"A system cannot understand itself." :: W Edwards Deming
Kurt Gödel stated two incompleteness theorems in 1931. Only the first is really of interest to business managers. It states the recursive reality that no system can understand itself, which has important consequences throughout all aspects of cybernetic management and computing.
Gödel's Theorem has been used to argue that a computer can never be as smart as its human user because the extent of its knowledge is limited by a fixed set of axioms, whereas people can discover insights and unexpected truths.
His theorem also plays a role in modern linguistic theories, which emphasize the power of language to find new ways to express old or new ideas. It also explains why you'll never entirely understand yourself, since your mind, like any other closed system, can only be sure of what it knows about itself by relying on what it knows about itself from an outside observer.
Hofstadter, in his masterly book Gödel, Escher, Bach, asked " How can you decide if you are sane? Once you begin to question your own sanity, you get trapped in an ever-tighter vortex of self-fulfilling prophecies, though the process is by no means inevitable. Everyone knows that the insane interpret the world via their own peculiarly consistent logic; how can you tell if your own logic is 'peculiar' or not, given that you have only your own logic to judge itself? I don't see any answer. I am reminded of Gödel's second theorem, which implies that the only versions of formal number theory which assert their own consistency are inconsistent."
The true value of consultants, coaches and 'devil's advocates' can all be better understood in the light of Gödel' s theorem in contrast to the more generally simplistic and self-serving nature of many 'consultants' who are more closely related to soothsayers. (In the days of ancient Greece difficulty in resolving a problem or interpreting the offerings of an oracle, would be the task of a soothsayer - one of a select band who claimed that they were blessed, (some might say cursed) with the ability to see into the future.
Calchas and Tiresias were the most famous soothsayers in the ancient world. Calchas is the seer to follow the Achaeans to the Trojan War while Tiresias predicted that Thebes would obtain victory if King Creon’s Menoeceus was sacrificed.
The world of business is better served with soothsayers today - the large accounting firms that have set themselves up to serve the needs of the leaders of great corporations who realise their - and anyone else's - inability to manage the massive variety facing them as they, single-handedly, take 'responsibility' for guiding their corporate Leviathans (such as Ford and GM) through the turbulents oceans of global competition.