[...] reductionism is not so much a positive hypothesis, as the absence of belief—in particular, disbelief in a form of the Mind Projection Fallacy. [...] we use entirely different models to understand the aerodynamics of a 747 and a collision between gold nuclei in the Relativistic Heavy Ion Collider. A computer modeling the aerodynamics of a 747 may not contain a single token, a single bit of RAM, that represents a quark. So is the 747 made of something other than quarks? No, you're just modeling it with representational elements that do not have a one-to-one correspondence with the quarks of the 747. The map is not the territory. [...] As the saying goes, "The map is not the territory, but you can't fold up the territory and put it in your glove compartment." Sometimes you need a smaller map to fit in a more cramped glove compartment—but this does not change the territory. The scale of a map is not a fact about the territory, it's a fact about the map.
To build a fully accurate model of the 747, it is not necessary, in principle, for the model to contain explicit descriptions of things like airflow and lift. There does not have to be a single token, a single bit of RAM, that corresponds to the position of the wings. It is possible, in principle, to build an accurate model of the 747 that makes no mention of anything except elementary particle fields and fundamental forces.
"What?" cries the antireductionist. "Are you telling me the 747 doesn't really have wings? I can see the wings right there!"
The notion here is a subtle one. It's not just the notion that an object can have different descriptions at different levels.
It's the notion that "having different descriptions at different levels" is itself something you say that belongs in the realm of Talking About Maps, not the realm of Talking About Territory.
It's not that the airplane itself, the laws of physics themselves, use different descriptions at different levels—as yonder artillery gunner thought. Rather we, for our convenience, use different simplified models at different levels.
So when your mind simultaneously believes explicit descriptions of many different levels, and believes explicit rules for transiting between levels, as part of an efficient combined model, it feels like you are seeing a system that is made of different level descriptions and their rules for interaction.
But this is just the brain trying to be efficiently compress an object that it cannot remotely begin to model on a fundamental level. The airplane is too large. Even a hydrogen atom would be too large. Quark-to-quark interactions are insanely intractable. You can't handle the truth.
But the way physics really works, as far as we can tell, is that there is only the most basic level—the elementary particle fields and fundamental forces. You can't handle the raw truth, but reality can handle it without the slightest simplification. (I wish I knew where Reality got its computing power.)
The laws of physics do not contain distinct additional causal entities that correspond to lift or airplane wings, the way that the mind of an engineer contains distinct additional cognitive entities that correspond to lift or airplane wings.
This, as I see it, is the thesis of reductionism. Reductionism is not a positive belief, but rather, a disbelief that the higher levels of simplified multilevel models are out there in the territory. Understanding this on a gut level dissolves the question of "How can you say the airplane doesn't really have wings, when I can see the wings right there?" The critical words are really and see." -- Yudkowsky (http://lesswrong.com/lw/on/reductionism/)
DanielLC reply to another comment: "One minor quibble; how do we know there is any most basic level?". Levels are an attribute of the map. The territory only has one level. Its only level is the most basic one. Let's consider a fractal. The Mandelbrot set can be made by taking the union of infinitely many iterations. You could think of each additional iteration as a better map. That being said, either a point is in the Mandelbrot set or it is not. The set itself only has one level.