The late David Malet Armstrong has a serious claim to being Australia's greatest philosopher. His life work is summed up in his Sketch for a Systematic Metaphysics (Oxford UP, 2010). It is from the Introduction to this slim volume that I draw the following précis of his naturalism.
Armstrong on Naturalism
1. Naturalism for Armstrong is the thesis that "all that exists is the space-time world . . . ." The space-time world is the physical world. The thesis, then, is that reality is exhausted by the physical world.
2. Naturalism is an assumption: it is assumed to be true.
3. Armstrong admits that he has no argument for naturalism except that it is a position that many would accept, both philosophers and non-philosophers. There is no philosophical reasoning whereby one could prove that any metaphysical scheme, including naturalism, is correct. To think otherwise is "folly." I agree. One cannot prove naturalism or any form of anti-naturalism.
4. Armstrong also describes naturalism as an "hypothesis," one that many would accept as plausible. "The space-time entity seems obviously to exist. Other suggested beings seem much more hypothetical." (1)
5. Though naturalism cannot be proven, one can attempt to develop it into a coherent vision of the fundamental structure of the world or of the general nature of things, a vision (his word) that can then be put into competition with other visions. The development of a vision of things will involve argumentation but also bare assertion. "I argue where I can, but at times I simply assert."
6. The exclusion of so-called abstract entities or abstract objects such as mathematical sets, unexemplified universals, and numbers from the roster of the real is because of their lack of causal power. What causal role could they play? "And if they play no causal role it is hard to see how we can have good reasons for thinking that they exist." (2)
We ought to distinguish between
A. To exist is to be capable of entering into causal relations
B. We have no good reasons for postulating entities that are incapable of entering into causal relations.
Armstrong affirms (B), but he also seems committed to (A) since (A) is entailed by naturalism. Naturalism is the view that reality is exhausted by the space-time world, the view that nothing exists except what exists in the space-time world. Given that the space-time world is a world of causal interactions, it follows that all and only that which is causally active/passive exists. If you are an Armstrongian naturalist, then you cannot posit such causally inert entities as mathematical sets even if there are some good reasons for postulating them.
7. The space-time world, the physical world, is Wilfrid Sellars' world of the scientific image, not that of the manifest image. It is therefore the task of physics, or perhaps total natural science, to tell us what the physical world, and thus all of reality, is like.
8. Now if naturalism is true and physics (or total science) informs us as to nature's laws and properties, why do we need metaphysics? Why isn't physics all the metaphysics we need? Why shouldn't we embrace both the ontological thesis of naturalism and the epistemological thesis of scientism? After all, they seem to go together. If all that exists is the system of space-time-matter, and physics tells us what there is to know about it, then what room is there for metaphysics?
There is room for metaphysics according to Armstrong because we need a systematic account of such topic-neutral notions as cause, class, property, relation, quality, kind, resemblance, quantity, number, substance, fact, truth, law of nature, power, and others.
For example, common experience and the sciences inform us as to what causes what, but not as to what causation is. What is causation? What distinguishes a causal from a noncausal event sequence? Is causation 'in the objects' mere regular succession as Hume thought (or as Hume is often taken to have thought)? Or is there more to it? And what is that more? Does the cause produce the effect? Does the cause bring the effect into existence? Can x cause y even if the x-y sequence does not instantiate any regularity? What are the relata of the causal relation? Can a substance be a causal relatum? Is causation a relation at all? And so on. All of these are questions in metaphysics (ontology) for Armstrong.
So a thoroughgoing naturalist who restricts the real to the space-time system needn't embrace scientism; he can maintain that there is room for metaphysics in one sense of that ancient word: not an inquiry into what is beyond the physical or natural, but an inquiry into the deepest and most pervasive structures of the natural. (Armstrong does not mention scientism or make the point I just made, but it clearly follows from what he says.
Why I am Not a Naturalist (A Brief Sketch)
Armstrong is surely right that one cannot prove naturalism. Equally, one cannot disprove it. But there reasons that make its rejection reasonable.
There are questions that naturalism cannot satisfactorily answer. Among them: Why does anything at all exist? Or, more precisely, why does anything contingent at all exist? The space-time system exists and it exists contingently -- there is no logical or metaphysical necessity that there be a space-time system at all, or the precise one that we find ourselves in. But the space-time entity, as Armstrong calls it, lacks the resources to explain its own existence. I won't argue this here, but I have in other places. There are also good reasons to reject the suggestion that the space-time system exists as a matter of brute fact.
Deeper than the question, Why does anything at all exist? is the question, What is it for any contingent thing to exist? Does Armstrong have an answer for this question? Surely it is a central question of metaphysics. We cannot decide what exists or why anything exists unless we know what it is for something to exist. He doesn't deal with it as far as I know, but he does seem to have an implicit answer, (A) above which can also be formulated as follows:
A*. For any x, x exists iff x is possibly such as to be either a cause or an effect.
A**. For any x, x exists iff x has the power to bring about a change in itself or in another or the liability to have a change brought about in it.
But even if these biconditionals are true, they presuppose existence rather than accounting for it. A thing cannot have a causal power or a causal liability or stand in a relation unless it 'already' (logically speaking) exists. What makes a thing exist, therefore, cannot be its having a power or liability or its standing in a relation.
Long story short, A's naturalism has no satisfactory answer to either of my existence questions.
And then there are questions about mind, questions about consciousness, qualia, intentionality, reason, and the like. They notoriously resist naturalistic treatment. Armstrong, who is famous for his intellectual honesty, readily admits this:
I do not know how to refute the claim that intentionality is an irreducible phenomenon, a phenomenon that is something different from the physical processes in the brain. So in my philosophy of mind I face difficulties from the alleged qualia and from the phenomenon of intentionality that seem rather greater than anything I am aware of in the rest of my ontological scheme. (115)
That naturalism is not compelling is also evident from the fact that naturalists disagree bitterly among themselves as to what shape it should take. Some naturalists want to countenance abstracta while others are eliminativists about the mind.
But I don't reject naturalism simply because it does not have satisfactory answers to all the questions that need answering; I also reject it on the basis of all the experiences (mystical, religious, paranormal) that point to, though they do not prove, what William James calls the "reality of the unseen." Such experiences by themselves may not cut much ice, but in conjunction with an array of rigorous arguments against naturalism and an array of rigorous argments for some form or anti-naturalism, they play an important role in a cumulative case argument for the reasonableness of anti-naturalism.