Here is the idea of naturalness that I like the most:

A fact F is natural if and only if either (i) F is brutely natural or (ii) F explains (= substantively contributes to the best explanation of) at least one natural fact.

I'll explain how the idea works, and then I'll explain why I like it.

I've written about this idea in public places before, but I want to take another crack at it here, and I think that what I'll write today is probably going to be an improvement on things I've said elsewhere.

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There is a core set of facts that it is the business of natural science to explain. As is often said, "science begins in wonder," i.e., natural science is a form of inquiry that begins with an inquirer who is wondering why a certain range of facts obtain. The facts in that range are the brutely natural facts.

To illustrate, consider the following familiar example. Long ago, it was noticed that when a ship heads out toward the open ocean, the ship appears to people on shore to descend, as if it were sinking, until eventually even its topmost sail disappears. As soon as people started wondering why that happens, and began to consider and investigate hypotheses to explain it, they were doing natural science. The fact that that happens with ships is a paradigm example of what I'd like to call a brutely natural fact.

Because brutely natural facts are natural facts, they are among the facts that natural science properly investigates and seeks to explain. In other words, all brutely natural facts fall within the purview of natural science. (But not all facts in the purview of natural science are brutely natural.)

There is a

Negative condition: For any given brutely natural fact F, the fact that F falls within the purview of natural science is independent of whether F explains any other natural facts.

This means that if F is a brutely natural fact, then F can be rightly recognized as a natural fact even before F is shown to have any explanatory utility. Take the phenomenon of the disappearing ships: Early natural scientists investigated and tried to explain the fact that ships disappear when they head out to sea because they saw that that fact called for natural-scientific explanation in itself, as it were, and not because it was needed or thought to be needed to explain any further facts.

Beyond that negative condition, there will be various ways of spelling out a positive understanding of the brutely natural. On this point, we have a lot of options and, for reasons I'll explain momentarily, it might not matter that much which option we choose. But I'll mention six of the options here.

Before I do that, I need to define something. Let's say that a fact F is treated as brutely natural by a given natural scientist S if and only if (a) S makes it her business to explain F, and (b) S does so for reasons that are independent of whether F explains any other natural facts.

With that definition in place, here are the six options I'll offer for consideration:

The actual-history criterion: A fact F is brutely natural if and only if F is the sort of fact that the earliest natural scientists treated as brutely natural.

The state-of-the-art criterion: A fact F is brutely natural if and only if F is the sort of fact that natural scientists today treat as brutely natural.

The correctness criterion: A fact F is brutely natural if and only if F is the sort of fact that ought to be treated by natural scientists as brutely natural.

The individual-empirical criterion: A fact F is brutely natural for S if and only if F has been observed by S.

The collective-empirical criterion: A fact F is brutely natural for S if and only if S is part of a scientific community that has observed F.

The relativist criterion: A fact F is brutely natural, relative to a given actual or hypothetical natural-scientific practice P, if and only if practitioners of P treat F as brutely natural.

Some of these criteria (the first three) will allow us to talk about a fact being brutely natural without qualification, while others (the second three) will require qualification.

There are many (indefinitely many) further criteria that could be considered here. 

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According to the idea of the natural that I put at the top of this post, the natural realm is populated by (a) brutely natural facts, and (b) further facts that substantively contribute to the best explanations of those brutely natural facts, and (c) still-further facts that substantively contribute to the best explanations of the further facts mentioned in (b), and so on.

I claimed above that it might not matter very much what criterion of the brutely natural we choose. Here's why. Consider two facts:

F1: Ships seem to disappear as they get further away,

and 

F2: Our planet is round.

If we choose the actual-history criterion, F1 will be a brutely natural fact. F2 presumably won't be brutely natural (since the earliest natural scientists didn't even know about F2) but will nevertheless get to be a natural fact by virtue of the fact that it substantively contributes to (indeed, is the centerpiece of) the best explanation of F1.

If we choose the state-of-the-art criterion, F1 and F2 might both count as brutely natural (hence natural). That is, it may be that present-day scientists treat both the disappearing ships phenomenon and the roundness of our planet as facts that, in and of themselves, call for natural-scientific investigation.

So, although the actual-history criterion and the state-of-the-art criterion may have different implications about whether F2 is brutely natural, they will likely converge on the implication that F2 is, in any event, natural.

