The Wesleyan Quadrilateral is a theory that is credited to John Wesley, one of the leaders of the Methodist movement of the Protestant church in the late 18th Century. It is designed to work for Christians, but its basic idea can apply to virtually anyone.
The Quadrilateral says that there are four authorities that we should use for making decisions - the Bible, Reason, Tradition, and Experience - explaining them as follows:
The Bible: Assuming that a theistic God (omniscient, omnipotent, and benevolent) exists, the logical course of action would be to do whatever He says. He is God, therefore He can say what He wants to, even if His statement seems to contradict logic. If there is some sort of transcendent god, any form of special revelation that is received from him/her/it should be treated as the ultimate authority, since it comes from the being who created logic itself.
Reason: Most people in modern society would probably use reason before revelation, but to do so would be illogical. At its most basic form, logic does nothing more than distinguish between what is true and what is not true. God is necessarily the ultimate truth, so (again) anything that He says would supersede the human understanding of logic because His truth would be more true than ours. In most cases, though, there is no conflict between God and logic, so there usually is no need to choose between the two.
Tradition: While tradition1 is rarely the determining factor in an argument, it should never be discounted simply because it is tradition. Traditions, customs, and historical beliefs exist for some reason, and while that reason can sometimes be proven wrong, it is often valid. Traditions of a church or society can lend support to a position or belief, but they should never be used as a stand-alone argument.
Experience: Personal experience can be difficult to use in an argument because it is virtually impossible to prove day-to-day experiences after they have happened. However, one could say, 'Poodles cannot fly because a) I have never seen them fly, b) no one in my experience has seen them fly, and c) they do not have wings or rocket- packs, and I have seen few things that can fly without wings or rocket- packs'. There is no need to resort to tradition, reason, or revelation to make such a point. Like tradition, though, experience very often can only lend support to an argument.
The idea of a Quadrilateral comes into play in that all four parts are connected. Ideally, a statement or proposition should agree with all four parts, but revelation takes the ultimate precedence. Reason comes next, and tradition and experience tag along after that.