This is the core of his argument, and it is entirely unfounded.
It's not founded, but neither is it explicitly contradicted.
While nothing in chemistry is known to contradict the laws of physics, we have yet to conclusively show that chemistry can indeed be entirely explained by the laws of physics. It is still possible that there are laws of chemistry that cannot be derived from a complete set of laws of physics correctly and fully applied.
Occam's razor favors the idea that behaviors in chemistry we cannot currently predict directly from physics are results of our not-yet-complete understanding of physics and/or our lack of sufficient computational resources applied to the question. Postulating an additional "level" of rules that can't be derived from physics is not currently necessary to explain features of chemistry tat are not yet reduced to physics. But that's not the same as saying another level is ruled out.
Postulating an additional "level" of rules that can't be derived from physics is not currently necessary to explain features of chemistry tat are not yet reduced to physics. But that's not the same as saying another level is ruled out.
Physics is better than that. Lets say that there is another level of rules required to reduce chemistry. Then these rules are about physical systems in general, and lower-level than chemistry. We have found new laws of physics!
If they can't be derived from physics now then that doesn't mean physics won't figure them out in the future.
Concretizing the abstract is an interesting blog post in that it makes a relatively cogent argument for non-reductionism. While I don't agree with it, I found it useful in that it helped me better understand how intelligent non-reductionists think. It also helped clarify to me an old distinction, that of philosophers versus engineers.
I find this interesting in the way that smart people are likely to disagree with the correct interpretation of some of its claims - while others would say the post is worshipping the mysterious, others would say that it's just making reasonable cautions about the inherent methodological limitations of a certain approach. One might even think that it's essentially making a similar point as Eliezer's warning about floating beliefs, and therefore to agree with the Sequences. The caution of "beware of thinking that your abstractions say everything that there is to be said about something" is a reasonable one, and people do clearly make that mistake sometimes.
I expect that part of what influences how plausible one finds this argument depends on whether one has more of an "engineer's mindset" or a "philosopher's mindset". Somebody with an engineer's mindset will think that "yes, the abstractions we use might be imperfect, but what else do you propose we use? They're still the best tool for accomplishing stuff, and anything else is just philosophcial nonsense that isn't grounded in anything". Whereas the philosopher is less interested in using their knowledge to "accomplish stuff", and more interested in the ideas and their implications themselves.
As an aside, this distinction might be part of the reason why we have so many computer or hard science folks on this site. Partially it's because Eliezer used a lot of CS jargon in writing the Sequences, but probably also because the Sequences, while philosophical in nature, are also very focused on practical results and getting empirical predictions out of your beliefs.
Looking at what we could use this distinction for (and thus taking an engineer's mindset) some people here have mentioned getting an "ick" reaction from religious people, just due to those people having strong false beliefs. I think that, combined with properly understanding the emotional basis of religion, an understanding of the philosopher / engineer distinction can help avoid that reaction. Our values determine our beliefs, and there are plenty of religious people who aren't stupid, crazy, or anything like that. They might simply be philosophers instead of engineers, or they might be engineers who are more interested in the instrumental benefits of religion than the rather marginal benefits of x-rationality. (Amusingly, such a "religious engineer" might justifiably consider our obsession with "truth" as just an odd philosophical pursuit.)