I think this is how things will generally go. I think the actual-history criterion and the state-of-the-art criterion will generally disagree about which facts are brutely natural but will generally agree about which facts are natural. Further, I think most of the different positive criteria of the brutely natural that might be seriously considered will be like that. There will be broad convergence about what is and isn't in the natural realm.

I shouldn't overstate the present point. There are ways of designing a criterion of the brutely natural which are such that one ends up with (what might be called) a deviant natural realm.

To illustrate, suppose it is really the case that

F3: God exists.

Suppose it is also the case that God does not interact with any physical objects, and in general leaves no empirically detectable trace for us to find; God is a causally impotent "thought thinking itself," such that F3 does not substantively contribute to the best explanation of F1, or F2, or any other facts needing explanation.

In that case, if we were to adopt some criterion of the brutely natural that includes F3, we would end up with a natural realm that differs, in terms of its population, from the natural realm that we'll end up with if we choose to adopt, say, the state-of-the-art criterion (because the state-of-the-art criterion will never result in F3 being included in the natural realm). 

So, our selection of a criterion of the brutely natural does matter to some degree. It matters somewhat. If one has a weird idea of which facts get to be brutely natural, then one will end up with a weird idea of which facts get to be natural. That said, I suspect that most of the criteria of brute naturalness that will be regarded by most of us as reasonable will end up yielding similar, or even identical, pictures of the population of the natural realm. 

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Here's what I like about this way of thinking about the natural. First, it can be used to capture what is attractive (or what I, for one, find attractive) about moral non-naturalism. Second, it can be used to capture what is particularly problematic about moral non-naturalism.

The following claims all seem endorsable to me: (1) There are moral facts; (2) on any reasonable criterion of the brutely natural, moral facts will not count as brutely natural; (3) moral facts do not substantively contribute to the best explanation of any brutely natural facts or any other natural facts. From these points, I conclude, via the view of the natural that I have outlined in this post, that moral facts exist but are not natural facts, which is the core commitment of the version of moral non-naturalism that I want to be associated with.

This form of moral non-naturalism is attractive to me, but I also see it as problematic, because it engenders certain kinds of justifiable suspicions and worries about moral reality.

Many philosophers in the broad tradition of moral non-naturalism have tried to find "partners in crime" or "companions in innocence" for non-natural moral facts. They have observed, for example, that mathematical facts seem to be causally impotent in a way that resembles the causal impotence of moral facts. The wrongness of torture has never collided with a billiard ball, but 2+2=4 has never collided with a billiard ball, either. So if moral facts' causal impotence is supposed to make their inclusion in our ontology problematic, then inclusion of mathematical facts in our ontology should be equally problematic—or so goes a common line of reasoning.

But that line of reasoning fails to home in on what's most worrying about morality, I think. The reason why morality as it is understood from a non-naturalist perspective is particularly problematic has little to do with the causal impotence of moral facts, and much to do with the fact that moral facts do not explain anything in the natural world.

It is on that point that moral facts differ from mathematical facts. Whether or not mathematical reality is in any way causal, mathematical facts substantively contribute to the best explanations of natural facts. For example, mathematical facts are crucial in explanations of why our planet is round; why birds in flight rarely collide; why arched bridges stay upright, etc. Mathematical facts are, in this specific way, natural facts, according to the view of the natural that I'm laying out here.

Moral facts, by contrast, do not do any such explanatory work (I claim). I believe that there are no explanations of natural facts that can be improved by inclusion of moral facts, i.e., moral facts do not substantively contribute to any such explanations. That's why natural scientists need training in mathematics but not in ethics, etc.

In general, I think, the following will be a mostly good rule:

Knowers as natural scientists: S knows that p only if either (a) the fact that p is brutely natural, or (b) the fact that p substantively contributes to the best explanation of a natural fact, or (c) there is some natural fact that entails p.

I think that, if we are moral non-naturalists, and if we don't want to be moral skeptics, then we have to say that the above rule has at least one exception, namely an exception for moral knowledge.

Making that exception is a cost. The above rule seems good and it is a shame to have to break it. Additionally, it will be necessary to find a way to make an exception to the above rule without opening the floodgates, i.e., without giving license to everyone who wants to claim to have unscientific knowledge (angels, astrology, what have you) and this may be hard work. These are reasons why moral non-naturalism should be regarded as particularly problematic.

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