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Many contemporary philosophers describe themselves as naturalists. They mean that they believe something like this: there is only the natural world, and the best way to find out about it is by the scientific method. I am sometimes described as a naturalist. Why do I resist the description? Not for any religious scruple: I am an atheist of the most straightforward kind. But accepting the naturalist slogan without looking beneath the slick packaging is an unscientific way to form one’s beliefs about the world, not something naturalists should recommend.

What, for a start, is the natural world? If we say it is the world of matter, or the world of atoms, we are left behind by modern physics, which characterizes the world in far more abstract terms. Anyway, the best current scientific theories will probably be superseded by future scientific developments. We might therefore define the natural world as whatever the scientific method eventually discovers. Thus naturalism becomes the belief that there is only whatever the scientific method eventually discovers, and (not surprisingly) the best way to find out about it is by the scientific method. That is no tautology. Why can’t there be things only discoverable by non-scientific means, or not discoverable at all?

Still, naturalism is not as restrictive as it sounds. For example, some of its hard-nosed advocates undertake to postulate a soul or a god, if doing so turns out to be part of the best explanation of our experience, for that would be an application of scientific method. Naturalism is not incompatible in principle with all forms of religion. In practice, however, most naturalists doubt that belief in souls or gods withstands scientific scrutiny.

What is meant by “the scientific method”? Why assume that science only has one method? For naturalists, although natural sciences like physics and biology differ from each other in specific ways, at a sufficiently abstract level they all count as using a single general method. It involves formulating theoretical hypotheses and testing their predictions against systematic observation and controlled experiment. This is called the hypothetico-deductive method.

One challenge to naturalism is to find a place for mathematics. Natural sciences rely on it, but should we count it a science in its own right? If we do, then the description of scientific method just given is wrong, for it does not fit the science of mathematics, which proves its results by pure reasoning, rather than the hypothetico-deductive method. Although a few naturalists, such as W.V. Quine, argued that the real evidence in favor of mathematics comes from its applications in the natural sciences, so indirectly from observation and experiment, that view does not fit the way the subject actually develops. When mathematicians assess a proposed new axiom, they look at its consequences within mathematics, not outside. On the other hand, if we do not count pure mathematics a science, we thereby exclude mathematical proof by itself from the scientific method, and so discredit naturalism. For naturalism privileges the scientific method over all others, and mathematics is one of the most spectacular success stories in the history of human knowledge.

Which other disciplines count as science? Logic? Linguistics? History? Literary theory? How should we decide? The dilemma for naturalists is this. If they are too inclusive in what they count as science, naturalism loses its bite. Naturalists typically criticize some traditional forms of philosophy as insufficiently scientific, because they ignore experimental tests. How can they maintain such objections unless they restrict scientific method to hypothetico-deductivism? But if they are too exclusive in what they count as science, naturalism loses its credibility, by imposing a method appropriate to natural science on areas where it is inappropriate. Unfortunately, rather than clarify the issue, many naturalists oscillate. When on the attack, they assume an exclusive understanding of science as hypothetico-deductive. When under attack themselves, they fall back on a more inclusive understanding of science that drastically waters down naturalism. Such maneuvering makes naturalism an obscure article of faith. I don’t call myself a naturalist because I don’t want to be implicated in equivocal dogma. Dismissing an idea as “inconsistent with naturalism” is little better than dismissing it as “inconsistent with Christianity.”

Still, I sympathize with one motive behind naturalism — the aspiration to think in a scientific spirit. It’s a vague phrase, but one might start to explain it by emphasizing values like curiosity, honesty, accuracy, precision and rigor. What matters isn’t paying lip-service to those qualities — that’s easy — but actually exemplifying them in practice — the hard part. We needn’t pretend that scientists’ motives are pure. They are human. Science doesn’t depend on indifference to fame, professional advancement, money, or comparisons with rivals. Rather, truth is best pursued in social environments, intellectual communities, that minimize conflict between such baser motives and the scientific spirit, by rewarding work that embodies the scientific virtues. Such traditions exist, and not just in natural science.

The scientific spirit is as relevant in mathematics, history, philosophy and elsewhere as in natural science. Where experimentation is the likeliest way to answer a question correctly, the scientific spirit calls for the experiments to be done; where other methods — mathematical proof, archival research, philosophical reasoning — are more relevant it calls for them instead. Although the methods of natural science could beneficially be applied more widely than they have been so far, the default assumption must be that the practitioners of a well-established discipline know what they are doing, and use the available methods most appropriate for answering its questions. Exceptions may result from a conservative tradition, or one that does not value the scientific spirit. Still, impatience with all methods except those of natural science is a poor basis on which to identify those exceptions.

Naturalism tries to condense the scientific spirit into a philosophical theory. But no theory can replace that spirit, for any theory can be applied in an unscientific spirit, as a polemical device to reinforce prejudice. Naturalism as dogma is one more enemy of the scientific spirit.

Timothy Williamson is the Wykeham Professor of Logic at Oxford University, a Fellow of the British Academy and a Foreign Honorary Member of the American Academy of Arts and Sciences. He has been a visiting professor at M.I.T. and Princeton. His books include “Vagueness” (1994), “Knowledge and its Limits” (2000) and “The Philosophy of Philosophy” (2007).

