Check out the following article, by Marko Vojinovic:
A concise yet rigorous analysis of the concept of reductionism, the idea that all natural laws can be reduced to the fundamental laws of physics. A classical example is how chemical interactions between substances can be reduced to the quantum mechanics describing their molecules. The article is a pleasure to read, accessible to laymen, yet not dumbed down so as to loose it’s substance.
I was a little bit frustrated by the absence of any treatement of what I expected to be the usual candidates for the question “does reductionism always hold?”: Can psychology be reduced to neurochemistry? Can history be reduced to population dynamics?
Instead, all the examples he provides are cases where reductionism is intuitively expected, like reducing fluid mechanics to Netownian mechanics or reducing cosmology to particle physics (I’m oversimplifying the terms used for clarity and brevity’s sake).
More importantly, the author fails to mention some ideas by M. Gu et al  who provide evidence of emergent behavior in Ising lattices. They prove this behavior by showing that some macroscopic properties of the lattices are undecidable when considered as computations derived from its microscopic configuration. Since undecidablity in Turing machines (and therefore any finite calculation process) is a direct consequence (arguably a corollary) of Godel’s incompleteness theorem, Gu et al’s proof is just a more rigorous version of Dr Vojinovic statement that Godel’s theorem is evidence of strong emergent behavior in our universe.
Finally, I really wish that towards the very end, he didn’t go in the direction of “Godel’s incompleteness theorem as proof of the Mystical”. This idea has been put forth before, more than once, and most logicians would probably disapprove. Moreover, it would make the article open to polemic discussions, distracting debaters from the less controversial but still significant idea that Gödel’s theorem implies emergentism. (By the way, why hasn’t the incompleteness theorem been hijacked by the religious apologetics crowd yet?)
It it is interesting to note that the impossibility of a theory of everything is presented by Vojinovic as potential evidence for the existence of God (“as giving up reductionism generally weakens the arguments that a physicalist may have against dualism, a naturalist against the supernatural, an atheist against religion, etc.” ) . Marcelo Gleiser, in his book “A tear at the edge of creation” drew the exact opposite conclusion. He sees that the absence of a unifying theory of the universe as evidence of a radical from of atheism, were not only is there no personal Judeo-Christian deity, but there is not even a central set of rules governing the behavior of the Universe. He arrives at this conclusion from the idea that the search for a single theory of everything (in the form of a physical grand unification theory – GUT) is a holdover from monotheism, and that there is no a priori reason to believe that there will ever be a theory of everything once we let go of the idea of prime mover/first cause/monotheistic deity.
Every now and then, the question of reductionism is raised in philosophy of science: whether or not various sciences can be theoretically reduced to lower-level sciences. The answer to this question can have far-reaching consequences for our understanding of science both as a human activity and as our vehicle to gain knowledge about reality. From both ontological and epistemological perspectives, the crucial question is: are all real-world phenomena that we can observe “ultimately explainable” in terms of fundamental physics? What one typically imagines is something like a tower of science, where each high-level discipline can to be reduced to a lower-level one: economics to sociology to psychology to neurology to biology to biochemistry to chemistry to molecular physics to fundamental physics. Is such a chain of reductions possible, or desirable, or necessary, or important, or obvious, or tautological, or implicit in our very concept of science?
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