What, exactly, is Naturalism? The naïve definition would go: Naturalism is the belief that there are no supernatural entities. What, though, are supernatural entities? The go-to example would be God, but that’s an example rather than a definition. As far as definitions go, a typical place to start is to say that a supernatural entity is anything which is empirically undetectable, or not verifiable/falsifiable by the scientific method. However, plenty of unquestionably scientific beliefs are in things which are not strictly falsifiable (such as the existence of our universe), and a ‘scientific’ view of the world often involves commitment to beliefs which aren’t strictly verifiable (such as the legitimacy of inductive reasoning, or the reality of the past). Moreover, this definition entails that moral values, the laws of logic, the fundamental principles of arithmetic (and all mathematics), aesthetic qualities, facts themselves (as model-independent truth-makers), propositions (whether necessary, contingent, or necessarily false), the (noumenal) external world, and even purely mental phenomena (eg. qualia), will all be supernatural. Science itself, it turns out, is replete with presumptions of supernaturalism according to the stipulated definition.
Alvin Plantinga once defined Naturalism as the belief that there is no such being as God, nor anything like God. I used to think that this definition was serviceable, but I have come to see that it invites some of the most egregious difficulties of all. Buddhists and Mormons may qualify as Naturalists on this definition, and mathematical Platonists may not qualify as Naturalists! Surely that can’t be right. A definition of naturalism on which it turns out that Joseph Smith is a naturalist and Frege a supernaturalist cannot be right. The notorious difficulty of defining Naturalism should now be evident. What once looked like a trivially easy task now appears to be a herculean feat; how are we to draw the line between the natural and the supernatural? To echo (mutatis mutandis) a famous saying of St. Augustine: if nobody asks me what Naturalism is, I know, but if you ask me, I do not know.
One could always suggest that the term ‘Naturalism’ has no definition precisely because concepts have no definitions. Wittgenstein’s famous suggestion that concepts like ‘GAME’ have no definition, and Quine’s famous skepticism about analyticity, are just two of many factors which have contributed to the recent retreat from ‘definitions’ in the philosophy of concepts. This trend has led to the wide embrace of prototype theory, theory-theory, and other alternatives to the classical theory of concepts. If we must give up on definitions, it seems to me that we must largely give up on the project of analytic philosophy, and that makes me considerably uneasy; but then, I’ve always been squeamish about anti-rationalist sentiments. It may turn out we can do no better than to say something like that Naturalists adopt belief systems related by a mere family resemblance, but which cannot be neatly subsumed under one definition. I, however, (stubborn rationalist that I am) will not give up on definitions without a fight.
On the other hand, if Naturalism cannot be defined then those of us who wish to remain analytic philosophers can just cut our losses and accuse self-identifying naturalists of having an unintelligible worldview; one the expression of which involves a fundamental theoretical term for which no clear definition can be given. In other words, when somebody claims that Naturalism is true we can simply retort: “I don’t know what that means, and neither do you.” What kind of rejoinder could they give? Either they will provide us with an acceptable definition (so that we’ll have finally teased it out), or they will have to reconsider the philosophical foundations of everything they believe they believe. Win-win by my count.
In the meantime, let’s try on some definitions for size. Here’s one:
P is a naturalist =def. P is an atheist who believes that all that exists is discoverable by the scientific method.
This definition is bad for several reasons. To begin with, it isn’t clear that a Naturalist need be an atheist; why couldn’t they be a verificationist, or a Wittgensteinian? It seems, at first blush, sufficient that one not believe that “God exists” is a metaphysical truth, but then it also seems wrong to say that an agnostic can be a naturalist. An agnostic is agnostic with respect to supernatural entities, but a naturalist is not. So we’re left in a quandary with respect to the first half of our definition.
