While debating theists (as there are no atheists to be found where I am), I came across many people who insisted that the only way to argue was to show contradiction in the other side, i.e. Occam's Razor and weak/strong distinctions are right out, as are inductive evidential approaches. I think this is absurd, but no matter: the point I wish to make is that contradiction is a limited method of refutation. To use this method is simple: one shows that two ideas inherent in the opponent's views (or resulting from them) contradict in some fundamental way such that A is not A or an equivalent statement is made. After this, the opponent simply must concede the point; there is no way around it. This algorithm is flawed, however. One cannot show that contradiction is bad. One can show only that it leads to . . . well, contradiction. If one shows that contradiction leads to unhappiness, who's to say it doesn't also lead to happiness? Simply put, without the law of non-contradiction, a logical system cannot be refuted in this way. This may seem inapplicable, as nearly everyone on Earth uses the law of non-contradiction, but the idea is important. Many (perhaps most) realists "prove" that their logical system is the only "true" or "real" one by showing the inherent *contradiction* in all others. Obviously, this cannot be done for all logical systems, so any method attempting an exhaustive RAA of all other systems is bound to be incomplete. (P.S. Another way to phrase this conclusion is that transcendental argumentation rests upon a presupposed logical framework, and thus only connects some ideas to others; it doesn't ground the argument firmly in irrefutable soil.)
