**Note: I recently participated in the National Novel Writing Month, and this post is an adaptation of a chapter from that project, so it doesn't quite read like a standard post. A more technical summary of reductionism can be found on Less Wrong's reductionism sequence, and specifically this page.**
Plenty of materials have unique properties, but they're not fundamentally unique. The unique properties are traceable back to small differences in the underlying arrangement of matter- number of valence electrons in the outermost shell, or atomic weight, or electronegativity, etc. But the same structure is underpinning all of it. Materials aren't fundamentally complex, they're fundamentally simple- made up of electrons, neutrons, and protons. That's it.
Reality isn't fractal; the huge differences we see on the macro level don't translate to huge differences on the atomic level. You can zoom in farther and farther, and eventually you come to a level where everything is made out of the same basic stuff, and it's just the arrangement of that stuff that makes all the difference.
Thoughts and desires aren't fundamentally complex either. Sure, they're big and complicated at a macro level, but if you zoom in far enough, it's all electrical charges running around in your brain. There's no substance to them, no form, except that our bodies- our hardware- interpret them to mean something. Thoughts aren't real things outside of the environment of your own brain. Humans are really good at interpreting the thoughts of other humans because we share that context- our brains know about thoughts because our brains have thoughts. But there isn't some 'thought' form that actually exists in physical reality.
Consider the following thought experiment: you write the word 'blue' on a piece of paper, and when you place a rock down on the paper, the rock turns blue. Then, if you put the rock down on another paper with the word 'green' written on it, the rock turns green. What would this experimental result mean for your belief system?
For me, it would utterly destroy my belief system, because this result is fundamentally absurd. The words 'blue' and 'green' don't actually mean anything on their own. Green and blue are fundamental things, but the words 'green' and 'blue' aren't. From the rock's point of view- I can't believe I just said that, since rocks obviously have no point of view- they're just a collection of ink molecules spread out over the paper's surface. They only mean something in the context of the language they're written in- only people who read and speak english would know what those words meant.
If we saw this experimental result, there's only three possibilities I could think of to explain it. Either the rock does speak english, or someone who speaks english is controlling the rock, or 'green' and 'blue' are real things. Fundamental things. Things on which the laws of nature act. Obviously the words 'green' and 'blue' aren't real things outside of the english language, but thoughts...
And that's why religion is defeated by reductionism. Because if what religion claims is true, then thoughts are something other than neurons firing. And if that's true, then the brain is just an interface for something much bigger, much more complex. It's just a piece of machinery that interprets the form of thoughts into electrical signals capable of controlling material bodies.
Now you might ask, what's so wrong with that? Isn't that what people mean when they talk about souls?
Well, that's not actually how brains work. If you damage one part of the brain, the victim is left unable to speak. If you damage another, he falls asleep without warning. If you stimulate another part with electrodes, the test subject literally becomes a sociopath, no longer hindered by moral attachments. In the real world, the brain affects thoughts, not the other way around. It's not that the brain is some conduit that allows thoughts through, and brain damage means those thoughts come through muddled or somehow less clear. It's that damaging the brain fundamentally alters those thoughts. It alters the way we think, not just the output. Sociopaths aren't just outputting actions as if they have no conscience, they're thinking and making decisions as if their conscience doesn't exist.
More fundamentally, physics only acts on particles, not on forms. Physics doesn't care that you've assembled the particles into the shape of an airplane- it just goes ahead and applies gravity, strong force, weak force, and electromagnetism to each and every particle, and calculates the interaction of each particle with each neighboring particle, and the result is a solid object that flies through the air if you go fast enough. The form is important to us, but it's not important to physics.
But even if the soul was a thing, and even if the brain was acting purely as an interface between the mysterious soul and the physical world, we still have a problem. We've now posited the existence of a fundamentally complex thing- either that, or we're positing some simple “soulitrons” that combine to make up a soul. But the whole reason we wanted to invoke a soul in the first place was so that we could get away from the idea that all humans are is a complex arrangement of simple things! If we're willing to say souls are complex groups of soulitrons, then why aren't we willing to say that human behavior is better explained as being complex groups of electrons, protons, and neutrons?
At this point, the religious may raise an objection: I've already said that's it's possible someone who speaks english is controlling the metaphorical rock. What about God? Surely you can't rule out the mystery of God as the explanation of a soul?
There's really two problems with this. First, mysterious answers to mysterious questions simply aren't helpful. And second, now we're positing God as a fundamentally complex thing. What is God made of? Goditrons? God is infinitely more complex than we are. We can't posit God as a “necessary being” as a solution to the fundamental complexity problem- or, notably, the first mover problem- because the idea of God is way more complicated than, well, pretty much any other explanation.