The second half doesn’t fair much better. Apart from the fact that scientists routinely commit themselves to the reality of entities which are beyond the scope of strictly empirical discoverability (such as the existence of alternative space-times in a multiverse), there is an puzzle involved in stating what, precisely, qualifies as scientifically discoverable. For instance, many of the fundamental entities in particle physics are not directly empirically observable (they are, in fact, often referred to as ‘unobservable entities’), but we have good reasons to think they exist based on the hypothetico-deductive method (i.e., we know what empirical effects they would have if they did exist, and we can verify those). However, that amounts to having good scientific and empirical motivation for believing in unobservable entities. Is it impossible to have good scientific and empirical motivation for believing in ghosts, or numbers, or God? W.V.O. Quine famously stated that if he saw any empirically justifiable motivation for belief in things like God, or the soul, he would happily accept them into his ontology. In fact, in a move motivated by his commitment to his Naturalized Epistemology, Quine did eventually come to accept the existence of certain abstract objects (namely, sets). Quine leaves us with two choices: either we say that even Quine wasn’t really a (metaphysical) Naturalist in the end, or we find a way to allow Naturalists to believe in things like numbers, moral values, aesthetic facts, and other things which we don’t usually think of as ‘Natural’ entities. I suggest we make use of the notion of scientific/empirical motivation; in other words, we should make room for Naturalists to work out an ontology motivated by a scientific view of the world. The only danger I foresee in that move is that if even belief in abstract objects can be scientifically motivated, it seems as though belief in God, or anything, might turn out to be possibly scientifically motivated. Nevertheless, let us consider a second definition:
P is a naturalist =def. P believes that “God exists,” interpreted as a metaphysical statement, is untrue, and that the only entities which exist are the entities to which the acceptance of a literal interpretation of science commits us.
The first half of this definition seems fine to me, so that’s some progress. The second half is problematic because it implies that constructive empiricists, for instance, are not naturalists; the constructive empiricist agrees with the scientific realist that the statements of science should be literally construed/interpreted, but that when we accept a scientific theory we commit ourselves only to (i) the observable entities posited by the theory, and (ii) the empirical adequacy of the theory. Since the constructive empiricist adopts an agnostic attitude towards unobservable entities, none of them would qualify as naturalists on the above definition. In fact, anyone who adopts any version of scientific anti-realism (including the model-dependent realism of Stephen Hawking and Leonard Mlodinow, or even structural realism) will be disqualified from the running for candidate naturalists.
Let’s try a third:
P is a naturalist =def. P believes that “God exists,” interpreted as a metaphysical statement, is untrue, and P believes in some of, and only, the entities to which a literal interpretation of science commits us.
A possible problem with this definition might be that it threatens to include solipsists (though it isn’t clear what in science, interpreted literally, would commit anyone to the existence of persons). Perhaps we should replace “entities to which the acceptance of a literal interpretation of science commits us” with something like “entities to which our best understanding of science commits us.” That might be problematic since what the best understanding of science is seems up for debate. Perhaps it should be changed to: “entities to which a legitimate interpretation of science commits us.”
P is a naturalist =def. P believes that “God exists,” interpreted as a metaphysical statement, is untrue; P believes in some of the entities to which a legitimate understanding of science commits us; P does not believe in any entities belief in which cannot be motivated by a scientific view of the world (with the possible exception of God – caveat in casu necessitas).
This definition isn’t obviously problematic. It looks to be about as good as I can do, off the top of my head. Note that if this definition is successful, then we have also found the definition of supernaturalism, since (obviously) the definition of naturalism and the definition of supernaturalism bear a symmetrical relation of dependence to one another. This still has some notable disadvantages, including that naturalists will not be able to justify believing in moral facts unless they can generate motivation for believing in them given the resources of a scientific worldview. However, those disadvantages may just come with the territory; they may be the disadvantages not of our definition, but of the philosophy of metaphysical naturalism.
One final note; the term ‘supernaturalism’ has a bit of a bad rep because it is popularly associated with things like ghosts, energies, auras, mind-reading, witchcraft and (for better or worse) a variety of religious beliefs. Because of this many philosophers have opted for using synonyms such as ‘ultra-mundane’ to refer to things like moral facts, possible worlds, necessary beings, et alia. I don’t much mind which term is used, but one advantage to retaining the use of the term ‘supernatural’ is that it helps focus our attempt to define ‘natural’ and its cognates. If we had to define the terms ‘natural’ and ‘ultra-mundane’ it might be less apparent that whatever qualifies as unnatural is going to qualify as ultra-mundane, and vice versa.
 W.V.O. Quine, “Two Dogmas of Empiricism,” in The Philosophical Review vol. 60, no.1 (1951): 20-43.
 For more see: Stephen Laurence and Eric Margolis, “Concepts and Cognitive Science,” in Concepts: Core Readings (1999): 3-81.
 A verificationist, I mean, ‘about’ Theism.