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As our debates have demonstrated, the scientific method does very well even though fallible. The methods of evangelical scholarship seem highly error prone, and are aimed more at finding "proof" of preconceived notions than at getting at the truth.
I think you're trying to compare apples and oranges. That being said, I think the reason you find the arguments around capital punishment to be more like "evangelical scholarship," as you call it, is because many of the questions are not such that the scientific method readily applies. Is it just and moral to kill these people or not? Is it civilized or barbaric? What is the value of a human life? Science doesn't really make moral judgements and there are some things that simply cannot be measured by a ruler or scale.
As far as capital punishment goes, I don't think we need it. I think the primary purpose of the justice system to to protect the public from criminals. This does not require the use of execution. (Some argue that execution is a powerful deterrent and protects the public by preventing crimes. The evidence I've seen to that end is mirky at best.)
What if a jury could sentence a man to death but if he was ever later proven to be innocent beyond reasonable doubt, they themselves would be executed. Would you ever sentence a man to death under such rules? What about when the crime is horrific and the evidence overwhelming as it is in cases like Duncan in Idaho, who was caught with one of his victims, etc?
For me it comes down to one question really. Which is the greater injustice: to put an innocent man to death or to commute the execution of a mass murderer to life in prison without the chance for parole?