The ultimate weakness in logic is the unknown. This weakness is often fatal. For instance, it is possible to logically conclude that a suspect is guilty based on available evidence, but a single additional piece of knowledge may prove his or her innocence. Likewise, scientific studies may conclude that a particular substance causes cancer, only to discover later that their findings were influenced by a factor not considered before.
The same weakness exists when a person's religious persuasion is based in logic. Additional knowledge may thwart that person's confidence in their religion. In this way, intellectuals are "tossed to and fro... with every wind of doctrine," because their faith is based in reason only.
In contrast, when Jesus asked his apostles who they thought He was, Peter responded "Thou art the Christ, the Son of the Living God." No amount of worldly logic could have proved this true. Christ replied, "Blessed art thou, ... for flesh and blood hath not revealed this unto you, but my Father who is in Heaven." Peter's faith was rooted in a spiritual connection with God Himself. He believed what God told him even though it couldn't be proven mathematically, scientifically, or philosophically. Logic did not dictate his actions--he could hear what God Himself had to say on the matter, and that was sufficient.
This is not to say that logic is somehow bad or wrong--quite the reverse. We are commanded to reason and understand knowledge. But the only way to overcome logic's inherent weakness is to know everything. Once everything is perfectly known, there is no risk of missing something. So we cannot rely on our own knowledge to be the ultimate foundation of our faith. Rather, we must trust in the Lord's knowledge, for only God knows all things. Thus, only His logic is immutable.
No matter how much I learn, I must never place the foundation of my faith in my own logic and my own reason. I must believe what God tells me, no matter if it challenges my own logic or the logic of great thinkers. The scribes and Pharisees were the theologians of the day, and understood a great many things, but they did not recognize and would not accept the voice of their God when they heard and felt it.