A case-in-point of unbiblical methodology is Pascal's Wager. You can find the argument in Pensees. Click here for a synopsis.
The Argument
Premise 1 - If you believe in God, and find out your were wrong, you lose nothing.
Premise 2 - If you do not believe in God, and find out you were wrong, you lose everything.
Conclusion - You should believe in God.
The following will show this method to be unbiblical.
1 - Pascal assumes God is incomprehensible and therefore "we are then incapable of knowing either what He is or if He is." This premise is based on philosophy instead of the Bible. Romans 1:18-32 states that all men know God exist. They simply "suppress the truth in unrighteousness." Pascal's Wager allows man to remain unchallenged in his autonomy. Notice throughout the other points the wide-spread effects of this one belief.
2 - Pascal's wager gives up the certainty of God's existence in order to prove it. This method is condemned by Scripture. "Do not answer a fool according to his folly, or you will also be like him" (Proverbs 26:4). In other words, we are not to give up God in order to prove Him. We do answer the fool - we won't let him be wise in his own eyes. The answer, however, will be from the standpoint of certainty.
3 - Pascal's Wager destroys the meaning of faith. Since, in his view, "reason can decide nothing" he asks, "What will you wager?" In this system, faith is a leap in the dark. In other words, faith is believing something which could be true, but also could be utter foolishness. This is not the biblical definition of faith. "Faith is the assurance of things hoped for" (emphasis mine). Faith, in order to be biblical faith, must be based on the revelation of God. Once again, notice the devastating effects of not affirming the truth of Romans 1:19-32. All men know God exists - and they hate it.
4 - The premise flat-out contradicts the Bible. Pascal says, "If you gain, you gain all; if you lose, you lose nothing." Wrong. Read the context of 1 Corinthians 15:13-19. If I am wrong, I lose everything. Or, as Paul said, "If we have hoped in Christ in this life only, we are of all men most to be pitied."
Good men have used this method. And there may be some who have come to faith after hearing this presented. Nevertheless, we must not ask if the method works, we must ask if the method honors God. This is utterly crucial for a generation of Christians for which the end justifies the means. We are to love Him with all of our heart then love our neighbor. To seek to love the latter first is essentially to hate both.