Saturday, January 15, 2005

Self Defeating Argument

A Self-Defeating Argument is internally inconsistent (self-contradictory) and as such, by definition is false (and therefore meaningless). The proponent has inadvertently set up a paradoxical circular argument; if the conclusion is accepted as true, the premises must be false (which therefore means the conclusion must actually be false, which then could mean the premises are true... ad infinitum).

The liar paradox is an example of a Self-Defeating Argument (or rather, assertion):

The following sentence is false. The preceding sentence is true.

If we accept the first sentence, then we must conclude the second sentence is false. However, in doing this, we invalidate the "truthfulness" of the first sentence, but if that’s the case... okay my head hurts.

Examples of Self-Defeating Argument
(Note that a Self Defeating Argument is similar, in its circularity, to Begging the Question.)

Somewhat OT - my favourite paradox is from the Hitch Hiker's Guide to the Galaxy. In this universe of Douglas Adams' creation there is a remarkable little creature known as the Babel fish. It has the most useful property. If you stick it in your ear, you can understand anything said to you in any form of language:
Now it is such a bizarrely improbable coincidence that anything so mindbogglingly useful could have evolved by purely by chance that some thinkers have chosen to see it as a final and clinching proof of the non-existence of God.

The argument goes something like this: "I refuse to prove I exist," says God, "for proof denies faith, and without faith I am nothing."

"But," says Man, "the Babel fish is a dead giveaway isn't it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don't. QED."

""Oh dear," says God, "I hadn't thought of that," and promptly vanishes in a puff of logic.