Cosmos was a spontaneous self-organizing feedback (these days, cybernetic) system. It is the natural world, including the universe. It may or may not have an end purpose; some claim it does, and some that it does not.
"Taxis" was a system organized by man. It, too is a cybernetic feedback system, but one imposed by man. Taxis always has an end purpose, a human one.
In reality almost everything is a "cosmos." The free market, for example. It is an unbelievably complex, self-organizing system that is not designed by man. Just have some simple, basic laws and up pops the cosmos of the free market, which is based on economic and political liberty.
Richard Maybury wrote that political and economic liberty is based on "Do all you have agree to do" (tort law) and "Do not encroach on other people or their property" (criminal law). The basis of all these was religion, specifically in the West, Christianity. (You'd have a pretty good society based on the Ten Commandments - which is really the Ten Words or Ten Utterances - and even a moron can understand them.)
This just amazes me. A minimal state, with some basic laws, and up pops liberty and wealth! Automatically! This is why some refer to "natural law," i.e. the laws of the universe - the "cosmos."
The purpose of "reason" is to discover the law of the cosmos. For those who believe everything should be a taxis, the purpose of reason is to create and impose, rarely understanding the Law of Unintended Consequences and insteal expecting the end result to be what they anticipated.
Unfortunately we have people (and have had them for a long time) who think society is a taxis - designed by man. They're the kind who think that "We oughta pass a law" really works without those unintended consequences. That's because they don't understand everything is a cybernetic feedback system (I tell people linear cause-and-effect only works for pool balls, which includes shooting probes to Jupiter).
Let's take, as an example, governments in Europe letting in Muslims. That's a taxis, a system designed by man (the open borders types are, as always, clueless, thinking borders are "unnatural" rather than evolved as part of the cosmos). Some think, oh, Muslims will overwhelm Europe and take it over (they'd turn it into a poverty-stricken Trashcanastan, anyway).
(As an aside, whenever you see a border that is a straigtht line, it was generally imposed by man through violence - none of which changes the fact they aren't going to go away.)
The idea that Muslims are going to overwhelm Europe without that cybernetic feedback system coming into play is that simplistic linear cause-and-effect pool ball thinking. Again, in realty, everything is a cybernetic feedback system, which is why Eastern Europe has closed it borders in response to these Third World invaders, and in Northern Europe illegal aliens are being burned out of their residences. Sooner or later, they'll be lined up against a wall and shot or swim back to their hellholes, because no one makes war like Europeans.
I predicted this, since I understand the difference between cosmos and taxis.