> You think that just because our current understanding of psychology is fairly hazy, it must remain that way forever?

Sure but will that knowledge be so predictive as to be truly essentialist? After all, we can't provide tractably predictive models for even n-body systems for pretty small values of n, so I doubt we will for people. BTW, I believe that those answers we will be able to prove and reduce with any measure of definiteness will only tell us things we already know (or "know").

> Both constructivism and formalism yield neat interpretations of math as certain kinds of computations being done within human minds.

Ah, but here I think I can convince you, and make a much more powerful point than the one regarding intractability. Consider the universal Turing machine and its approximate physical manifestations. Whether or not it is truly universal is an open question, but most assume that it is, yet they are not perturbed by the following result: our universe may contain a machine that can simulate not only this universe but any universe, i.e. there are objects that can arise within our physical universe that are more universal than our universe itself. Can the simulated universe be reduced to the atoms and forces of the one containing the machine? Most people will say no, as universal computation breaks reduction. It is more general than the mechanism implementing it, with possibly more degrees of freedom.

> would rather read and write than dig a hole is simply inaccurate.

But the question is a different one. I wasn't asking what you want to do or even what you will do, but what you should do. The definition of "should" can live, if you will, as a concept within the Turing machine.

> This displays the funny post-religious misconception that values are relative to "the Universe" rather than to agents. This is incorrect.

That does not follow from what I said at all. I didn't say the universe or "morality" necessarily dictates an answer. What I said was that the answer -- even if it is subjective, if it exists at all -- does not necessarily follow the laws that gave rise the the being asking the question. Universal computation etc.

> you were never told ethical naturalism exists.

Again, I think there's a disagreement on definitions. It seems like naturalist ethics seems to say "if we know how people behave, we can deduce how they'll program their Turing machines (and they will always program them in a similar way), and we can therefore say something about the programs themselves", while non-naturalist ethics simply studies the "computer science" of those programs. I think both approaches are complementary, rather than contradictory, and really discuss different things, even if they give them the same name.

> B's parameter space is much smaller than that of A

So what? A's entire parameter space cannot be practically determined either (even if A is well understood), and the emergent property A may well require that in order to be explained in terms of B. For example, to explain psychology in terms of particle physics, we may need to understand the interactions of, say, 1e15 bodies. Since we cannot do that, we cannot explain A in terms of B.

Also, universal computation may arbitrarily increase (or reduce) degrees of freedom.

> It's just "irreducibility", or in other words, metaphysical handwaving and magical thinking, that aren't.

Let me make clear that I am not in any way opposed to the naturalist worldview. In fact I fully and utterly subscribe to it, just as I fully and utterly subscribe to non-naturalism. I see absolutely no contradiction between the two, just as I see no contradiction between simulating a universe with different physics in a computer that exists in ours.

When I say something is irreducible, I simply mean you cannot construct a useful model for it in terms of a lower abstraction -- not that it is not an emergent property of that lower abstraction; obviously, it is (unless it's a simulation run by universal computation).

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Of course, there is one glaring bug in my appeal to universal computation, and that is the composition not of the machines but of the programmers. Since there is no free will in the universe, the programmers are then deterministic, and therefore the programs themselves. Still, even though this greatly reduces the space of possible programs (and makes the naturalist approach to studying the programs sensible) I think that few people will consider this (i.e. a deterministic programmer) a useful reduction.

In any case, I think everyone will agree that the programs can be studied in isolation of the universe that created the programmers, and that doing so may be useful.