Naturalism is the philosophical theory that treats science as our most reliable source of knowledge and scientific method as the most effective route to knowledge. In a recent essay for The Stone, Timothy Williamson correctly reports that naturalism is popular in philosophy. In fact it is now a dominant approach in several areas of philosophy — ethics, epistemology, the philosophy of mind, philosophy of science and, most of in all, metaphysics, the study of the basic constituents of reality. Metaphysics is important: if it turns out that reality contains only the kinds of things that hard science recognizes, the implications will be grave for what we value in human experience.

Naturalism is itself a theory with a research agenda of unsolved problems. But naturalists’ confidence that it can solve them shouldn’t be mistaken for “dogmatism,” nor can its successes be written off as “slick packaging,” two terms Professor Williamson used in his essay to describe why he rejects naturalism.

Before taking up Professor Williamson’s challenges to naturalism, it’s worth identifying some of this success in applying science to the solution of philosophical problems, some of which even have pay-offs for science. Perhaps the most notable thing about naturalism is the way its philosophers have employed Darwin’s theory of natural selection to tame purpose. In 1784 Kant wrote, “There will never be a Newton for the blade of grass.” What he meant was that physical science could never explain anything with a purpose, whether it be human thought or a flower’s bending toward the sun. That would have made everything special about living things — and especially us — safe from a purely scientific understanding. It would have kept questions about humanity the preserve of religion, mythmaking and the humanities.

Only 25 years or so later, the Newton of the blade of grass was born to the Darwin family in Shropshire, England. “On the Origin of Species” revealed how physical processes alone produce the illusion of design. Random variation and natural selection are the purely physical source of the beautiful means/ends economy of nature that fools us into seeking its designer. Naturalists have applied this insight to reveal the biological nature of human emotion, perception and cognition, language, moral value, social bonds and political institutions. Naturalistic philosophy has returned the favor, helping psychology, evolutionary anthropology and biology solve their problems by greater conceptual clarity about function, adaptation, Darwinian fitness and individual-versus-group selection.

While dealing with puzzles that vexed philosophy as far back as Plato, naturalism has also come to grips with the very challenges Professor Williamson lays out: physics may be our best take on the nature of reality, but important parts of physics are not just “abstract,” as he says. Quantum mechanics is more than abstract. It’s weird. Since naturalistic philosophers take science seriously as the best description of reality, they accept the responsibility of making sense of quantum physics. Until we succeed, naturalists won’t be any more satisfied than Professor Williamson that we know what the natural world is. But 400 years of scientific success in prediction, control and technology shows that physics has made a good start. We should be confident that it will do better than any other approach at getting things right.

Naturalists recognize that science is fallible. Its self-correction, its continual increase in breadth and accuracy, give naturalists confidence in the resources they borrow from physics, chemistry and biology. The second law of thermodynamics, the periodic table, and the principles of natural selection are unlikely to be threatened by future science. Philosophy can therefore rely on them to answer many of its questions without fear of being overtaken by events.

“Why can’t there be things only discoverable by non-scientific means, or not discoverable at all?” Professor Williamson asked in his essay. His question may be rhetorical, but the naturalist has an answer to it: nothing that revelation, inspiration or other non-scientific means ever claimed to discover has yet to withstand the test of knowledge that scientific findings attain. What are those tests of knowledge? They are the experimental/observational methods all the natural sciences share, the social sciences increasingly adopt, and that naturalists devote themselves to making explicit. You can reject naturalists’ epistemology, or treat it as question begging, but you can’t accuse them of not having one.

As Professor Williamson notes, naturalism’s greatest challenge “is to find a place for mathematics.” The way it faces the challenge reveals just how undogmatic naturalism really is. It would be easy to turn one’s back on the problems mathematics presents (What are numbers? How can we have the certainty about them that math reveals?). One excuse to turn our backs is that mathematicians and scientists don’t care much about these problems; another is that no one has ever provided a satisfactory answer to these questions, so no other philosophy can be preferred to naturalism on this basis. But naturalism has invested a huge amount of ingenuity, even genius, seeking scientifically responsible answers to these hardest of questions. Not with much success as yet by our own standards, one must admit. But that is the nature of science.

Naturalism takes the problem of mathematics seriously since science cannot do with out it. So naturalism can’t either. But what about other items on Professor Williamson’s list of disciplines it would be hard to count as science: history, literary theory? Can science and naturalistic philosophy do without them? This is a different question from whether people, as consumers of human narratives and enjoyers of literature, can do without them. The question naturalism faces is whether disciplines like literary theory provide real understanding?

Naturalism faces these questions because it won’t uncritically buy into Professor Williamson’s “default assumption … that the practitioners of a well-established discipline know what they are doing, and use the … methods most appropriate for answering its questions.” If semiotics, existentialism, hermeneutics, formalism, structuralism, post-structuralism, deconstruction and post-modernism transparently flout science’s standards of objectivity, or if they seek arbitrarily to limit the reach of scientific methods, then naturalism can’t take them seriously as knowledge.

That doesn’t mean anyone should stop doing literary criticism any more than foregoing fiction. Naturalism treats both as fun, but neither as knowledge

What naturalists really fear is not becoming dogmatic or giving up the scientific spirit. It’s the threat that the science will end up showing that much of what we cherish as meaningful in human life is illusory.

Alex Rosenberg is the R. Taylor Cole Professor and philosophy department chair at Duke University. He is the author of 12 books in the philosophy of biology and economics. W.W. Norton will publish his latest book, “The Atheist’s Guide to Reality,” in October.