Ipso facto--Latin, "by the fact itself". A wonderful language, used by a great civilization, the basis of all the romantic languages and still relevant to the modern English language. In my mind Hayek's argument is boiled down to that single phrase, "by the fact itself".
The basis of this paper is that central economic planning cannot succeed because it's impossible to achieve perfect information by a single entity. The reason for this is that time and space knowledge, to borrow Hayek's definition, is distributed to all the individuals in a society and not initially known by a single individual or entity. If this knowledge were to remain fairly constant it might be possible, theoretically, to acummulate it over a period of time and feed it to some Central Planning Committtee, or Mega Super Computer, or All-Knowing Benevolent Economist, from whence informed and perfect economic decisions could then be dispersed. However, in reality, all this particular knowledge is constantly changing as the decisions of individuals interact with each other and their environment creating a shifting, changing fabric of economic processes. Because of this it is impossible to completely know the economic situation of a society, and because of imperfect knowledge, perfect economic decisions cannot be made.
However, Hayek states that ".....the method by which such knowledge can be made as widely available as possible is precisely the problem to which we have to find an answer." [Section III, Paragraph 10] So to play the devil's advocate, if a system could be devised that shares all this knowledge with essentially no limits, could a centrally planned economy then happen?
We have such an institution in our society for spreading information with virtually no constraints. The internet. So then, if we combined the endless processing power of numerous super-computers and the incredible data sharing device known as the internet, could we then achieve a planned economy?
I would argue no. I think the breakdown occurs when you consider that the internet is primarly an input device. You must input information into it. It doesn't go out and retrieve the information itself. And yes there are circumstances when it actually does, as I'm sure some antagonist will point out: viruses, cookies, Evil Government Internet Conspiracies, etc. But they still have to access that information from another input device--your computer.
My long-winded point is simply that individuals still hold all the bits and pieces of information and data needed by an economic system, and even though they could input all that data into some mega-information system such as the internet, it would be a horribly inefficient way to operate as it would consume many inviduals constant attention to update the changing data. Knowledge is distributed among all individuals, and, ipso facto, by that very fact itself, the price system stands as the only system that is an answer to modern society. Or better yet, as Hayek postulates, it is the cause of modern society. Ab uno disces omnes.