I think one ought to think about reductionism slightly separately from the particulars of the universe we actually live in. I think of it as rather like the opposite of a curiosity-stopper - instead of assuming that everything is ontologically basic and doesn't have underlying parts, we should assume that there may be underlying parts, and go look for them. Of course in our own universe that approach has been exceptionally fruitful.
The other part that works well is Occam's razor - the simplest explanation of any data set is not only the most lightweight way of explaining the facts, it's also the optimum way of expressing your state of ignorance as well. The simplest explanation is also the most compact way of explaining what you do know. That again arises purely out of the nature of information, and would be true in any universe, not just the noticeably elegant one we actually live in.
On the other hand, there may well be a final set of underlying parts that experiment actually points to, and there's nothing wrong with that as long as it covers your experimental data.
I have read the sequences on reductionism and quantum physics some time ago now and I was hoping for some help finding the right places to go back and re-read there to address a question. If the way I describe my question reveals other ignorance on my part, please feel free to add comments above and beyond sequence references.
When trying to talk a little about reductionism, most (non-LW) people I speak to seem to want to play the following game:
What's an airplane made out of? Molecules and atoms that comprise materials like metal, plastic, glass, rubber, etc. What are molecules and atoms made out of? Well, molecules are collections of atoms bonded together, and atoms are made up of three basic particles: protons, neutrons, and electrons. What are basic particles made out of? Well, here things start to get a little more dicey. Some of the basic particles are known to be made up of even smaller sub-atomic elementary particles, such as quarks, leptons, and bosons. Some of the basic particles are examples of these elementary particles. Well, what's an elementary particle made of? Well, that's a pretty tough one, but basically there's this sort of fabric of stuff underlying everything called quantum amplitude, and a certain configuration of quantum amplitude corresponds to an elementary particle. So what's quantum amplitude made up of? Well, I'm not sure that is a coherent question. It just sort of is. A ha! I've caught you. So ultimately way down at the bottom of it all, you're telling me that some something "just exists" (i.e. is ontologically basic). But then why do you call it reductionism if it ultimately boils down to a Platonistic ideal of quantum amplitude (no one actually says this, but it's my translation of the objections I tend to face).
Is it more or less right to say that, as far as we can tell, the only reasonable thing to which we can attribute ontologically basic status is quantum amplitude? Given that amplitude is a mathematical device that allows calculation of probability, and probability describes my ignorance about the world (i.e. my best guess as to what the territory is, as opposed to the actual territory), do we view quantum amplitude as some sort of pre-states-of-knowledge concept? How does that mesh up with "what is an elementary particle made of?" It makes me want to call it "the residue of intrinsic uncertainty" or something, but why would that "really exist?" I don't think that my uncertainty about tomorrow's weather "really exists" in any Platonistic way.
How do you explain to people that reductionism = (reduce until you have good reason not to); am I even right to say that or is this a harmful oversimplification?