With one contradiction, you can prove anything.
In logic, it’s called the Inconsistency Effect. Given some set of assumptions, if you can deduce a contradiction from them, then it is possible to deduce any arbitrary statement. Maybe it’s just abstract concepts and symbols, but I can see two important applications.
Immediately I was reminded of the article “Science and God” by Robert J. Sawyer, where he (implicitly) uses this idea addressing the question of intelligent design:
For instance, one creationist wrote to tell me I should believe in God because “of the awesome complexity in the universe, proclaiming God’s handiwork.”
I countered that in fact the human eye is incompetent handiwork. Not only is it prone to myopia, but it has a blind spot because of the way the optic nerve passes through the retina — and we know it didn’t have to be this way, since octopi and squids, whose eyes evolved independently of our own, don’t have blind spots.
My correspondent’s response? “God made it that way to remind fallen mankind that we don’t `see it all’ or `know it all’!”
Nonsense. If both perfection and imperfection are taken as proof of God’s existence, then the whole idea of proof simply falls apart.
But of course, if you believe in intelligent design, then you don’t see that as a probem.
The more problematic application of the inconsistency effect is in moral theory. This is a completely hand wavy argument and may be complete junk, but bear with me here.
Any moral theory needs a foundation of moral truths. Principles we can live by. Unfortunately, if these underlying principles ever lead to a conflict, then they can be used to say any arbitrary statement is moral.
But a set of moral principles that don’t lead to a conflict is notoriously hard to come by, if such a thing exists at all. More to the point, getting such a set that also agrees with our intuition about what is moral is notoriously hard. I almost suspect that avoiding moral dilemas isn’t as hard as it seems, but more often than not enough people are uncomfortable with the solution (justified or not) and refuse to accept it, opting instead to leave it undetermined.
If we ever want to have a rigorous moral and ethical framework for society to function upon, we’re going to have to stop depending solely upon our intuition, which has the inconsistencies built right into it. Otherwise conflict will be unavoidable.