The pillar are nothing special, they are just the laws or pillars of thought going back to Plato and Aristoteles. The pillars are the law of identity, the law of contradiction and the law of excluding the middle. All constructs and projects that have been successful in test of time have followed these laws. Additionally no one has really come up with a successful alternative in the last two and half thousand years.
The problem just occurs when one or more pillars are rejected. This happens more times than one may believe as architects have the tendency to please clients beyond the point where it makes sense, as well as to confuse the issues themselves. Architects in general are not very good in keeping to the same identity, by often giving the same multiple names and changing the meaning on existing identities. For any architecture to be reviewed and executed identities are crucial to stay the same. Thankfully standards offer a way out of this concussion in terms of keeping identities, however the individual architect is still tasked not to invent new identities if it can be helped.
The main problem in pleasing the clients usually comes up with the law of contradiction where an object cannot be black, red blue and yellow at the same time. The important thing especially for business architects is to remember to reject all input build against the law of contradiction. The last law or pillar is he law of excluding the middle as the middle will never be strong place needed for any construction or object to hold the test of time. However from management logic, which is not the same as logic architects will be pushed to compromises. While compromises are great in term of conflict resolution of a temporary problem the middle that they are usually resulting in is a very unstable as artificial state and no architect should build on such an instability.