>But this is yet another argument over definition or a value judgement. I have spent most of my life studying math and science, and yet reading Dostoyevsky has given me much more abundant insight into my life than anything science ever taught me.

And you think there is no science of people? You think that just because our current understanding of psychology is fairly hazy, it must remain that way forever?

Or worse: do you think that there is nothing psychological about what happens when you read Dostoyevsky, nothing that a science of human beings can say about your experience, even in principle? How much are you willing to multiply "irreducibility"? Until it covers your whole worldview like a cancer?

>As to non-naturalist ethics, I see absolutely no problem with concepts that are irreducible to atoms. Neither is math, even though math was created/discovered by humans, which live in this universe and are composed of atoms.

But of course math is reducible to atoms. Or, if that seems a strong statement, math is not irreducible by default: Platonism is not the only viable philosophy of mathematics, such that taking any other position generates an immediate internal (within math) or external (with our other knowledge of the world) contradiction. Both constructivism and formalism yield neat interpretations of math as certain kinds of computations being done within human minds.

>In short, I don't think you can reduce, say, literature, to atoms and forces even though the author and the reader are composed of atoms, and the reading process involves photons hitting receptors that start a chemical reaction in the retina. Doing so will teach us nothing of value about literature.

See above regarding psychology. Since atoms and forces make up the author and reader, we can use our theories about those to zero in on correct theories about the author and the reader, thus gaining an understanding of what the reader is experiencing and how he is playing an active part in reading a book. Certainly science can teach us more about literature!

You seem to be confusing naturalism with what's been called "greedy reductionism", which is a metaphilosophical - and therefore damn near nonsensical - view, namely that only the most ontologically basic level of description actually matters. In fact, if we don't employ our more abstract, high-level concepts like "human being" and "Dostoyevsky novel" and "armchair", we completely fail to make accurate predictions about the behavior of the very much natural world around us.

As long as these higher-level, and yet closer-to-experience, concepts possess causal power - as long as they make our predictions better and our counterfactual models more accurate upon interventional testing - we must use them. Your thoughts and feelings are utterly essential components of a naturalistic explanation of the world.

They are also, ultimately, made of particles, joules, and bits.

Likewise to such mental activities as math and morality.

>A shovel is more useful than a pen for digging holes, but who says digging holes is more worthwhile than writing? Even if you think it is, you cannot prove it scientifically, because science can say nothing about values, only point at relationships between causes and outcomes.

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

And, presto change-o, when speaking of a specific agent, I can certainly say whether digging a hole is more worthwhile than writing, or the other way around. Again: a scientist who fails to predict that I (to take the personal example) would rather read and write than dig a hole is simply inaccurate.

>That doesn't follow. First, I don't know how science can teach us that something is "wrong". I don't know by what scientific or mathematical mechanism you can ever make the jump from the "is" to the "ought" -- at the very best science can teach us that if we seek a certain outcome, we should take a certain action, but can it tell us what outcome we should seek?

Which shows a nasty hole in your philosophical education, but regrettably an all-too-common one: you were never told ethical naturalism (http://plato.stanford.edu/entries/naturalism-moral/) exists.

>But it's even worse than that because there is another philosophical, unscientific mediating factor here, which is "understanding". Being able to describe the universe and understanding it are two very different things. We can know without understanding.

You seem to be just pushing words around, but may I venture to guess that you mean to differentiate between discriminative "describing" and causal-counterfactual "understanding"?

>In fact, I can even give the last statement a more mathematical facet: that a process B reduces to a more fundamental process A, does not guarantee that fully knowing A will let us predict B because of intractability.

Certainly. In fact, this is the nature of reduction: to reduce B < A implies that B happens as a specific instance of A, which often means that B occupies a tiny corner of A's parameter space, and almost always means that B's parameter space is much smaller than that of A. For example, in describing gasses, we can describe the precise velocities of every single molecule (the more-reduced theory), or we can measure the temperature of the gas as a whole (the less-reduced, higher-level theory). The intractability is often both computational and informational.

This merely reinforces what I said above, which is that we need the higher-level concepts to correctly understand, interpret, and predict the world. Concepts like "human being", "sunset", "profundity", "confusion", and (just for the hell of it) "love" are also utterly inescapable components of a naturalistic worldview.

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