absurdity of self-defeat
Do you want to discredit someone or revoke a thesis? Be succinct. Use sarcasm. Aim at the underlying absurdities.
Here are three great examples where a doctrine is pointed out to be a self-defeating one:
Economist Frank Knight described the Chicago School's positivism as "the emotional pronouncement of value judgements condemning emotion and value judgements which seems to [me] a symptom of a defective sense of humor."
Philosopher Sidney Morgenbesser's response to P.F. Skinner (the founder of radical behaviorism): "Let me see if I understand your thesis. You think we shouldn’t anthropomorphize people?"
Philosopher Donald Davidson's take on relativism: "The dominant metaphor of conceptual relativism, that of different points of view, seems to betray an underlying paradox. Different points of view make sense, but only if there is a common coordinate system on which to plot them; yet the existence of a common system belies the claim of dramatic incomparability." (Similarly, Auguste Comte said “Everything is relative; and only that is absolute.”)
Philosopher Ken Wilber’s take on antihierarchy theorists:
Q: But many feminists and many ecophilosophers claim that any sort of hierarchy or "ranking" is oppressive, even fascist. They say that all such value ranking is "old paradigm" or "patriarchal" or oppressive, and it ought to be replaced with a linking, not a ranking, worldview. They're very aggressive with this point; they hurl rather harsh accusations.
KW: This is a bit disingenuous, because you can't avoid hierarchy. Even the antihierarchy theorists that you mention have their own hierarchy, their own ranking. Namely, they think linking is better than ranking. Well, that's a hierarchy, a ranking of values. But because they don't own up to this, then their hierarchy becomes unconscious, hidden, denied. Their hierarchy denies hierarchy. They have a ranking system that says ranking is bad.
Ken Wilber - A Brief History of Everything (Page 25)
A self-defeating argument arises strange feelings.
It is like a suicidal person who feels like he should have never been born in the first place. The fact that he kills himself at the end does not mean that his life was devoid of enlightening stories. Similarly, Søren Kierkegaard said the following in Concluding Unscientific Postscript to Philosophical Fragments: "[The reader] can understand that to write a book and to revoke it is not the same as refraining from writing it, that to write a book that does not demand to be important for anyone is still not the same as letting it be unwritten."
It is false, but nevertheless the very act of self-defeat can be illuminating. The proof of "P implies ¬P" may contain derivations of some non-trivially true statements.
It is valuable for the same reason why every false argument is valuable: It teaches a lesson.
It is poetic. It provides a glimpse of the fiery walls separating truth from falsehood.
It lies on the border between existence and non-existence. It is like a particle that spontaneously produces its own anti-particle and thereby annihilates itself out of existence.
It is like the Ouroboros, both scary and mystifying.
