientia nihil est—art without science is nothing. Their point was that in daily life science (knowing), ethics (doing), and art (making) cannot be separated. But just as art without science is nothing, it was realized at the height of nineteenth-century positivist influence that science without lofty purpose is brutality. That brutality centers on the denial of reason and virtue as a means of living a cultured life.
If science is reduced to mere fact and meaning to mere feeling, then reason does not really matter.
More about the book on the ISI website.