The market process is coherent and indivisible. It is an indissoluble intertwinement of actions and reactions, of moves and countermoves. But the insufficiency of our mental abilities enjoins upon us the necessity of dividing it into parts and analyzing each of these parts separately. In resorting to such artificial cleavages we must never forget that the seemingly autonomous existence of these parts is an imaginart makeshift of our minds. These are only parts, that is, they cannot even be thought of as existing outside the structure of which they are parts. (Ludwig von Mises, Human Action, 333)While all of this is true of market processes as well as other complex processes -- whether brains, bodies, ecosystems, or other spontaneous social orders, such as the arts, science, or religion -- Mises fails to make yet another distinction that I think is necessary in making divisions, a distinction Plato makes in the Phaedrus: that the divisions must be made in the proper places. Like a good butcher, the cuts must be made at the joins, and not just willy-nilly.
This of course only begs the question of where the proper divisions are to be made.
A living cell is, on the one hand, indivisible and, on the other hand, full of distinct parts. One can identify a nucleus, endoplasmic reticulum, mitochondria, ribosomes, chromosomes, etc. Various processes can also be distinguished in a cell, from regulatory networks to protein-creation processes to metabolic cycles. All of these interact to create a self-organized and self-organizing network.
Where does one make these divisions in an economy? Some obvious divisions would seem to be the individuals involved, firms (which have organizational network hierarchies similar to cellular regulatory networks), and various sectors, including the financial sector, etc. But we can see that these are in a real sense arbitrary, even as they make sense. The financial sector is impossible without firms to borrow, and firms don't need to borrow if they aren't going to make products, for which they need consumers. And it is individuals who are making these decisions.
More than this, we have a variety of spontaneous social orders which constitute what Hayek called The Great Society. These divisions seem logical -- who would confuse the artistic with the scientific order, after all? -- but upon closer inspection, we see a variety of ecotones, or overlapping areas. To what degree does a firm involved in the creation of technology need to be involved in the scientific order? Quite a bit, obviously. Does it need to be involved in the artistic order? Well, that order tells us something about how people respond to various aesthetic qualities, so the artistic order comes into play with things like advertising and design. Clearly the religious order overlaps the moral/common law order, which is involved in keeping scientists and CEOs (mostly) honest. There are overlaps everywhere.
Government is a tricky issue. Most governments are not spontaneous orders. Most are organizations, and are very often imposed by some one or group with enough power to impose their will on everyone else. The exception would be a democratic order, which can come in a variety of forms. Of course, either kind of government can provide the necessary protections for stabilizing the other orders, including property rights protections, contract enforcement, laws against the initiation of force or "bearing false witness," which are lies that benefit you at the expense of others. However, both can just as easily undermine these orders as well. If a democratic government voted for a common religion, that would all but destroy the religious social order, turning it into an organization (of that one religion). Whatever is left of the religious order would be driven underground and fragmented. This of course applies to other orders as well, whether it be censorship in the artistic orders, setting goals for the scientific order, or crony capitalism/interventionism or even outright socialism -- imposing organizational development onto the order, thus destroying it -- for the economy.
The divisions are necessary for understanding each, of course -- but these divisions are also necessary for understanding how each must relate to the other for the entire social system to be healthy. While the body is fully integrated, a doctor would be a fool to give you heart medicine for a liver ailment. He needs to know where the problem lies, and what are secondary effects on other organs. The social scientist then has two roles: that of biologist, trying to understand the system and its parts and those parts' relationships to each other to form a whole, and that of medical doctor, trying to understand where the illnesses are, to propose cures. Of course, for the social scientist, this job is practically impossible, as the system/process he studies is more complex than he is, while the system/process the biolgist/M.D. studies is less complex. As Hayek pointed out, we cannot fully understand any system as or more complex than ourselves. We can only understand the parts. Thus figuring out where the divisions lie, and why, is a far more difficult task, since we cannot even know what the entire organism could possibly look like.